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- 11:31, 15 February 2023 Locality-sensitive hashing (k Approximate Nearest Neighbors Search (k-ANNS) Nearest Neighbor Search) (hist | edit) [474 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(nLkt)$ (pre-processing) $O(L(kt+dnP_2^k))$ (query-time) == Space Complexity == $O(nL)$ hash table cells (https://en.wikipedia.org/wiki/Locality-sensitive_hashing#LSH_algorithm_for_nearest_neighbor_search) == Description == == Approximate? == Approximate Approximation Factor: c == Randomized? == No, deterministic == Model of Computation == == Year == 2010 == Reference == http://infolab.stanford.edu/~ullman/mmds/ch3n.pdf")
- 11:31, 15 February 2023 Hierarchical Navigable Small World (HNSW) (k Approximate Nearest Neighbors Search (k-ANNS) Nearest Neighbor Search) (hist | edit) [419 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(nlogn)$ == Space Complexity == $O(M)$ bytes of memory (https://arxiv.org/abs/1603.09320, "Memory usage is proportional to choice of M") == Description == == Approximate? == Approximate Approximation Factor: ? experimental results == Randomized? == No, deterministic == Model of Computation == == Year == 2018 == Reference == https://doi.org/10.1109/TPAMI.2018.2889473")
- 11:31, 15 February 2023 Larmore (Approximate OBST Optimal Binary Search Trees) (hist | edit) [402 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(n^{1.6})$ == Space Complexity == $O(n)$ (Derived: Computing and storing f_{d,l} for each n elements) == Description == == Approximate? == Approximate Approximation Factor: \epsilon = o(1) == Randomized? == No, deterministic == Model of Computation == == Year == 1987 == Reference == https://www.sciencedirect.com/science/article/pii/0196677487900526")
- 11:31, 15 February 2023 Klawe; Mumey (Alphabetic Tree Problem Optimal Binary Search Trees) (hist | edit) [339 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(n)$ == Space Complexity == $O(n)$ (Derived: uses a worklist of size O(n)) == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == == Year == 1993 == Reference == https://epubs.siam.org/doi/abs/10.1137/S0895480193256651?journalCode=sjdmec")
- 11:31, 15 February 2023 Karpinski (Approximate OBST Optimal Binary Search Trees) (hist | edit) [433 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(n^{0.6})$ == Space Complexity == $O({1})$ (Derived: dynamic programming and making use of Monge matrix properties) == Description == == Approximate? == Approximate Approximation Factor: \epsilon = o(1) == Randomized? == No, deterministic == Model of Computation == == Year == 1996 == Reference == https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.54.6940&rep=rep1&type=pdf")
- 11:31, 15 February 2023 Melhorn's Approximation algorithm (Approximate OBST Optimal Binary Search Trees) (hist | edit) [458 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(n)$ == Space Complexity == $O(n)$ (https://people.mpi-inf.mpg.de/~mehlhorn/ftp/mehlhorn3.pdf, storing left/right subtrees' weights) == Description == == Approximate? == Approximate Approximation Factor: 0.63 H \leq P_opt \leq P_balanced \leq 2 + 1.44 H == Randomized? == No, deterministic == Model of Computation == == Year == 1975 == Reference == https://people.mpi-inf.mpg.de/~mehlhorn/ftp/mehlhorn3.pdf")
- 11:31, 15 February 2023 Weak Parametrized Inapproximability Hypothesis (WPIH) (hist | edit) [432 bytes] Admin (talk | contribs) (Created page with "== Target Problem == Approximate 2-CSP == Description == There is some constant $\delta > 0$ such that given an instance $\varphi$ of 2-CSP on the Boolean hypercube graph $Q$ over alphabet of size $n$, it is W(1)-hard to distinguish == Implies the following Hypothesis == == Implied by the following Hypothesis == == Computation Model == == Proven? == No == Year == == References/Citation == ? CCC '22")
- 11:31, 15 February 2023 Parametrized Inapproximability Hypothesis (PIH) (hist | edit) [452 bytes] Admin (talk | contribs) (Created page with "== Target Problem == Approximate 2-CSP == Description == There is some constant $\delta > 0$ such that 2-CSP on $k$ vertices and alphabet size $n$ is W(1)-hard to approximate to a $(1-\delta)$ factor == Implies the following Hypothesis == == Implied by the following Hypothesis == == Computation Model == == Proven? == No == Year == 2017 == References/Citation == https://epubs.siam.org/doi/abs/10.1137/1.9781611975994.134")
- 11:31, 15 February 2023 $\delta$-Triangle Conjecture (hist | edit) [395 bytes] Admin (talk | contribs) (Created page with "== Target Problem == Triangle Detection == Description == Any Algorithm requires $m^{1+\delta-o(1)}$ time in expectation to detect whether an $m$ edge graph contains a triangle == Implies the following Hypothesis == == Implied by the following Hypothesis == == Computation Model == Word-Ram on $\log(n)$ bit words == Proven? == No == Year == == References/Citation ==")
- 11:30, 15 February 2023 Strong Triangle Conjecture (hist | edit) [705 bytes] Admin (talk | contribs) (Created page with "== Target Problem == Triangle Detection == Description == Any Algorithm requires $\min(n^{w-o(1)}, m^{2w/(w+1)-o(1)})$ time in expectation to detect whether an $n$ node $m$ edge graph contains a triangle. Moreover, any combinatorial algorithm requires $m^{3/2-o(1)}$ == Implies the following Hypothesis == == Implied by the following Hypothesis == == Computation Model == Word-Ram on $\log(n)$ bit words == Proven? == No == Year == 2014 == Referenc...")
- 11:30, 15 February 2023 More Believable Exponential Time Hypothesis (MBETH) (hist | edit) [567 bytes] Admin (talk | contribs) (Created page with "== Target Problem == k-SAT == Description == There exists a $k \geq 3$ and a $\delta > 0$ so that $k$-SAT on $n$ variables cannot be solved in $O(2^{\delta n})$ == Implies the following Hypothesis == ETH == Implied by the following Hypothesis == ETH, SETH == Computation Model == Word-Ram on $\log(n)$ bit words == Proven? == No ==...")
- 11:30, 15 February 2023 Nondeterministic Strong Exponential Time Hypothesis (NSETH) (hist | edit) [491 bytes] Admin (talk | contribs) (Created page with "== Target Problem == [[]] == Description == Refuting unsatisfiable $k$-CNF formulas on $n$ variables requires nondeterministic $2^{n-o(n)}$ time for unbounded $k$. == Implies the following Hypothesis == SETH == Implied by the following Hypothesis == == Computation Model == == Proven? == No (Variants have been disproved) == Year == == References/Citation == http://people.csail.mit.edu/virgi/eccentri.p...")
- 11:30, 15 February 2023 Online Matrix Vector Multiplication Hypothesis (OMV Hypothesis) (hist | edit) [541 bytes] Admin (talk | contribs) (Created page with "== Target Problem == OMV == Description == Every (randomized) algorithm that can process a given $n \times n$ Boolean matrix $A$, and then in an online way can compute the products $Av_i$ for any $n$ vectors $v_1,\ldots,v_n$, must take total time $n^{3-o(1)}$. == Implies the following Hypothesis == == Implied by the following Hypothesis == == Computation Model == Word-Ram on $\log(n)$ bit words == Proven? == No == Year == == References/Citatio...")
- 11:30, 15 February 2023 Boolean Matrix Multiplication Hypothesis (BMM Hypothesis) (hist | edit) [378 bytes] Admin (talk | contribs) (Created page with "== Target Problem == BMM == Description == Any combinatorial BMM algorithm requires $n^{3-o(1)}$ time. == Implies the following Hypothesis == == Implied by the following Hypothesis == == Computation Model == Word-Ram on $\log(n)$ bit words == Proven? == No == Year == == References/Citation == http://people.csail.mit.edu/virgi/eccentri.pdf Page 17")
- 11:30, 15 February 2023 Exact k-Clique Hypothesis (hist | edit) [521 bytes] Admin (talk | contribs) (Created page with "== Target Problem == Exact $k$-Clique == Description == The Exact $k$-Clique problem on $n$ node graphs with edge weights in $\{-n^{100k},\ldots,n^{100k}\}$ requires (randomized) $n^{k-o(1)}$ time. == Implies the following Hypothesis == OVH == Implied by the following Hypothesis == == Computation Model == Word-Ram on $\log(n)$ bit words == Proven? == No == Year == == References/Citation == http://people...")
- 11:30, 15 February 2023 Min-Weight k-Clique Hypothesis (hist | edit) [588 bytes] Admin (talk | contribs) (Created page with "== Target Problem == Min-Weight $k$-Clique == Description == The Min-Weight $k$-Clique problem on $n$ node graphs with edge weights in $\{-n^{100k},\ldots, n^{100k}}$ requires (randomized) $n^{k-o(1)}$ time. == Implies the following Hypothesis == Exact k-Clique Hypothesis, OVH == Implied by the following Hypothesis == == Computation Model == Word-Ram on $\log(n)$ bit words == Proven...")
- 11:30, 15 February 2023 Hitting Set Hypothesis (HS Hypothesis) (hist | edit) [442 bytes] Admin (talk | contribs) (Created page with "== Target Problem == HS == Description == No randomized algorithm can solve HS on $n$ vectors in $\{0,1\}^d$ in $n^{2-\epsilon}\poly(d)$ time for $\epsilon > 0$. == Implies the following Hypothesis == == Implied by the following Hypothesis == == Computation Model == Word-RAM on $\log(n)$ bit words == Proven? == No == Year == == References/Citation == http://people.csail.mit.edu/virgi/eccentri.pdf Hypothesis 5")
- 11:30, 15 February 2023 All Pairs Shortest Paths Hypothesis (APSP Hypothesis) (hist | edit) [517 bytes] Admin (talk | contribs) (Created page with "== Target Problem == APSP == Description == No randomized algorithm can solve APSP in $O(n^{3-\epsilon})$ time for $\epsilon > 0$ on $n$ node graphs with edge weights in $\{-n^c,\ldots,n^c\}$ and no negative cycles for large enough $c$. == Implies the following Hypothesis == == Implied by the following Hypothesis == == Computation Model == Word-RAM on $\log(n)$ bit words == Proven? == No == Year == == References/Citation == http://people.csa...")
- 11:30, 15 February 2023 3SUM Hypothesis (3-SUM Hypothesis) (hist | edit) [467 bytes] Admin (talk | contribs) (Created page with "== Target Problem == 3-SUM == Description == 3-SUM on $n$ integers in $\{-n^4,\ldots,n^4\}$ cannot be solved in $O(n^{2-\epsilon})$ time for any $\epsilon > 0$ by a randomized algorithm. == Implies the following Hypothesis == == Implied by the following Hypothesis == == Computation Model == Word-RAM on $\log(n)$ bit words == Proven? == No == Year == == References/Citation == http://people.csail.mit.edu/virgi/eccentri.pdf Hypothesis 2")
- 11:30, 15 February 2023 K-Clique Hypothesis (hist | edit) [480 bytes] Admin (talk | contribs) (Created page with "== Target Problem == [[$k$-Clique for all $k > 0$]] == Description == No randomized algorithm can detect a $k$-Clique in an $n$-node graph in $O(n^{\omega k / 3 - \epsilon})$ time for any $\epsilon > 0$. == Implies the following Hypothesis == == Implied by the following Hypothesis == == Computation Model == Word-RAM on $\log(n)$ bit words == Proven? == No == Year == == References/Citation == http://people.csail.mit.edu/virgi/eccentri.pdf Hypothe...")
- 11:30, 15 February 2023 K-OV Hypothesis (hist | edit) [450 bytes] Admin (talk | contribs) (Created page with "== Target Problem == k-OV == Description == No randomized algorithm can solve k-OV on instances of size $n$ in $n^{k-\epsilon}\poly(d)$ time for constant $\epsilon > 0$. == Implies the following Hypothesis == == Implied by the following Hypothesis == == Computation Model == Word-RAM on $\log(n)$ bit words == Proven? == No == Year == == References/Citation == http://people.csail.mit.edu/virgi/eccentri.pdf Hypothesis 4")
- 11:30, 15 February 2023 Unbalanced Orthogonal Vectors Hypothesis (UOVH) (hist | edit) [590 bytes] Admin (talk | contribs) (Created page with "== Target Problem == UOV == Description == Let $0 < \alpha \leq 1$. For no $\epsilon > 0$ there is an algorithm for OV, restricted to $m = \Theta(n^\alpha)$ and $d \leq n^{o(1)}$, that runs in time $O((nm)^{(1−\epsilon)})$. == Implies the following Hypothesis == SETH, OVH == Implied by the following Hypothesis == OVH == Computati...")
- 11:30, 15 February 2023 Orthogonal Vectors Hypothesis (OVH) (hist | edit) [594 bytes] Admin (talk | contribs) (Created page with "== Target Problem == OV == Description == For no $\epsilon > 0$ there is an algorithm for OV, restricted to $n = m$, that runs in time $O(n^{(2−\epsilon)}poly(d))$. == Implies the following Hypothesis == SETH, UOVH == Implied by the following Hypothesis == k-OV Hypothesis, UOVH == Compu...")
- 11:30, 15 February 2023 Strong Exponential Time Hypothesis (SETH) (hist | edit) [629 bytes] Admin (talk | contribs) (Created page with "== Target Problem == k-SAT == Description == For every $\epsilon > 0$, there exists an integer $k \geq 3$ such that $k$-SAT cannot be solved in $O(2^{(1-\epsilon) n})$ time. == Implies the following Hypothesis == MBETH, ETH == Implied by the following Hypothesis == OVH, [[Unbalanced Orthogonal Vectors Hypothesis (UOVH)|UOVH]...")
- 11:30, 15 February 2023 Exponential Time Hypothesis (ETH) (hist | edit) [579 bytes] Admin (talk | contribs) (Created page with "== Target Problem == 3SAT == Description == There is some constant $\delta > 0$ such that CNF-SAT requires $\Omega(2^{\delta n})$. == Implies the following Hypothesis == MBETH == Implied by the following Hypothesis == SETH, MBETH == Computation Model == Word-RAM on $\log(n)$ bit words == Proven? =...")
- 11:30, 15 February 2023 All-Integers 3SUM (hist | edit) [1,226 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:All-Integers 3SUM (3SUM)}} == Description == Given three lists $A, B, C$ of $n$ integers each, output the list of all integers $a \in A$ such that there exist $b \in B,c \in C$ with $a + b + c = 0$. == Related Problems == Generalizations: 3SUM Related: Real 3SUM, 3SUM' == Parameters == <pre>n: number of integers in each set</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem. == Reductions...")
- 11:30, 15 February 2023 3SUM' (hist | edit) [2,140 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:3SUM' (3SUM)}} == Description == Given three sets of integers $A, B, C$ of total size $n$, are there $a\in A, b\in B, c\in C$ such that $a + b = c$? == Related Problems == Generalizations: 3SUM Related: Real 3SUM, All-Integers 3SUM == Parameters == <pre>n: number of integers in each set</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem. == Reductions TO Problem == {| class="wikitable so...")
- 11:30, 15 February 2023 Real 3SUM (hist | edit) [1,344 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Real 3SUM (3SUM)}} == Description == Given a set $S$ of reals, determine whether there is a subset of $S$ of size 3 that sums to 0. == Related Problems == Subproblem: 3SUM Related: 3SUM', All-Integers 3SUM == Parameters == <pre>S: the set of reals n: the number of real numbers in the set</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approxim...")
- 11:30, 15 February 2023 3SUM (hist | edit) [4,609 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:3SUM (3SUM)}} == Description == Given a set $S$ of integers, determine whether there is a subset of $S$ of size 3 that sums to 0. == Related Problems == Generalizations: Real 3SUM Subproblem: 3SUM', All-Integers 3SUM Related: All-Integers 3SUM == Parameters == <pre>S: the set of integers n: the number of integers in the set</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem. == Reduc...")
- 11:30, 15 February 2023 Approximate Hard-Margin SVM (hist | edit) [1,216 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Approximate Hard-Margin SVM (Support Vector Machines (SVM))}} == Description == A (primal) hard-margin SVM is an optimization problem of the following form: $\min\limits_{\alpha_1,\ldots,\alpha_n\geq 0} \frac{1}{2} \sum \limits_{i,j = 1}^n \alpha_i \alpha_j y_i y_j k(x_i, x_j)$ subject to $y_i f(x_i) \geq 1, i = 1, \ldots, n$ where $f(x) := \sum_{i=1}^n \alpha_i y_i k(x_i, x)$ == Parameters == No parameters found. == Table of Algorithms == Curre...")
- 11:30, 15 February 2023 Bichromatic Hamming Close Pair (hist | edit) [1,893 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Bichromatic Hamming Close Pair (Bichromatic Hamming Close Pair)}} == Description == Given two sets $A = \{a_1, \ldots, a_n\} \subseteq \{0, 1\}^d$ and $B = \{b_1, \ldots, b_n\} \subseteq \{0, 1\}^d$ of $n$ binary vectors and an integer $t \in \{2, \ldots, d\}$, decide if there exists a pair $a \in A$ and $b \in B$ such that the number of coordinates in which they differ is less than $t$ (formally, $Hamming(a, b) := |a − b|1 < t$). If there is such a pa...")
- 11:30, 15 February 2023 Dynamic Dihedral Rotation Queries (hist | edit) [514 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Dynamic Dihedral Rotation Queries (Dihedral Rotation Queries)}} == Description == Determine whether a given dihedral rotation is feasible or not, and if it is, modify the chain by performing the rotation. == Related Problems == Related: Static Dihedral Rotation Queries == Parameters == <pre>n: number of edges in the chain</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem. == References/Citation ==...")
- 11:30, 15 February 2023 Static Dihedral Rotation Queries (hist | edit) [948 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Static Dihedral Rotation Queries (Dihedral Rotation Queries)}} == Description == Determine whether a given dihedral rotation is feasible or not, without modifying the chain. == Related Problems == Related: Dynamic Dihedral Rotation Queries == Parameters == <pre>n: number of edges in the chain</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem. == Reductions FROM Problem == {| class="wikitable sor...")
- 11:30, 15 February 2023 Generalized Büchi Games (hist | edit) [1,947 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Generalized Büchi Games (Model-Checking Problem)}} == Description == Given a model of a system and an objective, the model-checking problem asks whether the model satisfies the objective. In this case, the model is a standard graph, and the objective is Büchi: given a set of target vertices $T\subseteq V$, determine whether or not there is a path that visits the set $T$ an infinite amount of times. Furthermore, in the conjunctive problem, you are giv...")
- 11:30, 15 February 2023 Disjunctive coBüchi Objectives (hist | edit) [1,984 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Disjunctive coBüchi Objectives (Model-Checking Problem)}} == Description == Given a model of a system and an objective, the model-checking problem asks whether the model satisfies the objective. In this case, the model is a standard graph, and the objective is coBüchi: given a set of target vertices $T\subseteq V$, determine whether or not there is a path that visits the set $T$ a finite amount of times. Furthermore, in the disjunctive problem, you a...")
- 11:30, 15 February 2023 Disjunctive Queries of Safety in Graphs (hist | edit) [2,360 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Disjunctive Queries of Safety in Graphs (Model-Checking Problem)}} == Description == Given a model of a system and an objective, the model-checking problem asks whether the model satisfies the objective. In this case, the model is a standard graph, and the objective is safety: given a set of target vertices $T\subseteq V$, determine whether or not there is a path that does not visit any vertex in $T$ (i.e. you want to avoid all vertices in $T$). Furthe...")
- 11:30, 15 February 2023 Safety in Graphs (hist | edit) [1,054 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Safety in Graphs (Model-Checking Problem)}} == Description == Given a model of a system and an objective, the model-checking problem asks whether the model satisfies the objective. In this case, the model is a standard graph, and the objective is safety: given a set of target vertices $T\subseteq V$, determine whether or not there is a path that does not visit any vertex in $T$ (i.e. you want to avoid all vertices in $T$). == Related Problems == Subp...")
- 11:30, 15 February 2023 Conjunctive Safety Queries in MDPs (hist | edit) [1,311 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Conjunctive Safety Queries in MDPs (Model-Checking Problem)}} == Description == Given a model of a system and an objective, the model-checking problem asks whether the model satisfies the objective. In this case, the model is a Markov Decision Process (MDP), and the objective is safety: given a set of target vertices $T\subseteq V$, determine whether there is an infinite path that does not visit any vertex in $T$ (i.e. you want to avoid all vertices in...")
- 11:30, 15 February 2023 Disjunctive Safety Queries in MDPs (hist | edit) [1,309 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Disjunctive Safety Queries in MDPs (Model-Checking Problem)}} == Description == Given a model of a system and an objective, the model-checking problem asks whether the model satisfies the objective. In this case, the model is a Markov Decision Process (MDP), and the objective is safety: given a set of target vertices $T\subseteq V$, determine whether there is an infinite path that does not visit any vertex in $T$ (i.e. you want to avoid all vertices in...")
- 11:30, 15 February 2023 Safety in MDPs (hist | edit) [1,084 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Safety in MDPs (Model-Checking Problem)}} == Description == Given a model of a system and an objective, the model-checking problem asks whether the model satisfies the objective. In this case, the model is a Markov Decision Process (MDP), and the objective is safety: given a set of target vertices $T\subseteq V$, determine whether there is an infinite path that does not visit any vertex in $T$ (i.e. you want to avoid all vertices in $T$). == Related Pr...")
- 11:30, 15 February 2023 Conjunctive Reachability Queries in MDPs (hist | edit) [1,338 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Conjunctive Reachability Queries in MDPs (Model-Checking Problem)}} == Description == Given a model of a system and an objective, the model-checking problem asks whether the model satisfies the objective. In this case, the model is a Markov Decision Process (MDP), and the objective is reachability: given a set of target vertices $T\subseteq V$, determine whether there is an infinite path that visits a vertex in $T$ at least once (i.e. you want to reach...")
- 11:30, 15 February 2023 Disjunctive Reachability Queries in MDPs (hist | edit) [2,262 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Disjunctive Reachability Queries in MDPs (Model-Checking Problem)}} == Description == Given a model of a system and an objective, the model-checking problem asks whether the model satisfies the objective. In this case, the model is a Markov Decision Process (MDP), and the objective is reachability: given a set of target vertices $T\subseteq V$, determine whether there is an infinite path that visits a vertex in $T$ at least once (i.e. you want to reach...")
- 11:30, 15 February 2023 Reachability in MDPs (hist | edit) [1,082 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Reachability in MDPs (Model-Checking Problem)}} == Description == Given a model of a system and an objective, the model-checking problem asks whether the model satisfies the objective. In this case, the model is a Markov Decision Process (MDP), and the objective is reachability: given a set of target vertices $T\subseteq V$, determine whether there is an infinite path that visits a vertex in $T$ at least once (i.e. you want to reach some vertex in $T$)....")
- 11:30, 15 February 2023 Maximum Inner Product Search (hist | edit) [2,800 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Maximum Inner Product Search (Maximum Inner Product Search)}} == Description == Given a new query $q$, MIPS targets at retrieving the datum having the largest inner product with $q$ from the database $A$. Formally, the MIPS problem is formulated as below: $p = \arg \max \limits_{a \in A} a \top q$ == Parameters == No parameters found. == Table of Algorithms == Currently no algorithms in our database for the given problem. == Reductions TO Problem...")
- 11:29, 15 February 2023 RNA Folding (hist | edit) [1,330 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:RNA Folding (RNA Folding)}} == Description == In RNA Folding we are given a string over some alphabet (e.g. $\{A, C, G, T\}$) with a fixed pairing between its symbols (e.g. $A − T$ match and $C − G$ match), and the goal is to compute the maximum number of non-crossing arcs between matching letters that one can draw above the string (which corresponds to the minimum energy folding in two dimensions). == Parameters == <pre>n: length of the given str...")
- 11:29, 15 February 2023 Ap-reach (hist | edit) [1,069 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:ap-reach (Vertex Reachability)}} == Description == Given a directed graph $G=(V,E)$, determine for each pair $s \neq t \in V$ whether $t$ is reachable from $s$. == Related Problems == Generalizations: st-Reach Related: #SSR, sensitive incremental #SSR, ST-Reach, constant sensitivity incremental ST-Reach, 1-sensitive incremental ss-reach, 2-sensitive incremental st-reach == Parameters == <pre>n: number of vertices m: num...")
- 11:29, 15 February 2023 2-sensitive incremental st-reach (hist | edit) [1,152 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:2-sensitive incremental st-reach (Vertex Reachability)}} == Description == Given a directed graph $G=(V,E)$ and vertices $s, t \in V$, incrementally determine wheteher $t$ is reachable from $s$, with sensitivity 2, i.e. when 2 edges are added. == Related Problems == Generalizations: st-Reach Related: #SSR, sensitive incremental #SSR, ST-Reach, constant sensitivity incremental ST-Reach, 1-sensitive incremental ss-reach, ap-re...")
- 11:29, 15 February 2023 1-sensitive incremental ss-reach (hist | edit) [1,325 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:1-sensitive incremental ss-reach (Vertex Reachability)}} == Description == Given a directed graph $G=(V,E)$ and a source node $s \in G$, an incremental single-source reachability algorithm maintains the set of nodes reachable from $s$ (i.e., all nodes $v$ for which there is a path from $s$ to $v$ in the current version of $G$) during a sequence of edge insertions, with sensitivity 1, i.e. when 1 edge is inserted. == Related Problems == Generalizations...")
- 11:29, 15 February 2023 Constant sensitivity incremental ST-Reach (hist | edit) [688 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:constant sensitivity incremental ST-Reach (Vertex Reachability)}} == Description == Given a graph $G=(V,E)$, incrementally determine whether each node $s\in S\subseteq V$ can reach a node $t\in T \subseteq V$, with a constant sensitivity of $K(\epsilon, t)$, i.e. when $K(\epsilon, t)$ edges are added. == Related Problems == Generalizations: ST-Reach Related: #SSR, sensitive incremental #SSR, st-Reach, 1-sensitive incremental ss-reac...")
- 11:29, 15 February 2023 St-Reach (hist | edit) [663 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:st-Reach (Vertex Reachability)}} == Description == Given a directed graph $G=(V,E)$ and vertices $s, t \in V$, determine wheteher $t$ is reachable from $s$. == Related Problems == Subproblem: constant sensitivity incremental ST-Reach, 1-sensitive incremental ss-reach, 2-sensitive incremental st-reach, ap-reach Related: #SSR, sensitive incremental #SSR, ST-Reach, 1-sensitive incremental ss-reach, 2-sensitive increm...")
- 11:29, 15 February 2023 ST-Reach (hist | edit) [669 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:ST-Reach (Vertex Reachability)}} == Description == Given a graph $G=(V,E)$, determine whether each node $s\in S\subseteq V$ can reach a node $t\in T \subseteq V$. == Related Problems == Subproblem: constant sensitivity incremental ST-Reach, 1-sensitive incremental ss-reach, 2-sensitive incremental st-reach, ap-reach Related: #SSR, sensitive incremental #SSR, st-Reach, 1-sensitive incremental ss-reach, 2-sensitive...")
- 11:29, 15 February 2023 Sensitive incremental (hist | edit) [1,752 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:sensitive incremental #SSR (Vertex Reachability)}} == Description == A data structure with sensitivity $d$ for a problem $P$ has the following properties: It obtains an instance $p$ of $P$ and is allowed polynomial preprocessing time on $p$. After the preprocessing, the data structure must provide the following operations: (Batch) Update: Up to $d$ changes are performed to the initial problem instance $p$, e.g., $d$ edges are added to or removed from $p...")
- 11:29, 15 February 2023 Online Vector-Matrix-Vector Multiplication (hist | edit) [1,288 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Online Vector-Matrix-Vector Multiplication (Matrix-Vector Multiplication)}} == Description == Let $M$ be a binary $n \times n$ matrix than can be preprocessed. After preprocessing $n$ vector pairs $(u^1, v^1), \ldots, (u^n, v^n)$, arrive one at a time and the task is to compute $(u^i)^T M v^i$ before being presented with the $i+1$th vector pair for every $i$. == Related Problems == Related: Online Matrix-Vector Multiplication == Parameters == <...")
- 11:29, 15 February 2023 Online Matrix-Vector Multiplication (hist | edit) [690 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Online Matrix-Vector Multiplication (Matrix-Vector Multiplication)}} == Description == We are given an $n \times n$ matrix $M$ and will receive $n$ column-vectors of size $n$, denoted by $v_1, \ldots , v_n$, one by one. After seeing each vector $v_i$, we have to output the product $Mv_i$ before we can see the next vector. == Related Problems == Related: Online Vector-Matrix-Vector Multiplication == Parameters == <pre>n: dimension of square matr...")
- 11:29, 15 February 2023 Shortest k-Cycle (hist | edit) [1,042 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Shortest k-Cycle (Graph Cycles)}} == Description == Given a graph $G=(V,E)$ with non-negative weights, find a minimum weight cycle of length $k$. == Related Problems == Generalizations: Shortest Cycle == Parameters == <pre>n: number of vertices m: number of edges k: length of cycle</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem. == Reductions FROM Problem == {| class="wikitable sortable" sty...")
- 11:29, 15 February 2023 Shortest Cycle (hist | edit) [901 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Shortest Cycle (Graph Cycles)}} == Description == Given a graph $G=(V,E)$ with non-negative weights, find a minimum weight cycle. == Related Problems == Subproblem: Shortest k-Cycle == Parameters == <pre>n: number of vertices m: number of edges</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem. == Reductions FROM Problem == {| class="wikitable sortable" style="text-align:center;" width="100%"...")
- 11:29, 15 February 2023 Price Query (hist | edit) [1,235 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Price Query (Price Query)}} == Description == For a graph with edge weight function $c : E \rightarrow Z$, a price query is an assignment of node weights $p : V \rightarrow Z$. Such a query has a yes answer if and only if there is a $(u,v) \in E$ such that $p(u) + p(v) > c(u,v)$. (Intuitively, the $p(v)$ are “prices” on the nodes, the $c(u,v)$ are costs of producing $u$ and $v$, and a price query asks if there is an edge we are willing to “sell”...")
- 11:29, 15 February 2023 Independent Set Queries (hist | edit) [1,358 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Independent Set Queries (Independent Set Queries)}} == Description == For a graph $G=(V,E)$ and a given subset of vertices $S\subseteq G$, answer the query of the form "is $S$ an independent set?" == Parameters == <pre>n: number of vertices m: number of edges</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem. == Reductions FROM Problem == {| class="wikitable sortable" style="text-align:center;" width=...")
- 11:29, 15 February 2023 All Pairs Minimum Witness (hist | edit) [962 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:All Pairs Minimum Witness (Minimum Witness)}} == Description == Fix an instance of negative triangle with node sets $I, J, K$ and weight function $w$. Let $i \in I, j \in J, k \in K$. Recall that the triple $(i, j, k)$ is a negative triangle iff $(w(i, k) \odot w(k, j)) + w(i, j) < 0$. Fix a total ordering $<$ on the nodes in $K$ in the negative triangle instance. For any $i \in I, j \in J$, a node $k \in K$ is called a minimum witness for $(i, j)$ if $(...")
- 11:29, 15 February 2023 Minimum Witness Finding (hist | edit) [1,429 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Minimum Witness Finding (Minimum Witness)}} == Description == Fix an instance of negative triangle with node sets $I, J, K$ and weight function $w$. Let $i \in I, j \in J, k \in K$. Recall that the triple $(i, j, k)$ is a negative triangle iff $(w(i, k) \odot w(k, j)) + w(i, j) < 0$. Fix a total ordering $<$ on the nodes in $K$ in the negative triangle instance. For any $i \in I, j \in J$, a node $k \in K$ is called a minimum witness for $(i, j)$ if $(i,...")
- 11:29, 15 February 2023 Multiple Local Alignment (hist | edit) [1,031 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Multiple Local Alignment (Local Alignment)}} == Description == Given $k$ input strings and a scoring function on pairs of letters, one is asked to find the substrings of the $k$ input strings that are most similar under the scoring function. == Related Problems == Generalizations: Local Alignment == Parameters == <pre>k: number of input strings n: length of input strings?</pre> == Table of Algorithms == Currently no algorithms in our databas...")
- 11:29, 15 February 2023 Local Alignment (hist | edit) [1,348 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Local Alignment (Local Alignment)}} == Description == Given two input strings and a scoring function on pairs of letters, one is asked to find the substrings of the two input strings that are most similar under the scoring function. == Related Problems == Subproblem: Multiple Local Alignment == Parameters == <pre>n: length of input strings?</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem. == Red...")
- 11:29, 15 February 2023 Geometric Base (hist | edit) [3,034 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Geometric Base (Geometric Base)}} == Description == Given a set of $n$ points with integer coordinates on three horizontal lines $y = 0, y = 1$, and $y = 2$, determine whether there exists a non-horizontal line containing three of the points == Parameters == <pre>n: number of points</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem. == Reductions TO Problem == {| class="wikitable sortable" style="text...")
- 11:29, 15 February 2023 3D Motion Planning (hist | edit) [1,079 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:3D Motion Planning (Motion Planning Problems)}} == Description == Given a set of horizontal (that is, parallel to the xy-plane) non-intersecting, non-touching triangle obstacles in 3-space, and a vertical line segment as a robot, determine whether the robot can be moved, using translations only, from a source to a goal position without colliding with the obstacles. == Related Problems == Related: Planar Motion Planning == Parameters == <pre>n:...")
- 11:29, 15 February 2023 Planar Motion Planning (hist | edit) [1,158 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Planar Motion Planning (Motion Planning Problems)}} == Description == Given a set of non-intersecting, non-touching, axis-parallel line segment obstacles in the plane and a line segment robot (a rod or ladder), determine whether the rod can be moved (allowing both translation and rotation) from a given source to a given goal configuration without colliding with the obstacles. == Related Problems == Related: 3D Motion Planning == Parameters == <...")
- 11:29, 15 February 2023 Visible Triangle (hist | edit) [1,457 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Visible Triangle (Geometric Visibility Problems)}} == Description == Given a set $S$ of opaque horizontal triangles, another horizontal triangle $t$ and a viewpoint $p$, is there a point on $t$ that can be seen from $p$? == Related Problems == Related: Visibility Between Segments, Visibility From Infinity == Parameters == <pre>n: number of opaque horizontal triangles</pre> == Table of Algorithms == Currently no algorithms in our database...")
- 11:29, 15 February 2023 Visibility From Infinity (hist | edit) [1,088 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Visibility From Infinity (Geometric Visibility Problems)}} == Description == Given a set $S$ of axis-parallel line segments in the plane and one particular horizontal segments $s$, determine whether there is a point on $s$ that can be seen from infinity, that is, whether there exists an infinite ray starting at the point on $s$ that does not intersect any segment. == Related Problems == Related: Visibility Between Segments, Visible Triangle =...")
- 11:29, 15 February 2023 Visibility Between Segments (hist | edit) [1,088 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Visibility Between Segments (Geometric Visibility Problems)}} == Description == Given a set $S$ of $n$ horizontal line segments in the plane and two particular horizontal segments $s_1$ and $s_2$, determine whether there are points on $s_1$ and $s_2$ that can see each other, that is, such that the open segment between the points does not intersect any segment in $S$. == Related Problems == Related: Visibility From Infinity, Visible Triangle =...")
- 11:29, 15 February 2023 Weighted Depth (hist | edit) [1,239 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Weighted Depth (Geometric Covering Problems)}} == Description == Given a set of $n$ weighted axis-parallel boxes in $d$-dimensional space $\mathbb{R}^d$, find a point $p \in \mathbb{R}^d$ that maximizes the sum of the weights of the boxes containing $p$. == Related Problems == Related: Strips Cover Box, Triangles Cover Triangle, Hole in Union, Triangle Measure, Point Covering, Max-Weight Rectangle == Parameters == <pre>n: nu...")
- 11:29, 15 February 2023 Max-Weight Rectangle (hist | edit) [1,216 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Max-Weight Rectangle (Geometric Covering Problems)}} == Description == Given $n$ weighted points (positive or negative) in $d \geq 2$ dimensions, what is the axis-aligned box which maximizes the total weight of the points it contains? == Related Problems == Related: Strips Cover Box, Triangles Cover Triangle, Hole in Union, Triangle Measure, Point Covering, Weighted Depth == Parameters == <pre>n: number of points d: dimensio...")
- 11:29, 15 February 2023 Point Covering (hist | edit) [997 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Point Covering (Geometric Covering Problems)}} == Description == Given a set of $n$ halfplanes and a number $k$, determine whether there is a point $p$ that is covered by at least $k$ of the halfplanes. == Related Problems == Related: Strips Cover Box, Triangles Cover Triangle, Hole in Union, Triangle Measure, Max-Weight Rectangle, Weighted Depth == Parameters == <pre>n: number of halfplanes</pre> == Table of Algorithms ==...")
- 11:29, 15 February 2023 Triangle Measure (hist | edit) [951 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Triangle Measure (Geometric Covering Problems)}} == Description == Given a set of triangles in the plane, compute the measure of their union. == Related Problems == Related: Strips Cover Box, Triangles Cover Triangle, Hole in Union, Point Covering, Max-Weight Rectangle, Weighted Depth == Parameters == <pre>n: number of triangles</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem....")
- 11:29, 15 February 2023 Hole in Union (hist | edit) [1,425 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Hole in Union (Geometric Covering Problems)}} == Description == Given a set of triangles in the plane, does their union contain a hole? == Related Problems == Related: Strips Cover Box, Triangles Cover Triangle, Triangle Measure, Point Covering, Max-Weight Rectangle, Weighted Depth == Parameters == <pre>n: number of triangles</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem. =...")
- 11:29, 15 February 2023 Triangles Cover Triangle (hist | edit) [2,953 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Triangles Cover Triangle (Geometric Covering Problems)}} == Description == Given a set of triangles in the plane, does their union contain another given triangle? == Related Problems == Related: Strips Cover Box, Hole in Union, Triangle Measure, Point Covering, Max-Weight Rectangle, Weighted Depth == Parameters == <pre>n: number of triangles</pre> == Table of Algorithms == Currently no algorithms in our database for the g...")
- 11:29, 15 February 2023 Strips Cover Box (hist | edit) [1,712 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Strips Cover Box (Geometric Covering Problems)}} == Description == Given a set of strips in the plane, does their union contain a given axis-parallel rectangle? == Related Problems == Related: Triangles Cover Triangle, Hole in Union, Triangle Measure, Point Covering, Max-Weight Rectangle, Weighted Depth == Parameters == <pre>n: number of strips</pre> == Table of Algorithms == Currently no algorithms in our database for th...")
- 11:29, 15 February 2023 Separator2 (hist | edit) [831 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Separator2 (Geometric Separator Problems)}} == Description == Given a set $S$ of $n$ closed, non-intersecting (nor touching), axis-parallel line segments, is there a separator? == Related Problems == Related: Separator1 == Parameters == <pre>n: number of line segments</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem. == Reductions FROM Problem == {| class="wikitable sortable" style="text-align...")
- 11:29, 15 February 2023 Separator1 (hist | edit) [1,068 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Separator1 (Geometric Separator Problems)}} == Description == Given a set $S$ of $n$ possible half-infinite, closed horizontal line segments, is there a non-horizontal separator? Separator definition: Given a set $S$ of $n$ objects in the plane, we call a line $l$ a separator of $S$ if $l$ does not intersect any object in $S$ and both halfplanes bounded by $l$ contain a non-empty subset of the objects in $S$. == Related Problems == Related: Separat...")
- 11:28, 15 February 2023 Point on 3 Lines (hist | edit) [1,298 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Point on 3 Lines (Geometric Incidence Problems)}} == Description == Given a set of lines in the plane, is there a point that lies on at least three of them? == Related Problems == Related: 3 Points on Line == Parameters == <pre>n: number of lines</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem. == Reductions TO Problem == {| class="wikitable sortable" style="text-align:center;" width="100%"...")
- 11:28, 15 February 2023 3 Points on Line (hist | edit) [1,580 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:3 Points on Line (Geometric Incidence Problems)}} == Description == Given a set of points in the plane, is there a line that contains at least three of the points? == Related Problems == Related: Point on 3 Lines == Parameters == <pre>n: number of points</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem. == Reductions TO Problem == {| class="wikitable sortable" style="text-align:center;" width=...")
- 11:28, 15 February 2023 Partial Match (hist | edit) [1,585 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Partial Match (Partial Match)}} == Description == In the Partial Match problem, we are given a "database" of $n$ binary strings, and a list of $n$ "queries" which are strings in $\{0,1,?\}^*$. (Here, "?" represents a wildcard.) We say that a query $q=q_1,...,q_d$ matches a string $x=x_1,...,x_d$ if for all $i=1,...,d$, if $q_i$ in $\{0,1\}$ then $q_i = x_i$. Output: Determine for all $n$ queries, which of them match some string in the database. == Param...")
- 11:28, 15 February 2023 Dynamic Time Warping (hist | edit) [1,191 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Dynamic Time Warping (Dynamic Time Warping)}} == Description == Fix a metric space $(M, d)$. A sequence of points in $M$ is called a curve. Consider two curves $x, y$ of length $n, m (n \geq m)$. We may traverse $x$ and $y$ by starting in their first entries, in any time step advancing to the next entry in $x$ or $y$ or both, and ending in their last entries. The cost of such a traversal is the sum over all points in time of the distance between the curr...")
- 11:28, 15 February 2023 Frechet Distance (hist | edit) [981 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Frechet Distance (Frechet Distance)}} == Description == Intuitively, the (continuous) Fréchet distance of two curves $P, Q$ is the minimal length of a leash required to connect a dog to its owner, as they walk along $P$ or $Q$, respectively, without backtracking. == Parameters == <pre>n: length of first curve m: length of second curve</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem. == Reductions FRO...")
- 11:28, 15 February 2023 Metricity (hist | edit) [1,534 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Metricity (Metricity)}} == Description == Given an $n\times n$ nonnegative matrix $A$, determine whether $A$ defines a metric on $(n)$, that is, that A is symmetric, has 0s on the diagonal, and its entries satisfy the triangle inequality. == Parameters == <pre>n: dimensionality of matrix</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem. == Reductions TO Problem == {| class="wikitable sortable" style=...")
- 11:28, 15 February 2023 Triangle Collection* (hist | edit) [2,241 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Triangle Collection* (Graph Triangle Problems)}} == Description == See Definition 3 of reference. == Related Problems == Generalizations: Triangle Detection Related: Negative Triangle Detection, Negative Triangle Search, Negative Triangle Listing, Nondecreasing Triangle, Minimum Triangle, Triangle in Unweighted Graph == Parameters == <pre>n: number of vertices m: number of edges</pre> == Table of Algorithms == Curren...")
- 11:28, 15 February 2023 Triangle Detection (hist | edit) [4,387 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Triangle Detection (Graph Triangle Problems)}} == Description == Determine whether or not there is a triangle in a given graph == Related Problems == Subproblem: Negative Triangle Detection, Nondecreasing Triangle, Minimum Triangle, Triangle in Unweighted Graph, Triangle Collection* Related: Negative Triangle Search, Negative Triangle Listing, Nondecreasing Triangle, Minimum Triangle, Triangle in Unweighted G...")
- 11:28, 15 February 2023 Triangle in Unweighted Graph (hist | edit) [1,312 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Triangle in Unweighted Graph (Graph Triangle Problems)}} == Description == Find a triangle in an unweighted graph == Related Problems == Generalizations: Triangle Detection Related: Negative Triangle Detection, Negative Triangle Search, Negative Triangle Listing, Nondecreasing Triangle, Minimum Triangle, Triangle Collection* == Parameters == <pre>n: number of vertices m: number of edges</pre> == Table of Algorithms ==...")
- 11:28, 15 February 2023 Minimum Triangle (hist | edit) [1,092 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Minimum Triangle (Graph Triangle Problems)}} == Description == Find the triangle in a graph with minimum weight == Related Problems == Generalizations: Triangle Detection Related: Negative Triangle Detection, Negative Triangle Search, Negative Triangle Listing, Nondecreasing Triangle, Triangle in Unweighted Graph, Triangle Collection* == Parameters == <pre>n: number of vertices m: number of edges</pre> == Table of Algo...")
- 11:28, 15 February 2023 Nondecreasing Triangle (hist | edit) [1,133 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Nondecreasing Triangle (Graph Triangle Problems)}} == Description == Given a tripartite graph with partitions $I, J, K$ and real edge weights, find a triangle $i \in I, j \in J, k \in K$ such that $w(i, k) \leq w(k, j) \leq w(i, j)$. == Related Problems == Generalizations: Triangle Detection Related: Negative Triangle Detection, Negative Triangle Search, Negative Triangle Listing, Minimum Triangle, Triangle in Unweighted Graph...")
- 11:28, 15 February 2023 Negative Triangle Listing (hist | edit) [1,343 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Negative Triangle Listing (Graph Triangle Problems)}} == Description == Given an $n$ node graph $G = (V, E)$ with edge weights $w: E \rightarrow W$, list the negative triangles, i.e. three vertices that form a triangle with total edge weights summing to a negative number. == Related Problems == Generalizations: Negative Triangle Search Related: Negative Triangle Detection, Nondecreasing Triangle, Minimum Triangle, Triangle in Unweig...")
- 11:28, 15 February 2023 Negative Triangle Search (hist | edit) [1,166 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Negative Triangle Search (Graph Triangle Problems)}} == Description == Given an $n$ node graph $G = (V, E)$ with edge weights $w: E \rightarrow W$, find a negative triangle, i.e. three vertices that form a triangle with total edge weights summing to a negative number. == Related Problems == Generalizations: Negative Triangle Detection Subproblem: Negative Triangle Listing Related: Nondecreasing Triangle, Minimum Triangle, Triangle...")
- 11:28, 15 February 2023 Negative Triangle Detection (hist | edit) [8,122 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Negative Triangle Detection (Graph Triangle Problems)}} == Description == Given an $n$ node graph $G = (V, E)$ with edge weights $w: E \rightarrow W$, determine whether there is a negative triangle, i.e. three vertices that form a triangle with total edge weights summing to a negative number. == Related Problems == Generalizations: Triangle Detection Subproblem: Negative Triangle Search Related: Negative Triangle Listing, Nondecreasing...")
- 11:28, 15 February 2023 Approximate Reach Centrality (hist | edit) [1,693 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Approximate Reach Centrality (Vertex Centrality)}} == Description == The reach centrality of a node $w$ is the smallest distance $r$ such that any $s-t$ shortest path passing through $w$ has either $s$ or $t$ in the ball of radius $r$ around $w$. Approximate reach centrality is the approximation version of the problem. == Related Problems == Generalizations: Reach Centrality Related: Eccentricity, All-Nodes Median Parity, Betweenness C...")
- 11:28, 15 February 2023 Undirected All-Nodes Reach Centrality (hist | edit) [1,469 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Undirected All-Nodes Reach Centrality (Vertex Centrality)}} == Description == The reach centrality of a node $w$ is the smallest distance $r$ such that any $s-t$ shortest path passing through $w$ has either $s$ or $t$ in the ball of radius $r$ around $w$. Undirected All-Nodes Reach Centrality is the version of the problem in an undirected graph where you must calculate the reach centrality of each node. == Related Problems == Generalizations: Reach...")
- 11:28, 15 February 2023 Directed All-Nodes Reach Centrality (hist | edit) [1,458 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Directed All-Nodes Reach Centrality (Vertex Centrality)}} == Description == The reach centrality of a node $w$ is the smallest distance $r$ such that any $s-t$ shortest path passing through $w$ has either $s$ or $t$ in the ball of radius $r$ around $w$. Directed All-Nodes Reach Centrality is the version of the problem in a directed graph where you must calculate the reach centrality of each node. == Related Problems == Generalizations: Reach Centra...")
- 11:28, 15 February 2023 Reach Centrality (hist | edit) [2,611 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Reach Centrality (Vertex Centrality)}} == Description == The reach centrality of a node $w$ is the smallest distance $r$ such that any $s-t$ shortest path passing through $w$ has either $s$ or $t$ in the ball of radius $r$ around $w$. == Related Problems == Subproblem: Directed All-Nodes Reach Centrality, Undirected All-Nodes Reach Centrality, Approximate Reach Centrality Related: Eccentricity, All-Nodes Median Parity, Between...")
- 11:28, 15 February 2023 Undirected All-Nodes Positive Betweenness Centrality (hist | edit) [1,252 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Undirected All-Nodes Positive Betweenness Centrality (Vertex Centrality)}} == Description == Given an undirected graph, determine whether the betweenness centrality of all nodes is positive. == Related Problems == Generalizations: Positive Betweenness Centrality Related: Eccentricity, All-Nodes Median Parity, Betweenness Centrality, Approximate Betweenness Centrality, Directed All-Nodes Positive Betweenness Centrality, Reach...")
- 11:28, 15 February 2023 Directed All-Nodes Positive Betweenness Centrality (hist | edit) [1,243 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Directed All-Nodes Positive Betweenness Centrality (Vertex Centrality)}} == Description == Given a directed graph, determine whether the betweenness centrality of all nodes is positive. == Related Problems == Generalizations: Positive Betweenness Centrality Related: Eccentricity, All-Nodes Median Parity, Betweenness Centrality, Approximate Betweenness Centrality, Undirected All-Nodes Positive Betweenness Centrality, Reach Ce...")
- 11:28, 15 February 2023 Positive Betweenness Centrality (hist | edit) [2,749 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Positive Betweenness Centrality (Vertex Centrality)}} == Description == Given a graph $G=(V,E)$ and a vertex $v \in V$, determine whether the betweenness centrality of $v$ is positive. == Related Problems == Generalizations: Betweenness Centrality Subproblem: Directed All-Nodes Positive Betweenness Centrality, Undirected All-Nodes Positive Betweenness Centrality Related: Eccentricity, All-Nodes Median Parity, Approximate Betwe...")
- 11:28, 15 February 2023 Approximate Betweenness Centrality (hist | edit) [1,845 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Approximate Betweenness Centrality (Vertex Centrality)}} == Description == Given a graph $G = (V, E)$ and a vertex $v \in V$, approximate the betweenness centrality of vertex $v$ == Related Problems == Generalizations: Betweenness Centrality Related: Eccentricity, All-Nodes Median Parity, Positive Betweenness Centrality, Directed All-Nodes Positive Betweenness Centrality, Undirected All-Nodes Positive Betweenness Centrality, [...")
- 11:28, 15 February 2023 Betweenness Centrality (hist | edit) [1,101 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Betweenness Centrality (Vertex Centrality)}} == Description == Given a graph $G = (V, E)$ and a vertex $v \in V$, calculate the betweenness centrality of vertex $v$ (or the proportion of shortest paths that go through $v$), i.e. $BC(v) := \sum\limits_{s\neq t \neq v \in V} \frac{\sigma_{st}(v)}{\sigma_{st}}$ where $\sigma_{st}(v)$ is the number of shortest paths from $s$ to $t$ that go through $v$ and $\sigma_{st}$ is the number of shortest paths from $s...")
- 11:28, 15 February 2023 All-Nodes Median Parity (hist | edit) [1,876 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:All-Nodes Median Parity (Vertex Centrality)}} == Description == Given a graph $G = (V, E)$, compute $Med(v) (\mod 2)$ for all $v\in V$, where $Med(v) := \sum\limits_{w\in V} d(v, w)$ == Related Problems == Related: Eccentricity, Betweenness Centrality, Approximate Betweenness Centrality, Positive Betweenness Centrality, Directed All-Nodes Positive Betweenness Centrality, Undirected All-Nodes Positive Betweenness Centrality, R...")
- 11:28, 15 February 2023 Eccentricity (hist | edit) [871 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Eccentricity (Vertex Centrality)}} == Description == Given a graph $G = (V, E)$ and a vertex $v \in V$, calculate the eccentricity $\epsilon(v) := \max \limits_{u\in V} d(u, v)$ == Related Problems == Subproblem: Radius, Diameter, 1-sensitive (4/3)-approximate decremental eccentricity Related: All-Nodes Median Parity, Betweenness Centrality, Approximate Betweenness Centrality, Positive Betweenness Centrality, Directed...")
- 11:28, 15 February 2023 1-sensitive (4/3)-approximate decremental eccentricity (hist | edit) [1,297 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:1-sensitive (4/3)-approximate decremental eccentricity (Graph Metrics)}} == Description == Approximate the eccentricity of a graph decrementally within a factor of 4/3, with a sensativity of 1, i.e. when a single edge is removed. == Related Problems == Generalizations: Eccentricity Related: Median, Radius, Diameter, Diameter 2 vs 3, Diameter 3 vs 7, Approximate Diameter, Decremental Diameter, 1-sensitive (4/3)-approx...")
- 11:28, 15 February 2023 Constant sensitivity (4/3)-approximate incremental diameter (hist | edit) [1,407 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:constant sensitivity (4/3)-approximate incremental diameter (Graph Metrics)}} == Description == Approximate the diameter of a graph decrementally within a factor of 4/3, with a constant sensitivity of $K(\epsilon, t)$, i.e. when a $K(\epsilon, t)$ edges are removed. == Related Problems == Generalizations: Decremental Diameter Related: Median, Radius, Diameter, Diameter 2 vs 3, Diameter 3 vs 7, Approximate Diameter, 1-sen...")
- 11:28, 15 February 2023 1-sensitive decremental diameter (hist | edit) [1,300 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:1-sensitive decremental diameter (Graph Metrics)}} == Description == Determine the diameter of a graph decrementally, with a sensativity of 1, i.e. when a single edge is removed. == Related Problems == Generalizations: Decremental Diameter Subproblem: 1-sensitive (4/3)-approximate decremental diameter Related: Median, Radius, Diameter, Diameter 2 vs 3, Diameter 3 vs 7, Approximate Diameter, constant sensitivity (4/3...")
- 11:28, 15 February 2023 1-sensitive (4/3)-approximate decremental diameter (hist | edit) [1,303 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:1-sensitive (4/3)-approximate decremental diameter (Graph Metrics)}} == Description == Approximate the diameter of a graph decrementally within a factor of 4/3, with a sensativity of 1, i.e. when a single edge is removed. == Related Problems == Generalizations: 1-sensitive decremental diameter Related: Median, Radius, Diameter, Diameter 2 vs 3, Diameter 3 vs 7, Approximate Diameter, Decremental Diameter, constant sen...")
- 11:28, 15 February 2023 Decremental Diameter (hist | edit) [788 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Decremental Diameter (Graph Metrics)}} == Description == Determine the diameter of a graph decrementally, i.e. by removing edges and querying the resulting graph. == Related Problems == Generalizations: Diameter Subproblem: 1-sensitive decremental diameter, constant sensitivity (4/3)-approximate incremental diameter Related: Median, Radius, Diameter 2 vs 3, Diameter 3 vs 7, Approximate Diameter, 1-sensitive (4/3)-a...")
- 11:28, 15 February 2023 Approximate Diameter (hist | edit) [1,219 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Approximate Diameter (Graph Metrics)}} == Description == Given a graph $G = (V, E)$, approximate the diameter within a given factor. == Related Problems == Generalizations: Diameter Subproblem: Diameter 2 vs 3, Diameter 3 vs 7 Related: Median, Radius, Diameter 3 vs 7, Decremental Diameter, 1-sensitive (4/3)-approximate decremental diameter, 1-sensitive decremental diameter, constant sensitivity (4/3)-approximat...")
- 11:28, 15 February 2023 Diameter 3 vs 7 (hist | edit) [1,212 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Diameter 3 vs 7 (Graph Metrics)}} == Description == Given a graph $G = (V, E)$, distinguish between diameter 3 and diameter 7. In other words, approximate diameter within a factor of $9/4-\epsilon$. == Related Problems == Generalizations: Approximate Diameter Related: Median, Radius, Diameter, Diameter 2 vs 3, Decremental Diameter, 1-sensitive (4/3)-approximate decremental diameter, 1-sensitive decremental diameter, ...")
- 11:28, 15 February 2023 Diameter 2 vs 3 (hist | edit) [1,264 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Diameter 2 vs 3 (Graph Metrics)}} == Description == Given a graph $G = (V, E)$, distinguish between diameter 2 and diameter 3. In other words, approximate diameter within a factor of $4/3-\epsilon$. == Related Problems == Generalizations: Approximate Diameter Related: Median, Radius, Diameter, Diameter 3 vs 7, Decremental Diameter, 1-sensitive (4/3)-approximate decremental diameter, 1-sensitive decremental diameter, ...")
- 11:28, 15 February 2023 Diameter (hist | edit) [3,741 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Diameter (Graph Metrics)}} == Description == Given a graph $G = (V, E)$, determine the diameter $d$ of the graph, i.e. the maximum eccentricity over all of the vertices of the graph == Related Problems == Generalizations: Eccentricity Subproblem: Approximate Diameter, Decremental Diameter Related: Median, Radius, Diameter 2 vs 3, Diameter 3 vs 7, Decremental Diameter, 1-sensitive (4/3)-approximate decremental diame...")
- 11:28, 15 February 2023 Radius (hist | edit) [1,280 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Radius (Graph Metrics)}} == Description == Given a graph $G = (V, E)$, determine the radius $r$ of the graph, i.e. the minimum eccentricity over all of the vertices of the graph == Related Problems == Generalizations: Eccentricity Related: Median, Diameter, Diameter 2 vs 3, Diameter 3 vs 7, Approximate Diameter, Decremental Diameter, 1-sensitive (4/3)-approximate decremental diameter, 1-sensitive decremental diameter...")
- 11:27, 15 February 2023 Median (hist | edit) [1,236 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Median (Graph Metrics)}} == Description == Given a graph $G = (V, E)$, determine the median $m$ of the graph, where $m := \min\limits_{v\in V} \sum\limits_{u\in V} d(u, v)$ == Related Problems == Related: Radius, Diameter, Diameter 2 vs 3, Diameter 3 vs 7, Approximate Diameter, Decremental Diameter, 1-sensitive (4/3)-approximate decremental diameter, 1-sensitive decremental diameter, constant sensitivity (4/3)-approxi...")
- 11:27, 15 February 2023 Unbalanced OV (hist | edit) [1,257 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Unbalanced OV (Orthogonal Vectors)}} == Description == Let $0 < \alpha \leq 1$. UOV is the OV problem with the specifications that $A$ is of size $n$ and $B$ is of size $m=\Theta(n^\alpha)$ and $d\leq n^{o(1)}$. == Related Problems == Generalizations: OV Related: k-OV, 3-OV == Parameters == <pre>$n$: size of $A$ $m$: size of $B$ $d$: dimensionality of vectors</pre> == Table of Algorithms == Currently no algorithms in our database fo...")
- 11:27, 15 February 2023 3-OV (hist | edit) [1,200 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:3-OV (Orthogonal Vectors)}} == Description == Given 3 sets of $d$-dimensional vectors $A_1, A_2, A_3$, each of size $n$, does there exist $a_1 \in A_1, a_2 \in A_2, a_3 \in A_3$ such that $a_1 * a_2 * a_3 = 0$? == Related Problems == Generalizations: k-OV Related: OV, Unbalanced OV == Parameters == <pre>$n$: number of vectors per set $d$: dimension of each vector; $d = omega(log(n))$</pre> == Table of Algorithms == Currently no algo...")
- 11:27, 15 February 2023 K-OV (hist | edit) [2,102 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:k-OV (Orthogonal Vectors)}} == Description == Given $k$ sets of $d$-dimensional vectors $A_1, A_2, \ldots, A_k$, each of size $n$, does there exist $a_1 \in A_1, a_2 \in A_2, \ldots, a_k \in A_k$ such that $a_1 * a_2 * \ldots * a_k = 0$? == Related Problems == Subproblem: OV, 3-OV Related: 3-OV, Unbalanced OV == Parameters == <pre>$n$: number of vectors per set $k$: number of sets $d$: dimension of each vector; $d = omega(log(n))$...")
- 11:27, 15 February 2023 OV (hist | edit) [5,802 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:OV (Orthogonal Vectors)}} == Description == Given $n$ vectors in $\{0,1\}^{O(\log n)}$, are two of them orthogonal? == Related Problems == Generalizations: k-OV Subproblem: Unbalanced OV Related: 3-OV == Parameters == <pre>$n$: number of vectors $d$: dimension of each vector; $d = O(log(n))$ typically</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Sp...")
- 11:27, 15 February 2023 MaxSAT (hist | edit) [2,980 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:MaxSAT (Boolean Satisfiability)}} == Description == Given an instance of SAT represented in Conjunctive Normal Form (CNF), compute an assignment to the variables that maximizes the number of satisfied clauses. == Related Problems == Generalizations: Conjunctive Normal Form SAT Related: SAT, Disjunctive Normal Form SAT, 1-in-3SAT, Monotone 1-in-3SAT, Monotone Not-Exactly-1-in-3SAT, All-Equal-SAT, Not-All-Equal 3-SAT (NAE...")
- 11:27, 15 February 2023 Renamable Horn (hist | edit) [1,109 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Renamable Horn (Boolean Satisfiability)}} == Description == Renamable Horn asks the question whether or not there exists a subset of variables that can be negated such that the boolean formula is turned into a Horn formula == Related Problems == Generalizations: Horn SAT Related: SAT, Conjunctive Normal Form SAT, Disjunctive Normal Form SAT, 1-in-3SAT, Monotone 1-in-3SAT, Monotone Not-Exactly-1-in-3SAT, All-Equal-SAT,...")
- 11:27, 15 February 2023 Dual-Horn SAT (hist | edit) [784 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Dual-Horn SAT (Boolean Satisfiability)}} == Description == Dual-Horn SAT restricts the boolean formula to the conjunction of dual-Horn clauses, i.e. clauses with at most one negated literal == Related Problems == Generalizations: Horn SAT Related: SAT, Conjunctive Normal Form SAT, Disjunctive Normal Form SAT, 1-in-3SAT, Monotone 1-in-3SAT, Monotone Not-Exactly-1-in-3SAT, All-Equal-SAT, [[Not-All-Equal 3-SAT (NAE 3SAT)]...")
- 11:27, 15 February 2023 Horn SAT (hist | edit) [808 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Horn SAT (Boolean Satisfiability)}} == Description == Horn SAT restricts the boolean formula to the conjunction of Horn clauses, i.e. clauses with at most one positive literal == Related Problems == Generalizations: Conjunctive Normal Form SAT Subproblem: Dual-Horn SAT, Renamable Horn Related: SAT, Disjunctive Normal Form SAT, 1-in-3SAT, Monotone 1-in-3SAT, Monotone Not-Exactly-1-in-3SAT, All-Equal-SAT, Not-All...")
- 11:27, 15 February 2023 XOR-SAT (hist | edit) [695 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:XOR-SAT (Boolean Satisfiability)}} == Description == XOR-SAT replaces the ORs in CNF with XORs == Related Problems == Generalizations: Conjunctive Normal Form SAT Related: SAT, Disjunctive Normal Form SAT, 1-in-3SAT, Monotone 1-in-3SAT, Monotone Not-Exactly-1-in-3SAT, All-Equal-SAT, Not-All-Equal 3-SAT (NAE 3SAT), Monotone Not-All-Equal 3-SAT (Monotone NAE 3SAT), k-SAT, 2SAT, 3SAT, 3SAT-5, 4SAT,...")
- 11:27, 15 February 2023 Monotone 3SAT (hist | edit) [772 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Monotone 3SAT (Boolean Satisfiability)}} == Description == Monotone 3SAT is 3SAT with the restriction that all of the literals in a clause are either all negated or all positive == Related Problems == Generalizations: 3SAT Related: SAT, Conjunctive Normal Form SAT, Disjunctive Normal Form SAT, 1-in-3SAT, Monotone 1-in-3SAT, Monotone Not-Exactly-1-in-3SAT, All-Equal-SAT, Not-All-Equal 3-SAT (NAE 3SAT), Monotone No...")
- 11:27, 15 February 2023 4SAT (hist | edit) [1,033 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:4SAT (Boolean Satisfiability)}} == Description == 4SAT restricts the boolean formula to CNF with (at most) 4 literals per clause == Related Problems == Generalizations: k-SAT Related: SAT, Conjunctive Normal Form SAT, Disjunctive Normal Form SAT, 1-in-3SAT, Monotone 1-in-3SAT, Monotone Not-Exactly-1-in-3SAT, All-Equal-SAT, Not-All-Equal 3-SAT (NAE 3SAT), Monotone Not-All-Equal 3-SAT (Monotone NAE 3SAT), [[2SAT]...")
- 11:27, 15 February 2023 3SAT-5 (hist | edit) [736 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:3SAT-5 (Boolean Satisfiability)}} == Description == 3SAT-5 is 3SAT with the restriction that each variable occurs in at most 5 clauses == Related Problems == Generalizations: 3SAT Related: SAT, Conjunctive Normal Form SAT, Disjunctive Normal Form SAT, 1-in-3SAT, Monotone 1-in-3SAT, Monotone Not-Exactly-1-in-3SAT, All-Equal-SAT, Not-All-Equal 3-SAT (NAE 3SAT), Monotone Not-All-Equal 3-SAT (Monotone NAE 3SAT), ...")
- 11:27, 15 February 2023 3SAT (hist | edit) [1,486 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:3SAT (Boolean Satisfiability)}} == Description == 3SAT restricts the boolean formula to CNF with (at most) 3 literals per clause == Related Problems == Generalizations: k-SAT Subproblem: 1-in-3SAT, Not-All-Equal 3-SAT (NAE 3SAT), 3SAT-5, Monotone 3SAT Related: SAT, Conjunctive Normal Form SAT, Disjunctive Normal Form SAT, Monotone 1-in-3SAT, Monotone Not-Exactly-1-in-3SAT, All-Equal-SAT, Not-All-Equal...")
- 11:27, 15 February 2023 2SAT (hist | edit) [732 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:2SAT (Boolean Satisfiability)}} == Description == 2SAT restricts the boolean formula to CNF with (at most) 2 literals per clause == Related Problems == Generalizations: k-SAT Related: SAT, Conjunctive Normal Form SAT, Disjunctive Normal Form SAT, 1-in-3SAT, Monotone 1-in-3SAT, Monotone Not-Exactly-1-in-3SAT, All-Equal-SAT, Not-All-Equal 3-SAT (NAE 3SAT), Monotone Not-All-Equal 3-SAT (Monotone NAE 3SAT), [[3SAT]...")
- 11:27, 15 February 2023 K-SAT (hist | edit) [1,694 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:k-SAT (Boolean Satisfiability)}} == Description == k-SAT restricts the boolean formula to CNF with (at most) k literals per clause == Related Problems == Generalizations: Conjunctive Normal Form SAT Subproblem: 2SAT, 3SAT, 4SAT Related: SAT, Disjunctive Normal Form SAT, 1-in-3SAT, Monotone 1-in-3SAT, Monotone Not-Exactly-1-in-3SAT, All-Equal-SAT, Not-All-Equal 3-SAT (NAE 3SAT), Monotone Not-All-Equal 3...")
- 11:27, 15 February 2023 Monotone Not-All-Equal 3-SAT (Monotone NAE 3SAT) (hist | edit) [780 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Monotone Not-All-Equal 3-SAT (Monotone NAE 3SAT) (Boolean Satisfiability)}} == Description == Monotone NAE 3SAT is NAE 3SAT with the restriction that all of the literals in a clause are either all negated or all positive == Related Problems == Generalizations: Not-All-Equal 3-SAT (NAE 3SAT) Related: SAT, Conjunctive Normal Form SAT, Disjunctive Normal Form SAT, 1-in-3SAT, Monotone 1-in-3SAT, Monotone Not-Exactly-1-in-3SAT,...")
- 11:27, 15 February 2023 Not-All-Equal 3-SAT (NAE 3SAT) (hist | edit) [876 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Not-All-Equal 3-SAT (NAE 3SAT) (Boolean Satisfiability)}} == Description == NAE 3SAT restricts the boolean formula to CNF with 3 literals per clause and determines whether there is an assignment of variables such that, for none of the clauses, all 3 literals have the same boolean value == Related Problems == Generalizations: 3SAT Subproblem: Monotone Not-All-Equal 3-SAT (Monotone NAE 3SAT) Related: SAT, Conjunctive Normal Form SAT, [...")
- 11:27, 15 February 2023 All-Equal-SAT (hist | edit) [839 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:All-Equal-SAT (Boolean Satisfiability)}} == Description == All-Equal-SAT restricts the boolean formula to CNF and determines whether there is an assignment of variables such that, for all of the clauses, all literals have the same boolean value == Related Problems == Generalizations: Conjunctive Normal Form SAT Related: SAT, Disjunctive Normal Form SAT, 1-in-3SAT, Monotone 1-in-3SAT, Monotone Not-Exactly-1-in-3SAT, Not-All-E...")
- 11:27, 15 February 2023 Monotone Not-Exactly-1-in-3SAT (hist | edit) [847 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Monotone Not-Exactly-1-in-3SAT (Boolean Satisfiability)}} == Description == Monotone Not-Exactly-1-in-3SAT is Monotone 1-in-3SAT, except that rather than exactly one variable in a clause being true, it requires exactly 0, 2, or 3 of the variables in a clause being true == Related Problems == Generalizations: 1-in-3SAT Related: SAT, Conjunctive Normal Form SAT, Disjunctive Normal Form SAT, Monotone 1-in-3SAT, All-Equal-SAT, N...")
- 11:27, 15 February 2023 Monotone 1-in-3SAT (hist | edit) [824 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Monotone 1-in-3SAT (Boolean Satisfiability)}} == Description == Monotone 1-in-3SAT is 1-in-3SAT with the restriction that all of the literals in a clause are all positive (note: here, we don't allow clauses to be all negated literals) == Related Problems == Generalizations: 1-in-3SAT Related: SAT, Conjunctive Normal Form SAT, Disjunctive Normal Form SAT, Monotone Not-Exactly-1-in-3SAT, All-Equal-SAT, Not-All-Equal 3-SAT (NAE...")
- 11:27, 15 February 2023 1-in-3SAT (hist | edit) [896 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:1-in-3SAT (Boolean Satisfiability)}} == Description == 1-in-3SAT restricts the boolean formula to CNF with 3 literals per clause and determines whether there is an assignment of variables such that exactly 1 of the 3 literals in each clause is TRUE == Related Problems == Generalizations: 3SAT Subproblem: Monotone 1-in-3SAT, Monotone Not-Exactly-1-in-3SAT Related: SAT, Conjunctive Normal Form SAT, Disjunctive Normal Form SAT,...")
- 11:27, 15 February 2023 Disjunctive Normal Form SAT (hist | edit) [755 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Disjunctive Normal Form SAT (Boolean Satisfiability)}} == Description == DNF-SAT restricts the boolean formula to disjunctive normal form (DNF), meaning it is the OR of ANDs. == Related Problems == Generalizations: SAT Related: Conjunctive Normal Form SAT, 1-in-3SAT, Monotone 1-in-3SAT, Monotone Not-Exactly-1-in-3SAT, All-Equal-SAT, Not-All-Equal 3-SAT (NAE 3SAT), Monotone Not-All-Equal 3-SAT (Monotone NAE 3SAT), k-S...")
- 11:27, 15 February 2023 Conjunctive Normal Form SAT (hist | edit) [9,078 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Conjunctive Normal Form SAT (Boolean Satisfiability)}} == Description == CNF-SAT restricts the boolean formula to conjunctive normal form (CNF), meaning it is the AND of ORs. == Related Problems == Generalizations: SAT Subproblem: All-Equal-SAT, k-SAT, XOR-SAT, Horn SAT, MaxSAT Related: Disjunctive Normal Form SAT, 1-in-3SAT, Monotone 1-in-3SAT, Monotone Not-Exactly-1-in-3SAT, Not-All-Equal 3-SAT (NAE 3S...")
- 11:27, 15 February 2023 SAT (hist | edit) [3,026 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:SAT (Boolean Satisfiability)}} == Description == Boolean satisfiability problems involve determining if there is an assignment of variables that satisfies a given boolean formula. == Related Problems == Subproblem: Conjunctive Normal Form SAT, Disjunctive Normal Form SAT Related: Disjunctive Normal Form SAT, 1-in-3SAT, Monotone 1-in-3SAT, Monotone Not-Exactly-1-in-3SAT, All-Equal-SAT, Not-All-Equal 3-SAT (NAE 3SAT), [...")
- 11:27, 15 February 2023 Chromatic Polynomial (hist | edit) [31 bytes] Admin (talk | contribs) (Created page with "#REDIRECT #k-Graph Coloring")
- 11:26, 15 February 2023 5-Graph Coloring (hist | edit) [689 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:5-Graph Coloring (Graph Coloring)}} == Description == In this case, we wish to determine whether or not a graph is 5-colorable. == Related Problems == Generalizations: k-Graph Coloring Related: Chromatic Number, 2-Graph Coloring, 3-Graph Coloring, 4-Graph Coloring, #k-Graph Coloring, #2-Graph Coloring, #3-Graph Coloring, #4-Graph Coloring, #5-Graph Coloring == Parameters == <pre>n: number of vertices m: numb...")
- 11:26, 15 February 2023 4-Graph Coloring (hist | edit) [1,659 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:4-Graph Coloring (Graph Coloring)}} == Description == In this case, we wish to determine whether or not a graph is 4-colorable. == Related Problems == Generalizations: k-Graph Coloring Related: Chromatic Number, 2-Graph Coloring, 3-Graph Coloring, 5-Graph Coloring, #k-Graph Coloring, #2-Graph Coloring, #3-Graph Coloring, #4-Graph Coloring, #5-Graph Coloring == Parameters == <pre>n: number of vertices m: numb...")
- 11:26, 15 February 2023 3-Graph Coloring (hist | edit) [3,281 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:3-Graph Coloring (Graph Coloring)}} == Description == In this case, we wish to determine whether or not a graph is 3-colorable. == Related Problems == Generalizations: k-Graph Coloring Related: Chromatic Number, 2-Graph Coloring, 4-Graph Coloring, 5-Graph Coloring, #k-Graph Coloring, #2-Graph Coloring, #3-Graph Coloring, #4-Graph Coloring, #5-Graph Coloring == Parameters == <pre>n: number of vertices m: numb...")
- 11:26, 15 February 2023 2-Graph Coloring (hist | edit) [578 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:2-Graph Coloring (Graph Coloring)}} == Description == In this case, we wish to determine whether or not a graph is 2-colorable. == Related Problems == Generalizations: k-Graph Coloring Related: Chromatic Number, 3-Graph Coloring, 4-Graph Coloring, 5-Graph Coloring, #k-Graph Coloring, #2-Graph Coloring, #3-Graph Coloring, #4-Graph Coloring, #5-Graph Coloring == Parameters == <pre>n: number of vertices m: numb...")
- 11:26, 15 February 2023 Chromatic Number (hist | edit) [709 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Chromatic Number (Graph Coloring)}} == Description == In this case, we wish to compute the chromatic number of a graph; that is, the smallest number of colors needed to color the graph. == Related Problems == Related: k-Graph Coloring, 2-Graph Coloring, 3-Graph Coloring, 4-Graph Coloring, 5-Graph Coloring, #k-Graph Coloring, #2-Graph Coloring, #3-Graph Coloring, #4-Graph Coloring, #5-Graph Coloring == Parameter...")
- 11:26, 15 February 2023 K-Graph Coloring (hist | edit) [962 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:k-Graph Coloring (Graph Coloring)}} == Description == Graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In this case, the number of colors we have is given as an input. == Related Problems == Subproblem: 2-Graph Coloring, 3-Graph Coloring, 4-Graph Coloring, 5-Graph Coloring, #k-Graph Coloring Related: Chromati...")
- 11:26, 15 February 2023 Link Analysis (hist | edit) [3,244 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Link Analysis (Link Analysis)}} == Description == Unlike "flat" document collections, the World Wide Web is hypertext and provides considerable auxiliary information on top of the text of the web pages, such as link structure and link text. With link analysis, we take advantage of the link structure of the Web to produce a global "importance" ranking of every web page that helps search engines and users quickly make sense of the vast heterogeneity of the...")
- 11:26, 15 February 2023 No-Steal/Force (hist | edit) [470 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:No-Steal/Force (Recovery)}} == Description == Recovery is the process of reverting back to a safe state prior to a system failure. With a No-Steal/Force policy, the recovery algorithm will never write uncommited data to memory, but will force all commits to memory. == Related Problems == Related: Steal/No-Force == Parameters == No parameters found. == Table of Algorithms == Currently no algorithms in our database for the given problem.")
- 11:26, 15 February 2023 Steal/No-Force (hist | edit) [554 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Steal/No-Force (Recovery)}} == Description == Recovery is the process of reverting back to a safe state prior to a system failure. With a Steal/No-Force policy, the recovery algorithm will write possibly uncommited data to memory, while not forcing all commits to memory. == Related Problems == Related: No-Steal/Force == Parameters == No parameters found. == Table of Algorithms == Currently no algorithms in our database for the given problem...")
- 11:26, 15 February 2023 Online (hist | edit) [2,107 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Online (Page Replacements)}} == Description == When page fault occurs during the program execution, operating systems use page replacement algorithms to select a victim page from primary memory and makes room for the required page. == Related Problems == Related: Offline == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Ap...")
- 11:26, 15 February 2023 Offline (hist | edit) [866 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Offline (Page Replacements)}} == Description == When page fault occurs during the program execution, operating systems use page replacement algorithms to select a victim page from primary memory and makes room for the required page. == Related Problems == Related: Online == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Ap...")
- 11:26, 15 February 2023 Dining Philosophers Problem (hist | edit) [1,486 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Dining Philosophers Problem (Deadlock Avoidance)}} == Description == There are $n$ philosophers numbered 0 through $n-1$, seated around a circle table. Their only problem--besides philosophy--is that the dish served is a very difficult kind of spaghetti, that has to be eaten with two forks. There are two forks next to each plate, so that presents no difficulty: as a consequence, however, no two neighbors may be eating simultaneously. The philosophers' li...")
- 11:26, 15 February 2023 Deadlock Avoidance (hist | edit) [748 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Deadlock Avoidance (Deadlock Avoidance)}} == Description == A deadlock means that the processing of some parts, once started, cannot finish because each of these parts requests for its advancement some resource(s) currently held by some other part(s) in this set. In a deadlock avoidance approach, the controller must ensure that the granting of resources to any process will lead to a resulting state which is “safe,” i.e., a state from which all the p...")
- 11:26, 15 February 2023 Weighted Interval Schedule Maximization Problem (ISMP) (hist | edit) [567 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Weighted Interval Schedule Maximization Problem (ISMP) (Interval Scheduling)}} == Description == In Weighted Interval Scheduling, each interval has an associated weight. The goal is to maximize the weights of the accepted (and not interrupted) intervals. == Related Problems == Related: Unweighted Interval Scheduling == Parameters == <pre>n: number of tasks (intervals) k: number of machines (resources)</pre> == Table of Algorithms == Currentl...")
- 11:26, 15 February 2023 Unweighted Interval Scheduling (hist | edit) [2,931 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Unweighted Interval Scheduling (Interval Scheduling)}} == Description == Given are $n$ intervals of the form $(s_j , f_j)$ with $s_j < f_j$, for $j = 1, \ldots , n$. These intervals are the jobs that require uninterrupted processing during that interval. We will assume (without loss of generality) that the $s_j$’s and the $f_j$’s are nonnegative integers. We say that two intervals (or jobs) overlap if their intersection is nonempty, otherwise they ar...")
- 11:26, 15 February 2023 Polynomial Interpolation (hist | edit) [1,549 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Polynomial Interpolation (Polynomial Interpolation)}} == Description == Given a finite number of points $x_1, \ldots , x_n$, some real constants $y_1, \ldots , y_n$ and a subspace $V$ of $\Pi^d$, find a polynomial $p \in V$, such that $p(x_j) = y_j$, $j = 1, ... , n$ == Parameters == <pre>n: number of points d: dimension of space</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem. == Time Complexity grap...")
- 11:26, 15 February 2023 Block Ciphers (hist | edit) [1,395 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Block Ciphers (Block Ciphers)}} == Description == A block cipher is a pair of functions $E: \{0, 1\}^k \times \{0, 1\}^n \rightarrow \{0, 1\}^n$ and $D: \{0, 1\}^k \times \{0, 1\}^n \rightarrow \{0, 1\}^n$ that encode and decode a length $n$ string with a length $k$ key. == Parameters == <pre>n: text length (block size) k: key length</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Ye...")
- 11:26, 15 February 2023 Solutions to Nonlinear Equations (hist | edit) [1,307 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Solutions to Nonlinear Equations (Solutions to Nonlinear Equations)}} == Description == Compute the solutions to a given nonlinear equation of the form $f(x) = 0$. == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Reference |- | Bisection method (Solutions to Nonlinear Equations Solutions to N...")
- 11:26, 15 February 2023 Secret Sharing (hist | edit) [1,127 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Secret Sharing (Secret Sharing)}} == Description == Secret Sharing is the splitting up of a secret amongst a group such that no individual can learn the entire secret alone, but when a sufficient amount of the group comes together with their parts of the secret, they can reconstruct the secret. == Parameters == <pre>n: size of the group the secret is being shared with</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:...")
- 11:26, 15 February 2023 Unkeyed Hash Functions (hist | edit) [1,908 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Unkeyed Hash Functions (One-Way Hash Functions)}} == Description == A hash function, otherwise known as a one-way hash function, takes an arbitrary message of arbitrary length and creates an output (a hash) of a fixed length. The main characteristics of a cryptographic hash function are that given a message, it is easy to compute the hash; given the hash, it is difficult to compute the message; and that given a message, it is difficult to find a differen...")
- 11:26, 15 February 2023 Keyed Hash Functions (hist | edit) [1,062 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Keyed Hash Functions (One-Way Hash Functions)}} == Description == A hash function, otherwise known as a one-way hash function, takes an arbitrary message of arbitrary length and creates an output (a hash) of a fixed length. The main characteristics of a cryptographic hash function are that given a message, it is easy to compute the hash; given the hash, it is difficult to compute the message; and that given a message, it is difficult to find a different...")
- 11:26, 15 February 2023 Volterra Equations (hist | edit) [670 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Volterra Equations (Integral Equations)}} == Description == Integral equations are equations where an unknown function appears under an integral sign. Volterra equations have one limit of integration fixed while the other is a variable. == Related Problems == Related: Fredholm Equations == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Ti...")
- 11:26, 15 February 2023 Fredholm Equations (hist | edit) [691 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Fredholm Equations (Integral Equations)}} == Description == Integral equations are equations where an unknown function appears under an integral sign. Fredholm equations have both limits of integration fixed, and there are three types of Fredholm equations. == Related Problems == Related: Volterra Equations == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%"...")
- 11:26, 15 February 2023 The Frequent Words Problem (hist | edit) [1,059 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:The Frequent Words Problem (The Frequent Words Problem)}} == Description == Given a string of length $n$ and in input integer $k$, determine the most frequent $k$-mers in the string, i.e. the most frequent words of length $k$. == Parameters == <pre>n: length of string k: length of words sigma: size of alphabet</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! A...")
- 11:26, 15 February 2023 Tower of Hanoi (hist | edit) [1,595 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Tower of Hanoi (Tower of Hanoi)}} == Description == The Tower of Hanoi puzzle consists of $n$ discs, no two of the same size, stacked on $p \geq 3$ vertical pegs, in such a way that no disc lies on top of a smaller disc. A permissible $move$ is to take the top disc from one of the pegs and move it to one of the other pegs, as long as it is not placed on top of a smaller disc. Initially, they are all stacked on the first peg. The goal is to end up with th...")
- 11:26, 15 February 2023 Frequent Words with Mismatches Problem (hist | edit) [995 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Frequent Words with Mismatches Problem (Frequent Words with Mismatches Problem)}} == Description == Given two strings, determine the most frequent substring with at most $k$ mismatches, where mismatches are not counted towards the length of the substring. == Parameters == <pre>n: length of string k: length of words d: number of allowed mismatches sigma: size of alphabet</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-alig...")
- 11:26, 15 February 2023 Median String Problem with Binary Alphabets (hist | edit) [674 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Median String Problem with Binary Alphabets (Median String Problem)}} == Description == Given a binary alphabet $\Sigma$, a set $W$ of strings over $\Sigma$, and the Levenshtein distance between strings, find a string over $\Sigma$ that minimizes the sum of distances to the strings of $W$. == Related Problems == Related: Median String Problem with Unbounded Alphabets, Median String Problem with Bounded Alphabets == Parameters == <pre>n: num...")
- 11:26, 15 February 2023 Median String Problem with Bounded Alphabets (hist | edit) [675 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Median String Problem with Bounded Alphabets (Median String Problem)}} == Description == Given a bounded alphabet $\Sigma$, a set $W$ of strings over $\Sigma$, and the Levenshtein distance between strings, find a string over $\Sigma$ that minimizes the sum of distances to the strings of $W$. == Related Problems == Related: Median String Problem with Unbounded Alphabets, Median String Problem with Binary Alphabets == Parameters == <pre>n: nu...")
- 11:26, 15 February 2023 Median String Problem with Unbounded Alphabets (hist | edit) [1,075 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Median String Problem with Unbounded Alphabets (Median String Problem)}} == Description == Given an unbounded alphabet $\Sigma$, a set $W$ of strings over $\Sigma$, and the Levenshtein distance between strings, find a string over $\Sigma$ that minimizes the sum of distances to the strings of $W$. == Related Problems == Related: Median String Problem with Bounded Alphabets, Median String Problem with Binary Alphabets == Parameters == <pre>n:...")
- 11:26, 15 February 2023 N-Queens Completion (hist | edit) [782 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:n-Queens Completion (n-Queens Problem)}} == Description == Given an $n \times n$ chessboard that already has $k$ queens on it, complete the board such that there are $n$ queens, all of which cannot attack each other. == Related Problems == Related: Counting Solutions, Constructing Solutions == Parameters == <pre>n: size of chessboard k: number of queens given</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-alig...")
- 11:26, 15 February 2023 Constructing Solutions (hist | edit) [506 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Constructing Solutions (n-Queens Problem)}} == Description == What are all of the ways can one put $n$ queens on an $n \times n$ chessboard so that no two queens attack each other? == Related Problems == Related: Counting Solutions, n-Queens Completion == Parameters == <pre>n: number of queens, size of chessboard</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem. == References/Citation == ht...")
- 11:26, 15 February 2023 Counting Solutions (hist | edit) [1,926 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Counting Solutions (n-Queens Problem)}} == Description == How many ways can one put $n$ queens on an $n \times n$ chessboard so that no two queens attack each other? In other words, how many points can be placed on an $n \times n$ grid so that no two are on the same row, column, or diagonal? == Related Problems == Related: Constructing Solutions, n-Queens Completion == Parameters == <pre>n: number of queens, size of chessboard</pre> == Tab...")
- 11:26, 15 February 2023 Turnpike Problem (hist | edit) [705 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Turnpike Problem (Turnpike Problem)}} == Description == Given $n$ points and $\binom{n}{2}$ distances, find each distance's corresponding pair of points. == Parameters == <pre>n: number of points</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Reference |- | Outside-In algorithm (Turnpike Problem Turnpike Problem)|Outside-...")
- 11:26, 15 February 2023 Change-Making Problem (hist | edit) [1,207 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Change-Making Problem (Change-Making Problem)}} == Description == Given an unlimited amount of coins of denominations $c_1, \ldots, c_n$, and a desired sum $S$, find the minimum number of coins necessary to make $S$. == Parameters == <pre>n: number of coin denominations S: sum to be made</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !!...")
- 11:25, 15 February 2023 Transitive Reduction Problem of Directed Graphs (hist | edit) [4,028 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Transitive Reduction Problem of Directed Graphs (Transitive Reduction Problem)}} == Description == A directed graph $G^t$ is said to be a transitive reduction of the directed graph $G$ provided that (i) $G$ has a directed path from vertex $u$ to vertex $v$ if and only if $G$ has a directed path from vertex $u$ to vertex $v$, and (ii) there is no graph with fewer arcs than $G^t$ satisfying condition (i). The problem asks to find such a graph $G^t$ for a g...")
- 11:25, 15 February 2023 Self-Balancing Trees Search (hist | edit) [1,814 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Self-Balancing Trees Search (Self-Balancing Trees Search)}} == Description == Search for a given element within a self-balancing tree. == Parameters == <pre>n: size of tree</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Reference |- | Hopcroft 2-3 Tree || 1970 || $O(logn)...")
- 11:25, 15 February 2023 Self-Balancing Trees Deletion (hist | edit) [1,633 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Self-Balancing Trees Deletion (Self-Balancing Trees Deletion)}} == Description == Delete a given element from a self-balancing tree. == Parameters == <pre>n: size of tree</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Reference |- | Hopcroft 2-3 Tree || 1970 || $O(logn)...")
- 11:25, 15 February 2023 Self-Balancing Trees Insertion (hist | edit) [1,643 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Self-Balancing Trees Insertion (Self-Balancing Trees Insertion)}} == Description == Insert a given element into a self-balancing tree. == Parameters == <pre>n: size of tree</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Reference |- | Hopcroft 2-3 Tree || 1970 || $O(lo...")
- 11:25, 15 February 2023 Self-Balancing Trees Creation (hist | edit) [1,834 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Self-Balancing Trees Creation (Self-Balancing Trees Creation)}} == Description == Create a self-balancing tree given a list of elements. == Parameters == <pre>n: size of tree</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Reference |- | AVL Tree || 1962 || $O(nlogn)$ || $O(n)$ |...")
- 11:25, 15 February 2023 Rod-Cutting Problem (hist | edit) [909 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Rod-Cutting Problem (Rod-Cutting Problem)}} == Description == Given a rod of length $n$, and prices $p_i$ for which one can sell a segment of the rod of length $i$ ($1 \leq i \leq n$), find the splitting of the rod for which one can earn the most money once they sell the rod segments produced. == Parameters == <pre>n: length of rod</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year...")
- 11:25, 15 February 2023 Discrete Logarithm Over Finite Fields (hist | edit) [2,884 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Discrete Logarithm Over Finite Fields (Logarithm Calculations)}} == Description == Let $F_{p^n}$ denote the finite field of $p^n$ elements, where $p$ is a prime. Let $x$ be a generator for the multiplicative group of $F_{p^n}$. The discrete logarithm problem over $F_{p^n}$ is to compute, for any given nonzero $h \in F_{p^n}$, the least nonnegative integer $e$ such that $x^e=h$. In this context we shall write $e=\log_x h$. == Parameters == <pre>n: numb...")
- 11:25, 15 February 2023 Sequence-To-Graph Alignment (hist | edit) [1,162 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Sequence-To-Graph Alignment (Sequence-to-Graph Alignment)}} == Description == This is pattern matching where you are given a pattern and a hypertext graph. The hypertext model is that the text forms a graph of $N$ nodes and $E$ edges, where a string is stored inside each node, and the edges indicate alternative texts that may follow the current node. The pattern is still a simple string of length $m$. It is also customary to transform this graph into a o...")
- 11:25, 15 February 2023 Integer Relation Among Integers (hist | edit) [790 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Integer Relation Among Integers (Integer Relation)}} == Description == Given a vector $x \in \mathbb{Z}^n$, find an integer relation, i.e. a non-zero vector $m \in \mathbb{Z}^n$ such that $<x, m> = 0$ == Related Problems == Generalizations: Integer Relation Among Reals == Parameters == <pre>n: dimensionality of vectors</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Ti...")
- 11:25, 15 February 2023 Integer Relation Among Reals (hist | edit) [785 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Integer Relation Among Reals (Integer Relation)}} == Description == Given a vector $x \in \mathbb{R}^n$, find an integer relation, i.e. a non-zero vector $m \in \mathbb{Z}^n$ such that $<x, m> = 0$ == Related Problems == Subproblem: Integer Relation Among Integers == Parameters == <pre>n: dimensionality of vectors</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !!...")
- 11:25, 15 February 2023 Determinant of Matrices with Integer Entries (hist | edit) [1,238 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Determinant of Matrices with Integer Entries (Determinant of Matrices with Integer Entries)}} == Description == Calculate the determinant of a given matrix with integer matrices. For such matrices, the determinant is also an integer. == Parameters == <pre>n: dimension of matrix</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! R...")
- 11:25, 15 February 2023 Undirected Wiener Index (hist | edit) [977 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Undirected Wiener Index (Wiener Index)}} == Description == Calculate the sum of the lengths of the shortest paths between all pairs of vertices in an undirected graph (typically in the chemical graph representing the non-hydrogen atoms in the molecule). == Related Problems == Related: Minimum Wiener Connector Problem == Parameters == <pre>n: number of vertices (number of non-hydrogen atoms in the molecule)</pre> == Table of Algorithms == Cur...")
- 11:25, 15 February 2023 Minimum Wiener Connector Problem (hist | edit) [629 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Minimum Wiener Connector Problem (Wiener Index)}} == Description == Given a connected graph $G = (V, E)$ and a set $Q \subseteq V$ of query vertices, find a subgraph of $G$ that connects all query vertices and has minimum Wiener index. == Related Problems == Related: Undirected Wiener Index == Parameters == <pre>n: number of vertices m: number of edges q: number of query vertices</pre> == Table of Algorithms == Currently no algorithms in our...")
- 11:25, 15 February 2023 Maximum Cut (hist | edit) [1,989 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Maximum Cut (Maximum Cut)}} == Description == Given a graph $G=(V, E)$ with edge weights $c_e > 0$ for all $e\in E$, find a cut $\delta(W)$ such that $c(\delta(W)):=\Sigma_{e\in \dela(W)} c_e$ is as large as possible. == Parameters == <pre>n: number of vertices m: number of edges</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !!...")
- 11:25, 15 February 2023 D-Neighborhood of a String (hist | edit) [978 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:d-Neighborhood of a String (d-Neighborhood of a String)}} == Description == Given a DNA string pattern and an integer $d$, find the collection of strings that are within a $d$-neighborhood of the given pattern. A $d$-neighborhood is the set of all $k$-mers whose Hamming distance from the pattern is at most $d$. == Parameters == <pre>n: length of string d: neighborhood distance threshold sigma: size of alphabet</pre> == Table of Algorithms == {| cla...")
- 11:25, 15 February 2023 SLAM Algorithms (hist | edit) [1,790 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:SLAM Algorithms (SLAM Algorithms)}} == Description == Simultaneous localization and mapping (SLAM) is the computational problem of constructing or updating a map of an unknown environment while simultaneously keeping track of an agent's location within it. == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !!...")
- 11:25, 15 February 2023 Occupancy Grid Mapping (hist | edit) [1,060 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Occupancy Grid Mapping (Occupancy Grid Mapping)}} == Description == Assuming a robot's pose is known, generate a occupancy grid mapping of the area. The occupancy grid is a multidimensional random field that maintains stochastic estimates of the occupancy state of the cells in a spatial lattice. To construct a sensor-derived map of the robot’s world, the cell state estimates are obtained by interpreting the incoming range readings using probabilistic s...")
- 11:25, 15 February 2023 Environment Mapping (hist | edit) [1,914 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Environment Mapping (Texture Mapping)}} == Description == Texture mapping means the mapping of a function onto a surface in 3D. The domain of the function can be one, two, or three dimensional, and it can be represented by either an array or a mathematical function. The source image (texture) is mapped onto a surface in 3D object space, which is then mapped to the destination image (screen) by the viewing projection. Texture space is labeled $(u, v)$, o...")
- 11:25, 15 February 2023 Rasterization (hist | edit) [908 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Rasterization (Rasterization)}} == Description == Raster-scan displays are most commonly driven by a frame buffer, a memory that stores the color value for every picture element on the screen and refreshes the display continuously. The process of generating these picture clement values from a geometric description of the image is known as rasterization. == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable sortable" s...")
- 11:25, 15 February 2023 POMDPs (hist | edit) [2,598 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:POMDPs (POMDPs)}} == Description == At (discrete) time step $t$, the environment is assumed to be in some state $X_t$. The agent then performs an action (control) $A_t$, whereupon the environment (stochastically) changes to a new state $X_{t+1}$. The agent doesn’t see the environment state, but instead receives an observation $Y_t$, which is some (stochastic) function of $X_t$. (If $Y_t = X_t$, the POMDP reduces to a fully observed MDP.) In addition, t...")
- 11:25, 15 February 2023 Clock Synchronization in Distributed Systems (hist | edit) [1,552 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Clock Synchronization in Distributed Systems (Clock Synchronization in Distributed Systems)}} == Description == The difference between the largest and the smallest clock values among all stations in a Mobile Ad Hoc Network (MANET) is called the maximum clock offset. The goal is to minimize the maximum clock offset. == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%"...")
- 11:25, 15 February 2023 Mesh Simplification (hist | edit) [4,955 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Mesh Simplification (Mesh Simplification)}} == Description == Given a surface mesh, accurately simplify it so that you may render the mesh accurately with less computing power. == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Reference |- | Coplanar facets merging - M.J. De Haemer and M.J. Zy...")
- 11:25, 15 February 2023 Image Segmentation (hist | edit) [3,924 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Image Segmentation (Image Segmentation)}} == Description == Image segmentation is the division of an image into different regions, each having certain properties. It is the first step of image analysis which aims at either a description of an image or a classification of the image if a class label is meaningful. An example of the former is the description of an office scene. An example of the latter is the classification of the image of a cancerous cell....")
- 11:25, 15 February 2023 Point-in-Polygon (hist | edit) [2,488 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Point-in-Polygon (Point-in-Polygon)}} == Description == With a given polygon $P$ and an arbitrary point $q$, determine whether point $q$ is enclosed by the edges of the polygon. == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Reference |- | Ray casting algorithm Shimrat; M (Point-in-Polygon...")
- 11:25, 15 February 2023 Specular Reflection (hist | edit) [1,646 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Specular Reflection (Texture Mapping)}} == Description == Texture mapping means the mapping of a function onto a surface in 3D. The domain of the function can be one, two, or three dimensional, and it can be represented by either an array or a mathematical function. The source image (texture) is mapped onto a surface in 3D object space, which is then mapped to the destination image (screen) by the viewing projection. Texture space is labeled $(u, v)$, o...")
- 11:25, 15 February 2023 Diffuse Reflection (hist | edit) [2,186 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Diffuse Reflection (Texture Mapping)}} == Description == Texture mapping means the mapping of a function onto a surface in 3D. The domain of the function can be one, two, or three dimensional, and it can be represented by either an array or a mathematical function. The source image (texture) is mapped onto a surface in 3D object space, which is then mapped to the destination image (screen) by the viewing projection. Texture space is labeled $(u, v)$, ob...")
- 11:25, 15 February 2023 Cyclic Peptide Sequencing Problem (hist | edit) [1,000 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Cyclic Peptide Sequencing Problem (Cyclic Peptide Sequencing Problem)}} == Description == Given an experimental $MS^3$ spectrum $S$, find a cyclic peptide $P$ maximizing the number of shared masses between $S$ and the theoretical spectrum of $P$. == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! R...")
- 11:25, 15 February 2023 Distributed Locking Algorithms (hist | edit) [1,654 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Distributed Locking Algorithms (Distributed Locking Algorithms)}} == Description == The purpose of a lock is to ensure that among several nodes that might try to do the same piece of work, only one actually does it (at least only one at a time). That work might be to write some data to a shared storage system, to perform some computation, to call some external API, or suchlike. At a high level, there are two reasons why you might want a lock in a distrib...")
- 11:25, 15 February 2023 Texture Synthesis (hist | edit) [2,195 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Texture Synthesis (Texture Synthesis)}} == Description == Given a texture sample, synthesize a new texture that, when perceived by a human observer, appears to be generated by the same underlying stochastic process. == Parameters == <pre>n: number of pixels</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Reference |- | tre...")
- 11:25, 15 February 2023 Image Compositing (hist | edit) [538 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Image Compositing (Image Compositing)}} == Description == Image compositing is the act of creating a single image from multiple images. == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Reference |- | Petro Vlahos Algorithm || 1985...")
- 11:25, 15 February 2023 InDegree Analysis (hist | edit) [1,166 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:InDegree Analysis (Link Analysis)}} == Description == A simple heuristic that can be viewed as the predecessor of all Link Analysis Ranking algorithms is to rank the pages according to their popularity (also referred to as visibility (Marchiori 1997)). The popularity of a page is measured by the number of pages that link to this page. We refer to this algorithm as the InDegree algorithm, since it ranks pages according to their in-degree in the graph $G$....")
- 11:25, 15 February 2023 All Maximal Non-Branching Paths in a Graph (hist | edit) [1,101 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:All Maximal Non-Branching Paths in a Graph (All Maximal Non-Branching Paths in a Graph)}} == Description == A node $v$ in a directed graph $G$ is called a 1-in-1-out node if its indegree and outdegree are both equal to 1, i.e., $in(v) = out(v) = 1$. We can rephrase the definition of a "maximal non-branching path" from the main text as a path whose internal nodes are 1-in-1-out nodes and whose initial and final nodes are not 1-in-1-out nodes. The proble...")
- 11:24, 15 February 2023 Weighted Set-Covering (hist | edit) [2,602 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Weighted Set-Covering (The Set-Covering Problem)}} == Description == The set-covering problem where each set $s\in S$ is assigned a weight and the goal is to find the minimum weight sub-collection of $S$ that covers the universe. == Related Problems == Subproblem: Unweighted Set-Covering == Parameters == <pre>n: number of elements in the universe m: number of sets in the collection d: size of the largest set in collection H(x): the xth Harmonic...")
- 11:24, 15 February 2023 Unweighted Set-Covering (hist | edit) [2,605 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Unweighted Set-Covering (The Set-Covering Problem)}} == Description == Given a universe $U$, i.e. a set of elements $\{1, 2, \ldots, n\}$, and a collection $S$ of $m$ sets whose union is the universe, identify the smallest sub-collection of $S$ whose union is the universe. == Related Problems == Generalizations: Weighted Set-Covering == Parameters == <pre>U: the universe of elements to be covered S: the collection of sets n: number of elements...")
- 11:24, 15 February 2023 Optimal Policies for MDPs (hist | edit) [1,352 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Optimal Policies for MDPs (Optimal Policies for MDPs)}} == Description == In an MDP, a policy is a choice of what action to choose at each state An Optimal Policy is a policy where you are always choosing the action that maximizes the “return”/”utility” of the current state. The problem here is to find such an optimal policy from a given MDP. == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable sortable" styl...")
- 11:24, 15 February 2023 Filtering Problem (Stochastic Processes) (hist | edit) [3,213 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Filtering Problem (Stochastic Processes) (Filtering Problem (Stochastic Processes))}} == Description == The filtering problem is to obtain the best linear estimate $\hat{z}_t$ of $z_t$ based on the past observations ($y_s | s\leq t)$. Abstractly, the solution to the problem of filtering corresponds to explicitly computing $\hat{z}_t = P_t^y(z_t)$ where $P_t^y$ is the projection operator onto the Hilbert space $H_t^y$. == Parameters == No parameters...")
- 11:24, 15 February 2023 Culling (hist | edit) [943 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Culling (Culling)}} == Description == Culling is the process of rejecting primitives or objects in their entireity before rendering in the case that they would not be shown in the view, reducing unnecessary computations. == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Reference |- | view fru...")
- 11:24, 15 February 2023 Blob Detection (hist | edit) [2,861 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Blob Detection (Feature Detection)}} == Description == The regions or points which have noticeable difference with their surroundings is called blob. Blob detection is the problem of detecting such blobs in a given image. == Related Problems == Related: Corner Detection == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! App...")
- 11:24, 15 February 2023 Corner Detection (hist | edit) [4,189 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Corner Detection (Feature Detection)}} == Description == Conventionally, a corner is defined as the intersection point or the junction point between two or more straight line edges (i.e. edges which have discontinuities along a straight line). Corner detection is the problem of detecting such corners in a given image. == Related Problems == Related: Blob Detection == Parameters == No parameters found. == Table of Algorithms == {| class="wiki...")
- 11:24, 15 February 2023 Matrix Factorization (hist | edit) [1,316 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Matrix Factorization (Collaborative Filtering)}} == Description == Collaborative filtering is a technique used in recommendation systems. It analyzes relationships between users and interdependencies among products to identify new user-item associations. A method of collaborative filtering uses matrix factorization. In its basic form, matrix factorization characterizes both items and users by vectors of factors inferred from item rating patterns. == Pa...")
- 11:24, 15 February 2023 Maximum Likelihood Methods in Unknown Latent Variables (hist | edit) [3,607 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Maximum Likelihood Methods in Unknown Latent Variables (Maximum Likelihood Methods in Unknown Latent Variables)}} == Description == In this problem, the goal is to compute maximum-likelihood estimates when the observations can be viewed as incomplete data. == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !!...")
- 11:24, 15 February 2023 Mesh Parameterization (hist | edit) [5,660 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Mesh Parameterization (Mesh Parameterization)}} == Description == Given any two surfaces with similar topology it is possible to compute a one-to-one and onto mapping between them. If one of these surfaces is represented by a triangular mesh, the problem of computing such a mapping is referred to as mesh parameterization. == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width=...")
- 11:24, 15 February 2023 Hyperbolic Spline Interpolation (hist | edit) [2,566 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Hyperbolic Spline Interpolation (Hyperbolic Spline Interpolation)}} == Description == The problem of restoring complex curves and surfaces from discrete data so that their shape is preserved is called isogeometric interpolation. A very popular tool for solving this problem are hyperbolic splines in tension, which were introduced in 1966 by Schweikert. These splines have smoothness sufficient for many applications; combined with algorithms for the automat...")
- 11:24, 15 February 2023 DAG Realization Problem (hist | edit) [1,159 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:DAG Realization Problem (Graph Realization Problems)}} == Description == Given a sequence $S := (a_1, b_1), \ldots, (a_n, b_n)$ with $a_i, b_i \in \mathbb{Z}_0^+$, does there exist a directed acyclic graph (DAG) (no parallel arcs allowed) with labeled vertex set $V := \{v_1, \ldots , v_n\}$ such that for all $v_i \in V$ indegree and outdegree of $v_i$ match exactly the given numbers $a_i$ and $b_i$, respectively? == Related Problems == Generalizations...")
- 11:24, 15 February 2023 Digraph Realization Problem (hist | edit) [1,531 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Digraph Realization Problem (Graph Realization Problems)}} == Description == Given a sequence $S := (a_1, b_1), \ldots, (a_n, b_n)$ with $a_i, b_i \in \mathbb{Z}_0^+$, does there exist a directed graph (no parallel arcs allowed) with labeled vertex set $V := \{v_1, \ldots , v_n\}$ such that for all $v_i \in V$ indegree and outdegree of $v_i$ match exactly the given numbers $a_i$ and $b_i$, respectively? == Related Problems == Subproblem: DAG Realiza...")
- 11:24, 15 February 2023 Subtree Isomorphism (hist | edit) [1,788 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Subtree Isomorphism (Graph Isomorphism Problem)}} == Description == Determine whether a given tree is contained within another tree. == Related Problems == Generalizations: Largest Common Subtree Related: Graph Isomorphism, General Graphs, Graph Isomorphism, Bounded Number of Vertices of Each Color, Graph Isomorphism, Trivalent Graphs, Graph Isomorphism, Bounded Vertex Valences == Parameters == <pre>n: number of vertices in the...")
- 11:24, 15 February 2023 Largest Common Subtree (hist | edit) [1,845 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Largest Common Subtree (Graph Isomorphism Problem)}} == Description == Find a largest tree which occurs as a common subgraph in a given collection of trees. == Related Problems == Generalizations: Graph Isomorphism, General Graphs Subproblem: Subtree Isomorphism Related: Graph Isomorphism, Bounded Number of Vertices of Each Color, Graph Isomorphism, Trivalent Graphs, Graph Isomorphism, Bounded Vertex Valences == Parameters ==...")
- 11:24, 15 February 2023 Graph Isomorphism, Bounded Vertex Valences (hist | edit) [1,580 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Graph Isomorphism, Bounded Vertex Valences (Graph Isomorphism Problem)}} == Description == Given two graphs with the degree of each vertex bounded, determine whether they are isomorphic to one another. == Related Problems == Generalizations: Graph Isomorphism, General Graphs Related: Graph Isomorphism, Bounded Number of Vertices of Each Color, Graph Isomorphism, Trivalent Graphs, Largest Common Subtree, Subtree Isomorphism == Par...")
- 11:24, 15 February 2023 Graph Isomorphism, Trivalent Graphs (hist | edit) [1,323 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Graph Isomorphism, Trivalent Graphs (Graph Isomorphism Problem)}} == Description == Given two trivalent graphs (AKA cubic graphs--graphs in which each vertex has degree 3), determine whether they are isomorphic to one another. == Related Problems == Generalizations: Graph Isomorphism, General Graphs Related: Graph Isomorphism, Bounded Number of Vertices of Each Color, Graph Isomorphism, Bounded Vertex Valences, Largest Common Subtree,...")
- 11:24, 15 February 2023 Graph Isomorphism, Bounded Number of Vertices of Each Color (hist | edit) [1,706 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Graph Isomorphism, Bounded Number of Vertices of Each Color (Graph Isomorphism Problem)}} == Description == Given two colored graphs with the number of vertices of each color bounded, determine whether they are isomorphic to one another. == Related Problems == Generalizations: Graph Isomorphism, General Graphs Related: Graph Isomorphism, Trivalent Graphs, Graph Isomorphism, Bounded Vertex Valences, Largest Common Subtree, Subtree Is...")
- 11:24, 15 February 2023 Graph Isomorphism, General Graphs (hist | edit) [1,715 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Graph Isomorphism, General Graphs (Graph Isomorphism Problem)}} == Description == Given two graphs, determine whether they are isomorphic to one another. == Related Problems == Subproblem: Graph Isomorphism, Bounded Number of Vertices of Each Color, Graph Isomorphism, Trivalent Graphs, Graph Isomorphism, Bounded Vertex Valences, Largest Common Subtree Related: Graph Isomorphism, Trivalent Graphs, Graph Isomorphism, Bounded Ve...")
- 11:24, 15 February 2023 Arithmetic Expression Binary Tree (hist | edit) [866 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Arithmetic Expression Binary Tree (AST to Code Translation)}} == Description == Translate a given arithmetic expression binary tree into machine-readable code that uses as few registers as possible. == Related Problems == Related: AST to Code Translation == Parameters == <pre>$n$: number of nodes in the tree</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space...")
- 11:23, 15 February 2023 AST to Code Translation (hist | edit) [498 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:AST to Code Translation (AST to Code Translation)}} == Description == Translate a given abstract syntax tree (AST) into machine-readable code that uses as few registers as possible. == Related Problems == Related: Arithmetic Expression Binary Tree == Parameters == <pre>$n$: number of nodes in the tree</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem. == Time Complexity graph == File:AST to Co...")
- 11:23, 15 February 2023 Longest Palindromic Substring (hist | edit) [1,621 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Longest Palindromic Substring (Longest Palindromic Substring)}} == Description == Given a string of length $n$, find the palindromic substrings of maximal length. == Parameters == <pre>n: length of given string</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Reference |- | Naive (Longest Palindromic Substring Longest Palin...")
- 11:23, 15 February 2023 Entity Resolution (hist | edit) [2,418 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Entity Resolution (Entity Resolution)}} == Description == Entity resolution (ER) is the problem of matching records that represent the same real-world entity and then merging the matching records. ER is a well known problem that arises in many applications. An exhaustive ER process involves comparing all the pairs of records, which can be very expensive for large datasets. == Parameters == No parameters found. == Table of Algorithms == {| class="wi...")
- 11:23, 15 February 2023 Ray Tracing (hist | edit) [1,257 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Ray Tracing (Ray Tracing)}} == Description == Ray tracing is an image rendering technique in which rays are cast from the viewpoint and followed as they reflect off of objects in the scene. == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Reference |- | Dürer rendering algorithm ( Ray Tracin...")
- 11:23, 15 February 2023 Constructing Suffix Trees (hist | edit) [3,185 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Constructing Suffix Trees (Constructing Suffix Trees)}} == Description == Let $T = t_1 t_2 \cdots t_n, be a string over an alphabet $\Sigma$. Each string $x$ such that $T = uxv$ for some (possibly empty) strings $u$ and $v$ is a substring of $T$, and each string $T_i = t_i \cdots t_n$, where $1 \leq i \leq n + 1$ is a suffix of $T$; in particular, $T_{n+1} = \epsilon$ is the empty suffix. The set of all suffixes of $T$ is denoted $\sigma(T)$. The suffix...")
- 11:23, 15 February 2023 Maximum Square Subarray (hist | edit) [931 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Maximum Square Subarray (Maximum Subarray Problem)}} == Description == Given an $n \times n$ matrix find a maximum subarray with sides of equal length. == Related Problems == Generalizations: Maximum Subarray Related: 1D Maximum Subarray, 2D Maximum Subarray == Parameters == <pre>n: dimension of array</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem. == Reductions FROM Problem == {| cl...")
- 11:23, 15 February 2023 2D Maximum Subarray (hist | edit) [1,454 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:2D Maximum Subarray (Maximum Subarray Problem)}} == Description == Given an $n \times n$ matrix $A$ of integers, find $i, j, k,l \in (n)$ with $i \leq j, k \leq l$ maximizing $\sum^j_{x=i}\sum^l_{y=k}A(x,y)$, that is, find a contiguous subarray of $A$ of maximum sum == Related Problems == Generalizations: Maximum Subarray Related: 1D Maximum Subarray, Maximum Square Subarray == Parameters == <pre>n: dimension of array</pre> == Table o...")
- 11:23, 15 February 2023 1D Maximum Subarray (hist | edit) [2,453 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:1D Maximum Subarray (Maximum Subarray Problem)}} == Description == Given an array $A$ of length $n$, find $i, j$ with $1\leq i \leq j \leq n$ maximizing $\sum^j_{x=i} A(x)$, that is, find a contiguous subarray of $A$ of maximum sum == Related Problems == Generalizations: Maximum Subarray Related: 2D Maximum Subarray, Maximum Square Subarray == Parameters == <pre>n: length of array</pre> == Table of Algorithms == {| class="wikitable...")
- 11:23, 15 February 2023 Maximum Subarray (hist | edit) [3,820 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Maximum Subarray (Maximum Subarray Problem)}} == Description == Given a $d$-dimensional array $M$ with $n^d$ real-valued entries, find the $d$-dimensional subarray of $M$ which maximizes the sum of the elements it contains. == Related Problems == Subproblem: 1D Maximum Subarray, 2D Maximum Subarray, Maximum Square Subarray Related: 2D Maximum Subarray, Maximum Square Subarray == Parameters == <pre>n: length of array d: dimens...")
- 11:23, 15 February 2023 Longest Path on Interval Graphs (hist | edit) [1,175 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Longest Path on Interval Graphs (Longest Path Problem)}} == Description == The longest path problem is the problem of finding a path of maximum length in a graph. A graph $G$ is called interval graph if its vertices can be put in a one-to-one correspondence with a family $F$ of intervals on the real line such that two vertices are adjacent in $G$ if and only if the corresponding intervals intersect; $F$ is called an intersection model for $G$. == Param...")
- 11:23, 15 February 2023 Stable Pair Checking (hist | edit) [2,059 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Stable Pair Checking (Stable Matching Problem)}} == Description == Verify that a given pairing is stable, given the preferences == Related Problems == Generalizations: Stable Marriage Problem Related: Almost Stable Marriage Problem, Stable Roommates Problem, Boolean d-Attribute Stable Matching, Stable Matching Verification == Parameters == No parameters found. == Table of Algorithms == Currently no algorithms in our database...")
- 11:23, 15 February 2023 Stable Matching Verification (hist | edit) [1,096 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Stable Matching Verification (Stable Matching Problem)}} == Description == Verify that a given matching is stable, given the preferences == Related Problems == Generalizations: Stable Marriage Problem Related: Almost Stable Marriage Problem, Stable Roommates Problem, Boolean d-Attribute Stable Matching, Stable Pair Checking == Parameters == No parameters found. == Table of Algorithms == Currently no algorithms in our databas...")
- 11:23, 15 February 2023 Boolean d-Attribute Stable Matching (hist | edit) [1,582 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Boolean d-Attribute Stable Matching (Stable Matching Problem)}} == Description == SMP in the d-attribute model. In the d-attribute model, we assume that there are d different attributes (e.g. income, height, sense of humor, etc.) with a fixed, possibly objective, ranking of the men for each attribute. Each woman’s preference list is based on a linear combination of the attributes of the men, where each woman can have different weights for each attribut...")
- 11:23, 15 February 2023 Stable Roommates Problem (hist | edit) [1,504 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Stable Roommates Problem (Stable Matching Problem)}} == Description == Given $2n$ participants, each of participant ranks the others in strict order of preference. A matching is a set of $n$ disjoint pairs of participants. A matching $M$ in an instance of SRP is stable if there are no two participants $x$ and $y$, each of whom prefers the other to their partner in $M$. Such a pair is said to block $M$, or to be a blocking pair with respect to $M$. == Re...")
- 11:23, 15 February 2023 Almost Stable Marriage Problem (hist | edit) [971 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Almost Stable Marriage Problem (Stable Matching Problem)}} == Description == The task in the Almost Stable Marriage Problem is to find a matching that minimises the number of unstable edges, but the matching does not have to be a maximum matching. == Related Problems == Generalizations: Stable Marriage Problem Related: Stable Roommates Problem, Boolean d-Attribute Stable Matching, Stable Matching Verification, Stable Pair Checking...")
- 11:23, 15 February 2023 Stable Marriage Problem (hist | edit) [3,036 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Stable Marriage Problem (Stable Matching Problem)}} == Description == Given $n$ men and $n$ women, where each person has ranked all members of the opposite sex in order of preference, marry the men and women together such that there are no two people of opposite sex who would both rather have each other than their current partners. When there are no such pairs of people, the set of marriages is deemed stable. == Related Problems == Generalizations: ...")
- 11:23, 15 February 2023 Factorization of Polynomials Over Finite Fields (hist | edit) [864 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Factorization of Polynomials Over Finite Fields (Factorization of Polynomials Over Finite Fields)}} == Description == Factor a given polynomial over a finite field into a product of irreducible polynomials. == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Reference |- | Schubert's algorithm (...")
- 11:23, 15 February 2023 Lossless Compression (hist | edit) [591 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Lossless Compression (Data Compression)}} == Description == The reduction or ideally elimination of redundancies in the original data to result in smaller required storage space is the goal of every compression scheme. There are two categories of data compression: lossy and lossless. Lossless compression is fully information-preserving and fully reversible. == Related Problems == Related: Lossy Compression == Parameters == No parameters found....")
- 11:23, 15 February 2023 Lossy Compression (hist | edit) [3,479 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Lossy Compression (Data Compression)}} == Description == The reduction or ideally elimination of redundancies in the original data to result in smaller required storage space is the goal of every compression scheme. There are two categories of data compression: lossy and lossless. Lossy compression is achieved by only discarding the redundancies and out of human perception information and getting rid of those extra bits. == Related Problems == Relat...")
- 11:23, 15 February 2023 Finding Frequent Itemsets (hist | edit) [1,631 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Finding Frequent Itemsets (Finding Frequent Itemsets)}} == Description == We assume there is a number $s$, called the support threshold. If $I$ is a set of items, the support for $I$ is the number of baskets for which $I$ is a subset. We say $I$ is frequent if its support is $s$ or more == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Sp...")
- 11:23, 15 February 2023 CFG Recognition (hist | edit) [1,934 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:CFG Recognition (CFG Problems)}} == Description == Given a grammar $G$ and a string $s$, determine if the string $s$ can be derived by the grammar $G$. == Related Problems == Related: CFG Parsing == Parameters == <pre>n: length of the given string</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Reference |- | Cocke...")
- 11:23, 15 February 2023 CFG Parsing (hist | edit) [2,174 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:CFG Parsing (CFG Problems)}} == Description == Given a grammar $G$ and a string $s$, find the parse structure, or analysis, assigned to the string $s$ by the grammar $G$. == Related Problems == Related: CFG Recognition == Parameters == <pre>n: length of the given string</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Re...")
- 11:23, 15 February 2023 The Vertex Cover Problem, Degrees Bounded By 3 (hist | edit) [1,254 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:The Vertex Cover Problem, Degrees Bounded By 3 (The Vertex Cover Problem)}} == Description == A vertex cover of a graph $G$ is a set $C$ of vertices such that every edge of $G$ has at least one endpoint in $C$. The vertex cover problem is to find a minimum-size vertex cover in a given graph $G$. This version of the problem is such that the input graph $G$ has all vertices' degree bounded by 3. == Related Problems == Generalizations: The Vertex Cover...")
- 11:23, 15 February 2023 The Vertex Cover Problem (hist | edit) [5,138 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:The Vertex Cover Problem (The Vertex Cover Problem)}} == Description == A vertex cover of a graph $G$ is a set $C$ of vertices such that every edge of $G$ has at least one endpoint in $C$. The vertex cover problem is to find a minimum-size vertex cover in a given graph $G$. == Related Problems == Subproblem: The Vertex Cover Problem, Degrees Bounded By 3 == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable sort...")
- 11:23, 15 February 2023 4NF Decomposition for Conflict-Free Dependency Sets (hist | edit) [2,820 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:4NF Decomposition for Conflict-Free Dependency Sets (4NF Decomposition)}} == Description == 4NF Decomposition is the problem of decomposing a relation schema into fourth normal form (4NF). This variation specifies that the input dependency set is conflict-free. A relation schema $R^*$ is in fourth normal form (4NF) if, whenever a nontrivial multivalued dependency $X \rightarrow \rightarrow Y$ holds for $R^*$, then so does the functiunal dependency $X \r...")
- 11:23, 15 February 2023 4NF Decomposition for Functional and Multivalued Dependency Sets (hist | edit) [3,069 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:4NF Decomposition for Functional and Multivalued Dependency Sets (4NF Decomposition)}} == Description == 4NF Decomposition is the problem of decomposing a relation schema into fourth normal form (4NF). This variation specifies that the input dependency set has only functional and multivalued dependencies. A relation schema $R^*$ is in fourth normal form (4NF) if, whenever a nontrivial multivalued dependency $X \rightarrow \rightarrow Y$ holds for $R^*$,...")
- 11:23, 15 February 2023 4NF Decomposition (hist | edit) [3,239 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:4NF Decomposition (4NF Decomposition)}} == Description == 4NF Decomposition is the problem of decomposing a relation schema into fourth normal form (4NF). A relation schema $R^*$ is in fourth normal form (4NF) if, whenever a nontrivial multivalued dependency $X \rightarrow \rightarrow Y$ holds for $R^*$, then so does the functiunal dependency $X \rightarrow A$ for every column name $A$ of $R^*$. Intuitively all dependencies are the result of keys. In pa...")
- 11:23, 15 February 2023 Decisional BCNF (hist | edit) [1,227 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Decisional BCNF (BCNF Decomposition)}} == Description == Decisional BCNF is the problem of deciding whether or not a relation schema can be turned into Boyce-Codd normal form (BCNF). A relation schema $R$ is in Boyce Codd Normal Form (abbr. BCNF) if for all non-trivial FDs $X \rightarrow Y$ in $F^+$, $X$ is a superkey. In extending this notion to database schemas, we must be conscious of the UR-assumption. We say that $R_i = <ATTR_i,F_i>$ is in BCNF if...")
- 11:22, 15 February 2023 Multivalued Dependency Inference Problem (hist | edit) [2,220 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Multivalued Dependency Inference Problem (Dependency Inference Problem)}} == Description == The multivalued dependency inference problem is to find a cover for the set of multivalued dependencies that hold in a given relation. A multivalued dependency (abbr. MVD), $g$, on a set of attributes $U$ is a statement $g: X \rightarrow \rightarrow Y$, where $X$ and $Y$ are subsets of $U$. Let $Z$ be the complement of the union of $X$ and $Y$ in $U$. A relation...")
- 11:22, 15 February 2023 Functional Dependency Inference Problem (hist | edit) [2,051 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Functional Dependency Inference Problem (Dependency Inference Problem)}} == Description == The functional dependency inference problem is to find a cover for the set of functional dependencies that hold in a given relation. A functional dependency (abbr. FD), $f$, is a statement $f: X \rightarrow Y$ where $X$ and $Y$ are sets of attributes. If $R(X, Y, \ldots)$ is a relation on a set of attributes that contains $X$ and $Y$, then $R$ obeys the FD $f$ if...")
- 11:22, 15 February 2023 Subset Sum (hist | edit) [4,859 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Subset Sum (The Subset-Sum Problem)}} == Description == Given a set $S$ of integers and a target sum $t$, determine whether there is a subset of $S$ that sum to $t$. == Parameters == <pre>S: the set of integers n: the number of integers in the set n': the number of distinct elements in the set t: the target sum σ: sum of elements in the set</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Na...")
- 11:22, 15 February 2023 De Novo Genome Assembly (hist | edit) [2,036 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:De Novo Genome Assembly (De Novo Genome Assembly)}} == Description == De novo sequencing refers to sequencing a novel genome where there is no reference sequence available for alignment. Sequence reads are assembled as contigs, and the coverage quality of de novo sequence data depends on the size and continuity of the contigs (ie, the number of gaps in the data). == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable so...")
- 11:22, 15 February 2023 Delaunay Triangulation (hist | edit) [3,906 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Delaunay Triangulation (Delaunay Triangulation)}} == Description == Given a set of points, the Delaunay Triangulation problem is to triangulate the points using the following notion of triangulation. $AB$ is an edge of the Delaunay triangulation iff there is a circle passing through $A$ and $B$ so that all other points in the point set, $C$, where $C$ is not equal to $A$ or $B$, lie outside the circle. Equivalently, all triangles in the Delaunay triangu...")
- 11:22, 15 February 2023 3-Dimensional Poisson Problem (hist | edit) [2,865 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:3-Dimensional Poisson Problem (Poisson Problem)}} == Description == Given $f$, solve for $u$ in the 3-dimensional Poisson equation: $u_{xx} + u_{yy} + u_{zz} = f(x,y,z)$ == Related Problems == Related: 2-Dimensional Poisson Problem == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Referenc...")
- 11:22, 15 February 2023 2-Dimensional Poisson Problem (hist | edit) [2,854 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:2-Dimensional Poisson Problem (Poisson Problem)}} == Description == Given $f$, solve for $u$ in the 2-dimensional Poisson equation: $u_{xx} + u_{yy} = f(x,y)$ == Related Problems == Related: 3-Dimensional Poisson Problem == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Reference |- | ...")
- 11:22, 15 February 2023 Approximate TSP (hist | edit) [2,382 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Approximate TSP (The Traveling-Salesman Problem)}} == Description == Approximate TSP is the problem of finding an approximate answer to Minimum TSP. In Minimum TSP, you are given a set $C$ of cities and distances between each distinct pair of cities. The goal is to find an ordering or tour of the cities, such that you visit each city exactly once and return to the origin city, that minimizes the length of the tour. This is the typical variation of TSP....")
- 11:22, 15 February 2023 Maximum TSP (hist | edit) [1,562 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Maximum TSP (The Traveling-Salesman Problem)}} == Description == In Maximum TSP, you are given a set $C$ of cities and distances between each distinct pair of cities. The goal is to find an ordering or tour of the cities, such that you visit each city exactly once and return to the origin city, that maximizes the length of the tour. == Related Problems == Related: Minimum TSP, Approximate TSP == Parameters == <pre>V: number of cities (nodes...")
- 11:22, 15 February 2023 Minimum TSP (hist | edit) [2,636 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Minimum TSP (The Traveling-Salesman Problem)}} == Description == In Minimum TSP, you are given a set $C$ of cities and distances between each distinct pair of cities. The goal is to find an ordering or tour of the cities, such that you visit each city exactly once and return to the origin city, that minimizes the length of the tour. This is the typical variation of TSP. == Related Problems == Related: Maximum TSP, Approximate TSP == Parameter...")
- 11:22, 15 February 2023 Max-Weight k-Clique (hist | edit) [1,360 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Max-Weight k-Clique (Clique Problems)}} == Description == Given a graph $G = (V, E)$, find the $k$-clique of maximum weight. == Related Problems == Generalizations: k-Clique Related: Enumerating Maximal Cliques, arbitrary graph, Exact k-Clique, Min-Weight k-Clique == Parameters == <pre>n: number of vertices k: size of clique</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem. == Reduct...")
- 11:22, 15 February 2023 Min-Weight k-Clique (hist | edit) [1,119 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Min-Weight k-Clique (Clique Problems)}} == Description == Given a graph $G = (V, E)$, find the $k$-clique of minimum weight. == Related Problems == Generalizations: k-Clique Related: Enumerating Maximal Cliques, arbitrary graph, Exact k-Clique, Max-Weight k-Clique == Parameters == <pre>n: number of vertices k: size of clique</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem. == Reduct...")
- 11:22, 15 February 2023 Exact k-Clique (hist | edit) [472 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Exact k-Clique (Clique Problems)}} == Description == Given a graph $G = (V, E)$, find a $k$-clique of weight 0. == Related Problems == Generalizations: k-Clique Related: Enumerating Maximal Cliques, arbitrary graph, Min-Weight k-Clique, Max-Weight k-Clique == Parameters == <pre>n: number of vertices k: size of clique</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem.")
- 11:22, 15 February 2023 K-Clique (hist | edit) [2,236 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:k-Clique (Clique Problems)}} == Description == For a constant $k \geq 3$, the $k$-Clique problem is as follows: given a graph $G = (V, E)$ on $n$ vertices, does $G$ contain $k$ distinct vertices $a_1, \ldots, a_k$ so that for every $(i, j)$, $i \neq j$, $(a_i, a_j ) \in E$? Such a $k$ node graph is called a $k$-clique. == Related Problems == Subproblem: Exact k-Clique, Min-Weight k-Clique, Max-Weight k-Clique Related: Enumerating Maxi...")
- 11:22, 15 February 2023 Enumerating Maximal Cliques, arbitrary graph (hist | edit) [3,728 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Enumerating Maximal Cliques, arbitrary graph (Clique Problems)}} == Description == A maximal clique (complete subgraph) is a clique that is not contained in any other clique. The goal here is to enumerate such maximal cliques in a given graph. == Related Problems == Related: k-Clique, Exact k-Clique, Min-Weight k-Clique, Max-Weight k-Clique == Parameters == <pre>n: number of vertices m: number of edges</pre> == Table of Algorithms...")
- 11:22, 15 February 2023 Inexact GED (hist | edit) [2,584 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Inexact GED (Graph Edit Distance Computation)}} == Description == The GED of two graphs is defined as the minimum cost of an edit path between them, where an edit path is a sequence of edit operations (inserting, deleting, and relabeling vertices or edges) that transforms one graph into another. Inexact GED computes an answer that is not gauranteed to be the exact GED. == Related Problems == Related: Exact GED == Parameters == <pre>V: number of...")
- 11:22, 15 February 2023 Exact GED (hist | edit) [1,601 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Exact GED (Graph Edit Distance Computation)}} == Description == The GED of two graphs is defined as the minimum cost of an edit path between them, where an edit path is a sequence of edit operations (inserting, deleting, and relabeling vertices or edges) that transforms one graph into another. Exact GED computes the GED exactly. == Related Problems == Related: Inexact GED == Parameters == <pre>V: number of vertices in the larger of the two grap...")
- 11:22, 15 February 2023 Lowest Common Ancestors with Linking and Cutting (hist | edit) [1,258 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Lowest Common Ancestors with Linking and Cutting (Lowest Common Ancestor)}} == Description == Given a collection of rooted trees, answer queries of the form, "What is the nearest common ancestor of vertices $x$ and $y$?" In this version of the problem, the queries are on-line. Interspersed with the queries are on-line commands of two types: $link(x, y)$, where $y$ but not necessarily $x$ is a tree root, and $cut (x)$, where $x$ is not a root. The effect...")
- 11:22, 15 February 2023 Lowest Common Ancestor with Linking (hist | edit) [2,841 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Lowest Common Ancestor with Linking (Lowest Common Ancestor)}} == Description == Given a collection of rooted trees, answer queries of the form, "What is the nearest common ancestor of vertices $x$ and $y$?" In this version of the problem, the queries are on-line. Interspersed with the queries are on-line commands $link(x, y)$ such that $y$, but not necessarily $x$, is a tree root. The effect of a command $link(x, y)$ is to combine the trees containing $...")
- 11:22, 15 February 2023 Lowest Common Ancestor with Linking Roots (hist | edit) [1,815 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Lowest Common Ancestor with Linking Roots (Lowest Common Ancestor)}} == Description == Given a collection of rooted trees, answer queries of the form, "What is the nearest common ancestor of vertices $x$ and $y$?" In this version of the problem, The queries are given on-line. Interspersed with the queries are on-line commands of the form $link(x, y)$ where $x$ and $y$ are tree roots. The effect of a command $link(x, y)$ is to combine the trees containing...")
- 11:22, 15 February 2023 Lowest Common Ancestor with Static Trees (hist | edit) [3,979 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Lowest Common Ancestor with Static Trees (Lowest Common Ancestor)}} == Description == Given a collection of rooted trees, answer queries of the form, "What is the nearest common ancestor of vertices $x$ and $y$?" In this version of the problem, the collection of trees is static but the queries are given on-line. That is, each query must be answered before the next one is known. == Related Problems == Generalizations: Lowest Common Ancestor Relate...")
- 11:22, 15 February 2023 Off-Line Lowest Common Ancestor (hist | edit) [1,783 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Off-Line Lowest Common Ancestor (Lowest Common Ancestor)}} == Description == Given a collection of rooted trees, answer queries of the form, "What is the nearest common ancestor of vertices $x$ and $y$?" In this version of the problem, the collection of trees is static and the entire sequence of queries is specified in advance. == Related Problems == Generalizations: Lowest Common Ancestor Related: Lowest Common Ancestor with Static Trees, ...")
- 11:22, 15 February 2023 Lowest Common Ancestor (hist | edit) [6,468 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Lowest Common Ancestor (Lowest Common Ancestor)}} == Description == Given a collection of rooted trees, answer queries of the form, "What is the nearest common ancestor of vertices $x$ and $y$?" == Related Problems == Subproblem: Off-Line Lowest Common Ancestor, Lowest Common Ancestor with Static Trees, Lowest Common Ancestor with Linking Roots, Lowest Common Ancestor with Linking, Lowest Common Ancestors with Linking and Cutting...")
- 11:22, 15 February 2023 Cyclic Nontrivial SCCs DFA Minimization (hist | edit) [1,030 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Cyclic Nontrivial SCCs DFA Minimization (DFA Minimization)}} == Description == Given an finite deterministic automaton (DFA) from a class $C$ of DFAs, whose nontrivial SCCs are cyclic, determine its minimal automaton given by the equivalence relation on states. == Related Problems == Generalizations: DFA Minimization Related: Acyclic DFA Minimization == Parameters == <pre>$n$: number of states $d$: number of transitions $k$: size of alphab...")
- 11:22, 15 February 2023 Acyclic DFA Minimization (hist | edit) [1,043 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Acyclic DFA Minimization (DFA Minimization)}} == Description == Given an acyclic finite deterministic automaton (DFA) from a class $C$ of DFAs, determine its minimal automaton given by the equivalence relation on states. == Related Problems == Generalizations: DFA Minimization Related: Cyclic Nontrivial SCCs DFA Minimization == Parameters == <pre>$n$: number of states $d$: number of transitions $k$: size of alphabet</pre> == Table of Algo...")
- 11:22, 15 February 2023 Variance Calculations (hist | edit) [1,510 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Variance Calculations (Variance Calculations)}} == Description == Given a set of n (real/integer) numbers, compute the variance (sample or population). Of interest is streaming algorithms and numerical stability. == Parameters == <pre>n: number of values</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Reference |- | Naïve...")
- 11:22, 15 February 2023 Voronoi Diagrams (hist | edit) [1,237 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Voronoi Diagrams (Voronoi Diagrams)}} == Description == Given a set of n points in 2-dimensional space, compute the Voronoi diagram with the n points as seeds. == Parameters == <pre>n: number of points</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Reference |- | Fortune's algorithm (Voronoi Diagrams Voronoi Diagrams)|For...")
- 11:22, 15 February 2023 Global Register Allocation (hist | edit) [2,685 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Global Register Allocation (Register Allocation)}} == Description == Register allocation is the process of mapping the unlimited number of symbolic registers assumed in the intermediate language into the limited real machine registers. Global register allocation deals with the allocation of registers in code containing branches (http://www.cs.ucr.edu/~gupta/research/Publications/Comp/p370-gupta.pdf). == Related Problems == Related: Local Register A...")
- 11:22, 15 February 2023 Local Register Allocation (hist | edit) [1,011 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Local Register Allocation (Register Allocation)}} == Description == Register allocation is the process of mapping the unlimited number of symbolic registers assumed in the intermediate language into the limited real machine registers. Local register allocation deals with the allocation of registers in straight-line code segments (http://www.cs.ucr.edu/~gupta/research/Publications/Comp/p370-gupta.pdf). == Related Problems == Related: Global Register...")
- 11:22, 15 February 2023 Cardinality Estimation (hist | edit) [1,750 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Cardinality Estimation (Cardinality Estimation)}} == Description == Given a multiset of (possibly hashed) values, estimate the number of distinct elements of the multiset. Of interest is minimizing storage usage. == Parameters == <pre>N: number of values in multiset n: cardinality of multiset (not known)</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approxi...")
- 11:21, 15 February 2023 Maximum Likelihood Parameters (hist | edit) [1,986 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Maximum Likelihood Parameters (Maximum Likelihood Parameters)}} == Description == In these algorithms, the goal is to estimate hyperparameters using maximum likelihood. == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Reference |- | Expectation–maximization (EM) algorithm ( Maximum Likeliho...")
- 11:21, 15 February 2023 K Approximate Nearest Neighbors Search (hist | edit) [513 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:k Approximate Nearest Neighbors Search (Nearest Neighbor Search)}} == Description == Within a dataset of $n$ points, find approximately the $k$ closest points to a specified point. == Related Problems == Generalizations: k Nearest Neighbors Search == Parameters == <pre>n: number of points in dataset k: number of neighbors to find</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem.")
- 11:21, 15 February 2023 K Nearest Neighbors Search (hist | edit) [491 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:k Nearest Neighbors Search (Nearest Neighbor Search)}} == Description == Within a dataset of $n$ points, find the $k$ closest points to a specified point. == Related Problems == Subproblem: k Approximate Nearest Neighbors Search == Parameters == <pre>n: number of points in dataset k: number of neighbors to find</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem.")
- 11:21, 15 February 2023 Root Computation (hist | edit) [3,105 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Root Computation (Root Computation)}} == Description == Given a real continuous function, compute one of the roots. == Parameters == No parameters found. == Table of Algorithms == Currently no algorithms in our database for the given problem.")
- 11:21, 15 February 2023 Eigenpair closest to mu (hist | edit) [1,834 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Eigenpair closest to mu (Eigenvalues (Iterative Methods))}} == Description == Given an $n \times n$ matrix $A$, find the eigenpair (eigenvalue and associated eigenvector) of $A$ with the eigenvalue closest to $\mu$. == Related Problems == Generalizations: Any Eigenpair Related: All Eigenvalues, Any Eigenvalue, All Eigenpairs, Eigenpair with the Largest Eigenvalue == Parameters == No parameters found. == Table of Algorithms ==...")
- 11:21, 15 February 2023 Eigenpair with the Largest Eigenvalue (hist | edit) [1,114 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Eigenpair with the Largest Eigenvalue (Eigenvalues (Iterative Methods))}} == Description == Given an $n \times n$ matrix $A$, find the eigenpair (eigenvalue and associated eigenvector) of $A$ with the largest eigenvalue. == Related Problems == Generalizations: Any Eigenpair Related: All Eigenvalues, Any Eigenvalue, All Eigenpairs, Eigenpair closest to mu == Parameters == No parameters found. == Table of Algorithms == {| clas...")
- 11:21, 15 February 2023 Any Eigenpair (hist | edit) [596 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Any Eigenpair (Eigenvalues (Iterative Methods))}} == Description == Given an $n \times n$ matrix $A$, find any eigenpair (eigenvalue and associated eigenvector) of $A$. == Related Problems == Subproblem: Any Eigenvalue, All Eigenpairs, Eigenpair with the Largest Eigenvalue, Eigenpair closest to mu Related: All Eigenvalues, All Eigenpairs, Eigenpair with the Largest Eigenvalue, Eigenpair closest to mu == Parameters...")
- 11:21, 15 February 2023 All Eigenpairs (hist | edit) [509 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:All Eigenpairs (Eigenvalues (Iterative Methods))}} == Description == Given an $n \times n$ matrix $A$, find all eigenpairs (eigenvalues and associated eigenvectors) of $A$. == Related Problems == Generalizations: Any Eigenpair Related: All Eigenvalues, Any Eigenvalue, Eigenpair with the Largest Eigenvalue, Eigenpair closest to mu == Parameters == No parameters found. == Table of Algorithms == Currently no algorithms in our d...")
- 11:21, 15 February 2023 Any Eigenvalue (hist | edit) [479 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Any Eigenvalue (Eigenvalues (Iterative Methods))}} == Description == Given an $n \times n$ matrix $A$, find any eigenvalue of $A$. == Related Problems == Generalizations: Any Eigenpair Subproblem: All Eigenvalues Related: All Eigenpairs, Eigenpair with the Largest Eigenvalue, Eigenpair closest to mu == Parameters == No parameters found. == Table of Algorithms == Currently no algorithms in our database for the given problem.")
- 11:21, 15 February 2023 All Eigenvalues (hist | edit) [468 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:All Eigenvalues (Eigenvalues (Iterative Methods))}} == Description == Given an $n \times n$ matrix $A$, find all eigenvalues of $A$. == Related Problems == Generalizations: Any Eigenvalue Related: All Eigenpairs, Any Eigenpair, Eigenpair with the Largest Eigenvalue, Eigenpair closest to mu == Parameters == No parameters found. == Table of Algorithms == Currently no algorithms in our database for the given problem.")
- 11:21, 15 February 2023 Line Simplification (hist | edit) [1,586 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Line Simplification (Line Simplification)}} == Description == Line simplification is the process of taking a line/curve as represented by a list of points and reducing the number of points needed to accurately represent the given line. == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Reference |...")
- 11:21, 15 February 2023 (3-Dimensional, i.e. project onto a 2D plane) (hist | edit) [2,113 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:(3-Dimensional, i.e. project onto a 2D plane) (Shown Surface Determination)}} == Description == This is the process of identifying what surfaces and parts of surfaces can be seen from a particular viewing angle. Given a set of obstacles in the Euclidean space, two points in the space are said to be visible to each other, if the line segment that joins them does not intersect any obstacles. == Parameters == <pre>n: number of polygons p: number of pixel...")
- 11:21, 15 February 2023 Polygon Clipping with Convex Clipping Polygon (hist | edit) [855 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Polygon Clipping with Convex Clipping Polygon (Polygon Clipping)}} == Description == Here, the clipping polygon is restricted to being convex. == Related Problems == Generalizations: Polygon Clipping with Arbitrary Clipping Polygon == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Reference...")
- 11:21, 15 February 2023 Polygon Clipping with Arbitrary Clipping Polygon (hist | edit) [1,909 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Polygon Clipping with Arbitrary Clipping Polygon (Polygon Clipping)}} == Description == Clipping is an essential part of image synthesis. Traditionally, polygon clipping has been used to clip out the portions of a polygon that lie outside the window of the output device to prevent undesirable effects. In the recent past polygon clipping is used to render 3D images through hidden surface removal and to produce high-quality surface details using techniques...")
- 11:21, 15 February 2023 Line Drawing (hist | edit) [1,609 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Line Drawing (Line Drawing)}} == Description == Given a line segment with endpoints $(x_0, y_0), (x_1, y_1)$ and a discrete graphical medium (like pixel-based displays and printers), draw/approximate the line segment on the medium, potentially with antialiasing. == Parameters == <pre>n: number of pixels the line goes through</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Tim...")
- 11:21, 15 February 2023 Constructing Eulerian Trails in a Graph (hist | edit) [1,550 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Constructing Eulerian Trails in a Graph (Constructing Eulerian Trails in a Graph)}} == Description == In graph theory, an Eulerian trail (or Eulerian path) is a trail in a finite graph that visits every edge exactly once (allowing for revisiting vertices). Similarly, an Eulerian circuit or Eulerian cycle is an Eulerian trail that starts and ends on the same vertex. == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable...")
- 11:21, 15 February 2023 Bipartite Maximum-Weight Matching (hist | edit) [1,383 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Bipartite Maximum-Weight Matching (Maximum-Weight Matching)}} == Description == In computer science, the maximum weight matching problem is the problem of finding, in a weighted graph, a matching in which the sum of weights is maximized. Here, the graph must be bipartite. == Related Problems == Generalizations: Maximum-Weight Matching == Parameters == <pre>n: number of vertices m: number of edges N: largest weight magnitude</pre> == Table of A...")
- 11:21, 15 February 2023 Maximum-Weight Matching (hist | edit) [1,590 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Maximum-Weight Matching (Maximum-Weight Matching)}} == Description == In computer science, the maximum weight matching problem is the problem of finding, in a weighted graph, a matching in which the sum of weights is maximized. Here, the graph is unrestricted; i.e. can be any general graph. == Related Problems == Subproblem: Bipartite Maximum-Weight Matching == Parameters == <pre>n: number of vertices m: number of edges N: largest weight magnit...")
- 11:21, 15 February 2023 N-Player (hist | edit) [335 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:n-Player (Nash Equilibria)}} == Description == Here, given the payoff matrices for an $n$-player game, determine a Nash equilibrium. == Related Problems == Subproblem: 2-Player == Parameters == <pre>n: number of players</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem.")
- 11:21, 15 February 2023 2-Player (hist | edit) [723 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:2-Player (Nash Equilibria)}} == Description == In game theory, the Nash equilibrium, named after the mathematician John Forbes Nash Jr., is a proposed solution of a non-cooperative game involving two or more players in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy. As an algorithmic problem, given the payoff matrices for a bimatrix game, determine...")
- 11:21, 15 February 2023 Alphabetic Tree Problem (hist | edit) [1,454 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Alphabetic Tree Problem (Optimal Binary Search Trees)}} == Description == A variant of the OBST problem is when only the gaps have nonzero access probabilities, and is called the optimal alphabetic tree problem. == Related Problems == Generalizations: Optimal Binary Search Tree Problem Related: Approximate OBST, Huffman Encoding == Parameters == <pre>n: number of elements</pre> == Table of Algorithms == {| class="wikitable sortable"...")
- 11:21, 15 February 2023 Approximate OBST (hist | edit) [2,086 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Approximate OBST (Optimal Binary Search Trees)}} == Description == Suppose we are given $n$ keys and the probabilities of accessing each key and those occurring in the gap between two successive keys. The approximate optimal binary search tree problem is to construct a binary search tree on these $n$ keys, whose expected access time is within an approximation factor of the optimal time. == Related Problems == Generalizations: Optimal Binary Search T...")
- 11:21, 15 February 2023 Optimal Binary Search Tree Problem (hist | edit) [678 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Optimal Binary Search Tree Problem (Optimal Binary Search Trees)}} == Description == Suppose we are given $n$ keys and the probabilities of accessing each key and those occurring in the gap between two successive keys. The optimal binary search tree problem is to construct a binary search tree on these $n$ keys that minimizes the expected access time. == Related Problems == Subproblem: Approximate OBST, Huffman Encoding, Alphabetic Tree Pr...")
- 11:21, 15 February 2023 All Permutations (hist | edit) [1,207 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:All Permutations (All Permutations)}} == Description == Generate all permuttaions of the characters/elements in a string/array. == Parameters == <pre>n: number of elements</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Reference |- | Steinhaus–Johnson–Trotter algorithm (All Permutations All Permutations)|Steinhaus–J...")
- 11:21, 15 February 2023 Minimum value in each row of an implicitly-defined totally monotone matrix (hist | edit) [1,585 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Minimum value in each row of an implicitly-defined totally monotone matrix (Minimum value in each row of an implicitly-defined totally monotone matrix)}} == Description == Given a totally monotone matrix $A$ whose entries $A(i, j)$ are implicitly defined by some function $f(i, j)$ (assume $f$ takes constant time to evaluate for all relevant $(i, j)$), determine the minimum value in each row. == Parameters == <pre>n, m: dimensions of matrix; assume m...")
- 11:21, 15 February 2023 Gröbner Bases (hist | edit) [1,658 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Gröbner Bases (Gröbner Bases)}} == Description == In mathematics, and more specifically in computer algebra, computational algebraic geometry, and computational commutative algebra, a Gröbner basis is a particular kind of generating set of an ideal in a polynomial ring $K(x_1, \ldots ,x_n)$ over a field $K$. As an algorithmic problem, given a set of polynomials in $K(x_1, \ldots,x_n)$, determine a Gröbner basis. == Parameters == <pre>n: number of...")
- 11:21, 15 February 2023 Convex Optimization (Non-linear) (hist | edit) [528 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Convex Optimization (Non-linear) (Convex Optimization (Non-linear))}} == Description == Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets. == Parameters == No parameters found. == Table of Algorithms == Currently no algorithms in our database for the given problem. == Time Complexity graph == 1000px == Space...")
- 11:21, 15 February 2023 Cyclic Permutations (hist | edit) [849 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Cyclic Permutations (Generating Random Permutations)}} == Description == Given an input string/array, generate a single random cyclic permutation of the characters/elements of the string/array. == Related Problems == Related: General Permutations == Parameters == <pre>n: number of elements</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation...")
- 11:21, 15 February 2023 General Permutations (hist | edit) [1,294 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:General Permutations (Generating Random Permutations)}} == Description == Given an input string/array, generate a single random permutation of the characters/elements of the string/array. == Related Problems == Related: Cyclic Permutations == Parameters == <pre>n: number of elements</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor...")
- 11:20, 15 February 2023 Inexact Laplacian Solver (hist | edit) [3,888 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Inexact Laplacian Solver (SDD Systems Solvers)}} == Description == This problem refers to solving equations of the form $Lx = b$ where $L$ is a Laplacian of a graph. In other words, this is solving equations of the form $Ax = b$ for a SDD matrix $A$. This variation of the problem permits some error. == Related Problems == Related: Exact Laplacian Solver == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable sort...")
- 11:20, 15 February 2023 Exact Laplacian Solver (hist | edit) [1,294 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Exact Laplacian Solver (SDD Systems Solvers)}} == Description == This problem refers to solving equations of the form $Lx = b$ where $L$ is a Laplacian of a graph. In other words, this is solving equations of the form $Ax = b$ for a SDD matrix $A$. This variation of the problem requires an exact solution with no error. == Related Problems == Related: Inexact Laplacian Solver == Parameters == <pre>n: dimension of matrix</pre> == Table of Algor...")
- 11:20, 15 February 2023 Key Exchange (hist | edit) [1,168 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Key Exchange (Key Exchange)}} == Description == Key exchange (also key establishment) is a method in cryptography by which cryptographic keys are exchanged between two parties, allowing use of a cryptographic algorithm. == Parameters == <pre>n: maximum size of numbers (prime, parameters, keys), in bits</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approxima...")
- 11:20, 15 February 2023 Planar Bipartite Graph Perfect Matching (hist | edit) [1,333 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Planar Bipartite Graph Perfect Matching (Maximum Cardinality Matching)}} == Description == The goal of maximum cardinality matching is to find a matching with as many edges as possible (equivalently: a matching that covers as many vertices as possible). Here, the graph is a planar bipartite graph. == Related Problems == Generalizations: Bipartite Graph MCM Related: General Graph MCM == Parameters == <pre>V: number of vertices E: number of...")
- 11:20, 15 February 2023 General Graph MCM (hist | edit) [1,737 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:General Graph MCM (Maximum Cardinality Matching)}} == Description == The goal of maximum cardinality matching is to find a matching with as many edges as possible (equivalently: a matching that covers as many vertices as possible). Here, the graph can be any general graph. == Related Problems == Subproblem: Bipartite Graph MCM Related: Planar Bipartite Graph Perfect Matching == Parameters == <pre>V: number of vertices E: number of edges</p...")
- 11:20, 15 February 2023 Bipartite Graph MCM (hist | edit) [2,906 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Bipartite Graph MCM (Maximum Cardinality Matching)}} == Description == The goal of maximum cardinality matching is to find a matching with as many edges as possible (equivalently: a matching that covers as many vertices as possible). Here, the graph is bipartite. == Related Problems == Generalizations: General Graph MCM Subproblem: Planar Bipartite Graph Perfect Matching == Parameters == <pre>V: number of vertices E: number of edges</pre>...")
- 11:20, 15 February 2023 Convex Polyhedral Window (hist | edit) [669 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Convex Polyhedral Window (Line Clipping)}} == Description == Line clipping is the process of removing lines or portions of lines outside an area of interest. Typically; any line or part thereof which is outside of the viewing area is removed. Here, the viewing area is a convex polyhedron. == Related Problems == Subproblem: Convex Polygonal Window Related: Rectangular Window == Parameters == <pre>n: number of lines p: number of faces on pol...")
- 11:20, 15 February 2023 Convex Polygonal Window (hist | edit) [1,178 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Convex Polygonal Window (Line Clipping)}} == Description == Line clipping is the process of removing lines or portions of lines outside an area of interest. Typically; any line or part thereof which is outside of the viewing area is removed. Here, the viewing area is a convex polygon. == Related Problems == Generalizations: Convex Polyhedral Window Subproblem: Rectangular Window == Parameters == <pre>n: number of lines p: number of edges o...")
- 11:20, 15 February 2023 Rectangular Window (hist | edit) [1,635 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Rectangular Window (Line Clipping)}} == Description == Line clipping is the process of removing lines or portions of lines outside an area of interest. Typically; any line or part thereof which is outside of the viewing area is removed. Here, the viewing area is rectangular. == Related Problems == Generalizations: Convex Polygonal Window Related: Convex Polyhedral Window == Parameters == <pre>n: number of lines</pre> == Table of Algorithm...")
- 11:20, 15 February 2023 Edit Sequence, constant-size alphabet (hist | edit) [1,287 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Edit Sequence, constant-size alphabet (Sequence Alignment)}} == Description == Given two strings, determine the shortest sequence of edits required to transform one of the strings into the other. Assume we have a constant-size alphabet. == Related Problems == Generalizations: Edit Distance, constant-size alphabet == Parameters == <pre>n, m: lengths of input strings; assume n≥m</pre> == Table of Algorithms == {| class="wikitable sortable"...")
- 11:20, 15 February 2023 Edit Distance, constant-size alphabet (hist | edit) [599 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Edit Distance, constant-size alphabet (Sequence Alignment)}} == Description == Given two strings, determine the minimum number of edits required to transform one of the strings into the other. Assume we have a constant-size alphabet. == Related Problems == Subproblem: Edit Sequence, constant-size alphabet == Parameters == <pre>n, m: lengths of input strings; assume n≥m</pre> == Table of Algorithms == Currently no algorithms in our database...")
- 11:20, 15 February 2023 Multiple String Search (hist | edit) [1,523 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Multiple String Search (String Search)}} == Description == Multiple string search algorithms try to find a place where one or several strings (also called patterns) are found within a larger string or text. == Related Problems == Related: Single String Search == Parameters == <pre>$m$: longest pattern length $n$: length of searchable text $s$: size of the alphabet $k$: number of patterns to search for $z$: number of matches</pre> == Table of A...")
- 11:20, 15 February 2023 Single String Search (hist | edit) [4,574 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Single String Search (String Search)}} == Description == Single string search algorithms try to find a place where a string (also called a pattern) is found within a larger string or text. == Related Problems == Related: Multiple String Search == Parameters == <pre>$m$: pattern length $n$: length of searchable text $s$: size of the alphabet</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%"...")
- 11:20, 15 February 2023 Square Matrix LU Decomposition (hist | edit) [2,138 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Square Matrix LU Decomposition (LU Decomposition)}} == Description == Lower–upper (LU) decomposition or factorization factors a matrix as the product of a lower triangular matrix and an upper triangular matrix. In this specific case, the input is a square $n \times n$ matrix == Related Problems == Generalizations: Rectangular Matrix LU Decomposition == Parameters == <pre>$n$: dimension of square matrix</pre> == Table of Algorithms == {| cl...")
- 11:20, 15 February 2023 Rectangular Matrix LU Decomposition (hist | edit) [1,067 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Rectangular Matrix LU Decomposition (LU Decomposition)}} == Description == Lower–upper (LU) decomposition or factorization factors a matrix as the product of a lower triangular matrix and an upper triangular matrix. In the general case, the input is an $m \times n$ matrix. == Related Problems == Subproblem: Square Matrix LU Decomposition == Parameters == <pre>$m$: number of rows in input matrix $n$: number of columns in input matrix $l$: numb...")
- 11:20, 15 February 2023 Smallest Factor (hist | edit) [513 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Smallest Factor (Integer Factoring)}} == Description == Given an $n$-bit integer $N$, find a non-trivial factorization $N=pq$ (where $p, q>1$ are integers) or return that $N$ is prime. For "second category" algorithms, the running time depends solely on the size of the integer to be factored == Related Problems == Related: Integer Factoring == Parameters == <pre>n: number of bits in the integer</pre> == Table of Algorithms == Currently no al...")
- 11:20, 15 February 2023 Integer Factoring (hist | edit) [5,101 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Integer Factoring (Integer Factoring)}} == Description == Given an $n$-bit integer $N$, find a non-trivial factorization $N=pq$ (where $p, q>1$ are integers) or return that $N$ is prime. For "first category" algorithms, the running time depends on the size of smallest prime factor. == Related Problems == Related: Smallest Factor == Parameters == <pre>n: number of bits in the integer B: bound parameter (if needed)</pre> == Table of Algorithms =...")
- 11:20, 15 February 2023 (5/3)-approximate ap-shortest paths (hist | edit) [1,489 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:(5/3)-approximate ap-shortest paths (All-Pairs Shortest Paths (APSP))}} == Description == Approximate APSP within a factor of 5/3. == Related Problems == Generalizations: APSP Related: APSP on Dense Directed Graphs with Arbitrary Weights, APSP on Dense Undirected Graphs with Arbitrary Weights, APSP on Geometrically Weighted Graphs, APSP on Dense Undirected Graphs with Positive Integer Weights, APSP on Sparse Directed Graphs with...")
- 11:20, 15 February 2023 APSP on Sparse Undirected Unweighted Graphs (hist | edit) [1,634 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:APSP on Sparse Undirected Unweighted Graphs (All-Pairs Shortest Paths (APSP))}} == Description == In this case, the graph $G=(V,E)$ that we consider is sparse ($m = O(n)$), is undirected, and is unweighted (or equivalently, has all unit weights). == Related Problems == Generalizations: APSP Related: APSP on Dense Directed Graphs with Arbitrary Weights, APSP on Dense Undirected Graphs with Arbitrary Weights, APSP on Geometrically Weighte...")
- 11:20, 15 February 2023 APSP on Sparse Directed Unweighted Graphs (hist | edit) [1,078 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:APSP on Sparse Directed Unweighted Graphs (All-Pairs Shortest Paths (APSP))}} == Description == In this case, the graph $G=(V,E)$ that we consider is sparse ($m = O(n)$), is directed, and is unweighted (or equivalently, has all unit weights). == Related Problems == Generalizations: APSP Related: APSP on Dense Directed Graphs with Arbitrary Weights, APSP on Dense Undirected Graphs with Arbitrary Weights, APSP on Geometrically Weighted Gr...")
- 11:20, 15 February 2023 APSP on Dense Undirected Unweighted Graphs (hist | edit) [1,634 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:APSP on Dense Undirected Unweighted Graphs (All-Pairs Shortest Paths (APSP))}} == Description == In this case, the graph $G=(V,E)$ that we consider is dense ($m = O(n^2)$), is undirected, and is unweighted (or equivalently, has all unit weights). == Related Problems == Generalizations: APSP Related: APSP on Dense Directed Graphs with Arbitrary Weights, APSP on Dense Undirected Graphs with Arbitrary Weights, APSP on Geometrically Weighte...")
- 11:20, 15 February 2023 APSP on Dense Directed Unweighted Graphs (hist | edit) [1,079 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:APSP on Dense Directed Unweighted Graphs (All-Pairs Shortest Paths (APSP))}} == Description == In this case, the graph $G=(V,E)$ that we consider is dense ($m = O(n^2)$), is directed, and is unweighted (or equivalently, has all unit weights). == Related Problems == Generalizations: APSP Related: APSP on Dense Directed Graphs with Arbitrary Weights, APSP on Dense Undirected Graphs with Arbitrary Weights, APSP on Geometrically Weighted Gr...")
- 11:20, 15 February 2023 APSP on Sparse Undirected Graphs with Arbitrary Weights (hist | edit) [1,608 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:APSP on Sparse Undirected Graphs with Arbitrary Weights (All-Pairs Shortest Paths (APSP))}} == Description == In this case, the graph $G=(V,E)$ that we consider is sparse ($m = O(n)$), is undirected, and has arbitrary weights. == Related Problems == Generalizations: APSP Related: APSP on Dense Directed Graphs with Arbitrary Weights, APSP on Dense Undirected Graphs with Arbitrary Weights, APSP on Geometrically Weighted Graphs, APSP o...")
- 11:20, 15 February 2023 APSP on Sparse Undirected Graphs with Positive Integer Weights (hist | edit) [1,731 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:APSP on Sparse Undirected Graphs with Positive Integer Weights (All-Pairs Shortest Paths (APSP))}} == Description == In this case, the graph $G=(V,E)$ that we consider is sparse ($m = O(n)$), is undirected, and has positive integer weights. == Related Problems == Generalizations: APSP Related: APSP on Dense Directed Graphs with Arbitrary Weights, APSP on Dense Undirected Graphs with Arbitrary Weights, APSP on Geometrically Weighted Grap...")
- 11:20, 15 February 2023 APSP on Sparse Directed Graphs with Arbitrary Weights (hist | edit) [1,046 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:APSP on Sparse Directed Graphs with Arbitrary Weights (All-Pairs Shortest Paths (APSP))}} == Description == In this case, the graph $G=(V,E)$ that we consider is sparse ($m = O(n)$), is directed, and has arbitrary weights. == Related Problems == Generalizations: APSP Related: APSP on Dense Directed Graphs with Arbitrary Weights, APSP on Dense Undirected Graphs with Arbitrary Weights, APSP on Geometrically Weighted Graphs, APSP on De...")
- 11:20, 15 February 2023 APSP on Dense Undirected Graphs with Positive Integer Weights (hist | edit) [1,731 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:APSP on Dense Undirected Graphs with Positive Integer Weights (All-Pairs Shortest Paths (APSP))}} == Description == In this case, the graph $G=(V,E)$ that we consider is dense ($m = O(n^2)$), is undirected, and has positive integer weights. == Related Problems == Generalizations: APSP Related: APSP on Dense Directed Graphs with Arbitrary Weights, APSP on Dense Undirected Graphs with Arbitrary Weights, APSP on Geometrically Weighted Grap...")
- 11:20, 15 February 2023 APSP on Geometrically Weighted Graphs (hist | edit) [1,608 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:APSP on Geometrically Weighted Graphs (All-Pairs Shortest Paths (APSP))}} == Description == In this case, the graph $G=(V,E)$ that we consider may be dense or sparse, may be directed or undirected, and has weights from a fixed set of $c$ values. == Related Problems == Generalizations: APSP Related: APSP on Dense Directed Graphs with Arbitrary Weights, APSP on Dense Undirected Graphs with Arbitrary Weights, APSP on Dense Undirected Graph...")
- 11:20, 15 February 2023 APSP on Dense Undirected Graphs with Arbitrary Weights (hist | edit) [1,917 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:APSP on Dense Undirected Graphs with Arbitrary Weights (All-Pairs Shortest Paths (APSP))}} == Description == In this case, the graph $G=(V,E)$ that we consider is dense ($m = O(n^2)$), is undirected, and has arbitrary weights. == Related Problems == Generalizations: APSP Related: APSP on Dense Directed Graphs with Arbitrary Weights, APSP on Geometrically Weighted Graphs, APSP on Dense Undirected Graphs with Positive Integer Weights, [...")
- 11:20, 15 February 2023 APSP on Dense Directed Graphs with Arbitrary Weights (hist | edit) [2,104 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:APSP on Dense Directed Graphs with Arbitrary Weights (All-Pairs Shortest Paths (APSP))}} == Description == In this case, the graph $G=(V,E)$ that we consider is dense ($m = O(n^2)$), is directed, and has arbitrary weights. == Related Problems == Generalizations: APSP Related: APSP on Dense Undirected Graphs with Arbitrary Weights, APSP on Geometrically Weighted Graphs, APSP on Dense Undirected Graphs with Positive Integer Weights, A...")
- 11:19, 15 February 2023 APSP (hist | edit) [4,258 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:APSP (All-Pairs Shortest Paths (APSP))}} == Description == The shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. == Related Problems == Subproblem: APSP on Dense Directed Graphs with Arbitrary Weights, APSP on Dense Undirected Graphs with Arbitrary Weights, APSP on Geometrically Weighted Graphs, APSP on Dense Undirec...")
- 11:19, 15 February 2023 Replacement Paths Problem (hist | edit) [869 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Replacement Paths Problem (Shortest Path (Directed Graphs))}} == Description == Given nodes $s$ and $t$ in a weighted directed graph and a shortest path $P$ from $s$ to $t$, compute the length of the shortest simple path that avoids edge $e$, for all edges $e$ on $P$ == Related Problems == Generalizations: st-Shortest Path Related: General Weights, Nonnegative Weights, Nonnegative Integer Weights, Second Shortest Simple Path, 1-...")
- 11:19, 15 February 2023 2-sensitive decremental st-shortest paths (hist | edit) [1,349 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:2-sensitive decremental st-shortest paths (Shortest Path (Directed Graphs))}} == Description == Determine the st-shortest path with a sensitivity of 2 using decremental techniques. == Related Problems == Generalizations: st-Shortest Path Related: General Weights, Nonnegative Weights, Nonnegative Integer Weights, Second Shortest Simple Path, 1-sensitive (3/2)-approximate ss-shortest paths, 2-sensitive (7/5)-approximate st-sho...")
- 11:19, 15 February 2023 1-sensitive decremental st-shortest paths (hist | edit) [1,748 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:1-sensitive decremental st-shortest paths (Shortest Path (Directed Graphs))}} == Description == Determine the st-shortest path with a sensitivity of 1 using decremental techniques. == Related Problems == Generalizations: st-Shortest Path Related: General Weights, Nonnegative Weights, Nonnegative Integer Weights, Second Shortest Simple Path, 1-sensitive (3/2)-approximate ss-shortest paths, 2-sensitive (7/5)-approximate st-sho...")
- 11:19, 15 February 2023 2-sensitive (7/5)-approximate st-shortest paths (hist | edit) [1,332 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:2-sensitive (7/5)-approximate st-shortest paths (Shortest Path (Directed Graphs))}} == Description == Approximate the st-shortest paths problem within a factor of 7/5 with a sensitivity of 2. == Related Problems == Generalizations: st-Shortest Path Related: General Weights, Nonnegative Weights, Nonnegative Integer Weights, Second Shortest Simple Path, 1-sensitive (3/2)-approximate ss-shortest paths, 1-sensitive decremental s...")
- 11:19, 15 February 2023 1-sensitive (3/2)-approximate ss-shortest paths (hist | edit) [1,326 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:1-sensitive (3/2)-approximate ss-shortest paths (Shortest Path (Directed Graphs))}} == Description == Approximate the single source shortest paths problem within a factor of 3/2 with a sensitivity of 1. == Related Problems == Related: General Weights, Nonnegative Weights, Nonnegative Integer Weights, Second Shortest Simple Path, st-Shortest Path, 2-sensitive (7/5)-approximate st-shortest paths, 1-sensitive decremental st-shor...")
- 11:19, 15 February 2023 St-Shortest Path (hist | edit) [957 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:st-Shortest Path (Shortest Path (Directed Graphs))}} == Description == Given a weighted digraph $G=(V,E)$, find the shortest path between two given vertices $s$ and $t$. == Related Problems == Subproblem: Second Shortest Simple Path, 2-sensitive (7/5)-approximate st-shortest paths, 1-sensitive decremental st-shortest paths, 2-sensitive decremental st-shortest paths, Replacement Paths Problem Related: General Weights, Non...")
- 11:19, 15 February 2023 Second Shortest Simple Path (hist | edit) [2,123 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Second Shortest Simple Path (Shortest Path (Directed Graphs))}} == Description == Given a weighted digraph $G=(V,E)$, find the second shortest path between two given vertices $s$ and $t$. == Related Problems == Generalizations: st-Shortest Path Related: General Weights, Nonnegative Weights, Nonnegative Integer Weights, 1-sensitive (3/2)-approximate ss-shortest paths, 2-sensitive (7/5)-approximate st-shortest paths, 1-sensiti...")
- 11:19, 15 February 2023 Nonnegative Integer Weights (hist | edit) [2,175 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Nonnegative Integer Weights (Shortest Path (Directed Graphs))}} == Description == The shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. Here, the weights are restricted to be nonnegative integers. == Related Problems == Generalizations: nonnegative weights Related: General Weights, Nonnegative Weights, Second Shortest...")
- 11:19, 15 February 2023 Nonnegative Weights (hist | edit) [2,754 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Nonnegative Weights (Shortest Path (Directed Graphs))}} == Description == The shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. Here, the weights are restricted to be nonnegative. == Related Problems == Generalizations: general weights Subproblem: Nonnegative Integer Weights Related: General Weights, Second Shortest S...")
- 11:19, 15 February 2023 General Weights (hist | edit) [892 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:General Weights (Shortest Path (Directed Graphs))}} == Description == The shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. Here, the weights can be any real number. == Related Problems == Subproblem: Nonnegative Weights Related: Nonnegative Integer Weights, Second Shortest Simple Path, st-Shortest Path, 1-sensitiv...")
- 11:19, 15 February 2023 2-dimensional array representation (hist | edit) [1,207 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:2-dimensional array representation (Closest Pair Problem)}} == Description == Given $n$ points in 2-dimensional space in array representation, find a pair of points with the smallest distance between them. == Related Problems == Related: k-dimensional space, $l_m$ (or $l_\infty$) norm, 2-dimensional space, $l_m$ (or $l_\infty$) norm, 2-dimensional space, Euclidean metric == Parameters == No parameters found. == Table of Algorithms ==...")
- 11:19, 15 February 2023 2-dimensional space, Euclidean metric (hist | edit) [1,306 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:2-dimensional space, Euclidean metric (Closest Pair Problem)}} == Description == Given $n$ points in 2-dimensional space equipped with the Eucildean metric, find a pair of points with the smallest distance between them. == Related Problems == Related: k-dimensional space, $l_m$ (or $l_\infty$) norm, 2-dimensional space, $l_m$ (or $l_\infty$) norm, 2-dimensional array representation == Parameters == No parameters found. == Table of Alg...")
- 11:19, 15 February 2023 2-dimensional space, $l m$ (or $l \infty$) norm (hist | edit) [1,002 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:2-dimensional space, $l_m$ (or $l_\infty$) norm (Closest Pair Problem)}} == Description == Given $n$ points in 2-dimensional space equipped with the $l_m$ (or $l_\infty$) norm, find a pair of points with the smallest distance between them. == Related Problems == Generalizations: k-dimensional space, $l_m$ (or $l_\infty$) norm Related: 2-dimensional space, Euclidean metric, 2-dimensional array representation == Parameters == No paramet...")
- 11:19, 15 February 2023 K-dimensional space, $l m$ (or $l \infty$) norm (hist | edit) [1,019 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:k-dimensional space, $l_m$ (or $l_\infty$) norm (Closest Pair Problem)}} == Description == Given $n$ points in metric space, typically $k$-dimensional space equipped with $l_m$ (or $l_\infty$) norm, find a pair of points with the smallest distance between them. == Related Problems == Subproblem: 2-dimensional space, $l_m$ (or $l_\infty$) norm Related: 2-dimensional space, Euclidean metric, 2-dimensional array representation == Parameter...")
- 11:19, 15 February 2023 Directed (Optimum Branchings), Super Dense MST (hist | edit) [1,378 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Directed (Optimum Branchings), Super Dense MST (Minimum Spanning Tree (MST))}} == Description == A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected; edge-weighted undirected graph that connects all the vertices together; without any cycles and with the minimum possible total edge weight. Here, we're given a directed graph with a root and $E=\Omega(V^2)$ edges, and we wish to find a spanning arborescence...")
- 11:19, 15 February 2023 Directed (Optimum Branchings), General MST (hist | edit) [2,137 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Directed (Optimum Branchings), General MST (Minimum Spanning Tree (MST))}} == Description == A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected; edge-weighted undirected graph that connects all the vertices together; without any cycles and with the minimum possible total edge weight. Here, we're given a directed graph with a root, and we wish to find a spanning arborescence of minimum weight that is root...")
- 11:19, 15 February 2023 Undirected, Integer Weights MST (hist | edit) [1,285 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Undirected, Integer Weights MST (Minimum Spanning Tree (MST))}} == Description == A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected; edge-weighted undirected graph that connects all the vertices together; without any cycles and with the minimum possible total edge weight. Here, we assume that the edges have integer weights, represented in binary. == Related Problems == Generalizations: Undirected,...")
- 11:19, 15 February 2023 Undirected, Planar MST (hist | edit) [1,206 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Undirected, Planar MST (Minimum Spanning Tree (MST))}} == Description == A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected; edge-weighted undirected graph that connects all the vertices together; without any cycles and with the minimum possible total edge weight. Here, we assume that the graph is planar. == Related Problems == Generalizations: Undirected, General MST Related: Undirected, Dense...")
- 11:19, 15 February 2023 Undirected, Dense MST (hist | edit) [1,226 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Undirected, Dense MST (Minimum Spanning Tree (MST))}} == Description == A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected; edge-weighted undirected graph that connects all the vertices together; without any cycles and with the minimum possible total edge weight. Here, we assume that the graph is dense (i.e. $E = \Omega(V)$). == Related Problems == Generalizations: Undirected, General MST Related...")
- 11:19, 15 February 2023 Undirected, General MST (hist | edit) [5,489 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Undirected, General MST (Minimum Spanning Tree (MST))}} == Description == A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected; edge-weighted undirected graph that connects all the vertices together; without any cycles and with the minimum possible total edge weight. Here, there are no restrictions on edge weights or graph density. == Related Problems == Subproblem: Undirected, Dense MST, Undirec...")
- 11:19, 15 February 2023 Connected Subgraph (hist | edit) [744 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Connected Subgraph (Strongly Connected Components)}} == Description == Subgraph connectivity asks us to maintainan understanding of connectivity under vertex updates: updates can turn vertices on and off, and queries refer to the subgraph induced by "on" vertices. (For instance, this is closer to applications in networks of routers, where node faults may occur.) == Related Problems == Related: Strongly Connected Components, Transitive Closure,...")
- 11:19, 15 February 2023 2 Strong Components (dynamic) (hist | edit) [1,193 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:2 Strong Components (dynamic) (Strongly Connected Components)}} == Description == maintain: a directed graph, under: edge insertion/deletions, answer: are there more than 2 strongly connected components? == Related Problems == Related: Strongly Connected Components, Transitive Closure, Maximum Strongly Connected Component, Strong Connectivity (dynamic), Connected Subgraph == Parameters == No parameters found. == Table of Algori...")
- 11:19, 15 February 2023 Strong Connectivity (dynamic) (hist | edit) [1,263 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Strong Connectivity (dynamic) (Strongly Connected Components)}} == Description == maintain: a directed graph, under edge insertions/deletions, answer: is the graph strongly connected? == Related Problems == Related: Strongly Connected Components, Transitive Closure, Maximum Strongly Connected Component, 2 Strong Components (dynamic), Connected Subgraph == Parameters == No parameters found. == Table of Algorithms == Currently...")
- 11:19, 15 February 2023 Maximum Strongly Connected Component (hist | edit) [557 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Maximum Strongly Connected Component (Strongly Connected Components)}} == Description == maintain: a directed graph, under: edge insertions/deletions, answer: what is the size of the largest SCC? == Related Problems == Related: Strongly Connected Components, Transitive Closure, Strong Connectivity (dynamic), 2 Strong Components (dynamic), Connected Subgraph == Parameters == No parameters found. == Table of Algorithms == Curre...")
- 11:19, 15 February 2023 Transitive Closure (hist | edit) [1,060 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Transitive Closure (Strongly Connected Components)}} == Description == In this problem, we also want to compute the transitive closure of a graph. (Perhaps this should be a separate problem?) == Related Problems == Related: Strongly Connected Components, Maximum Strongly Connected Component, Strong Connectivity (dynamic), 2 Strong Components (dynamic), Connected Subgraph == Parameters == <pre>V: number of vertices E: number of e...")
- 11:19, 15 February 2023 2-dimensional Convex Hull, Dynamic (hist | edit) [1,411 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:2-dimensional Convex Hull, Dynamic (Convex Hull)}} == Description == Here, the input points may be sequentially inserted or deleted, and the convex hull must be updated after each insert/delete operation. == Related Problems == Generalizations: 2-dimensional Convex Hull Related: 3-dimensional Convex Hull, d-dimensional Convex Hull, 2-dimensional Convex Hull, Online == Parameters == <pre>n: number of line segments h: number of point...")
- 11:19, 15 February 2023 2-dimensional Convex Hull, Online (hist | edit) [1,340 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:2-dimensional Convex Hull, Online (Convex Hull)}} == Description == Here, we are given the input points one by one, and must maintain the current convex hull after each input point. == Related Problems == Generalizations: 2-dimensional Convex Hull Related: 3-dimensional Convex Hull, d-dimensional Convex Hull, 2-dimensional Convex Hull, Dynamic == Parameters == <pre>n: number of line segments h: number of points on the convex hull</...")
- 11:19, 15 February 2023 D-dimensional Convex Hull (hist | edit) [1,690 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:d-dimensional Convex Hull (Convex Hull)}} == Description == Here, we are looking at the general d-dimensional case. == Related Problems == Subproblem: 2-dimensional Convex Hull, 3-dimensional Convex Hull Related: 3-dimensional Convex Hull, 2-dimensional Convex Hull, Online, 2-dimensional Convex Hull, Dynamic == Parameters == <pre>n: number of line segments h: number of points on the convex hull f_1: number of facets on the con...")
- 11:19, 15 February 2023 3-dimensional Convex Hull (hist | edit) [932 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:3-dimensional Convex Hull (Convex Hull)}} == Description == Here, we are looking at the 3-dimensional case. == Related Problems == Generalizations: d-dimensional Convex Hull Related: 2-dimensional Convex Hull, 2-dimensional Convex Hull, Online, 2-dimensional Convex Hull, Dynamic == Parameters == <pre>n: number of line segments h: number of points on the convex hull</pre> == Table of Algorithms == {| class="wikitable sortable" s...")
- 11:19, 15 February 2023 2-dimensional Convex Hull (hist | edit) [1,996 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:2-dimensional Convex Hull (Convex Hull)}} == Description == The convex hull or convex envelope or convex closure of a set X of points in the Euclidean plane or in a Euclidean space (or; more generally; in an affine space over the reals) is the smallest convex set that contains X. Here, we are looking at the 2-dimensional case. == Related Problems == Generalizations: d-dimensional Convex Hull Subproblem: 2-dimensional Convex Hull, Online, 2...")
- 11:19, 15 February 2023 Counting number of intersection points, line segments (hist | edit) [792 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Counting number of intersection points, line segments (Line segment intersection)}} == Description == In this case, we are supplied with a list of line segments, and we wish to count the number of points of intersection. == Related Problems == Generalizations: Reporting all intersection points, line segments Related: Reporting all intersection points, generalized segments, Reporting all intersection points, convex polygons, Reporting al...")
- 11:18, 15 February 2023 Reporting all intersection points, general polygons (hist | edit) [811 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Reporting all intersection points, general polygons (Line segment intersection)}} == Description == In this case, we are supplied with a list of polygons (not necessarily convex), and we wish to report all regions of intersection. == Related Problems == Subproblem: Reporting all intersection points, convex polygons Related: Reporting all intersection points, line segments, Reporting all intersection points, generalized segments, Countin...")
- 11:18, 15 February 2023 Reporting all intersection points, convex polygons (hist | edit) [1,428 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Reporting all intersection points, convex polygons (Line segment intersection)}} == Description == In this case, we are supplied with a list of convex polygons, and we wish to report all regions of intersection. == Related Problems == Generalizations: Reporting all intersection points, general polygons Related: Reporting all intersection points, line segments, Reporting all intersection points, generalized segments, Counting number of i...")
- 11:18, 15 February 2023 Reporting all intersection points, generalized segments (hist | edit) [1,961 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Reporting all intersection points, generalized segments (Line segment intersection)}} == Description == In this case, the segments are generalized (i.e. have algebraic degree ≥1); we still wish to report all points of intersection. == Related Problems == Subproblem: Reporting all intersection points, line segments Related: Reporting all intersection points, convex polygons, Reporting all intersection points, general polygons, Counting...")
- 11:18, 15 February 2023 Reporting all intersection points, line segments (hist | edit) [2,457 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Reporting all intersection points, line segments (Line segment intersection)}} == Description == The line segment intersection problem supplies a list of line segments in the Euclidean plane and asks about the points where they intersect (cross), if any. In this case, we wish to report all points of intersection. == Related Problems == Generalizations: Reporting all intersection points, generalized segments Subproblem: Counting number of inters...")
- 11:18, 15 February 2023 0-1 Linear Programming (hist | edit) [3,138 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:0-1 Linear Programming (Linear Programming)}} == Description == In this case, we require all of the variables to be either 0 or 1. == Related Problems == Generalizations: Integer Linear Programming Related: General Linear Programming, Linear Programming with Reals == Parameters == <pre>n: number of variables m: number of constraints L: length of input, in bits</pre> == Table of Algorithms == {| class="wikitable sortable" style="tex...")
- 11:18, 15 February 2023 Integer Linear Programming (hist | edit) [3,145 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Integer Linear Programming (Linear Programming)}} == Description == In this case, we require all of the variables to be integers. == Related Problems == Generalizations: Linear Programming with Reals Subproblem: 0-1 Linear Programming Related: General Linear Programming == Parameters == <pre>n: number of variables m: number of constraints L: length of input, in bits</pre> == Table of Algorithms == {| class="wikitable sortable" sty...")
- 11:18, 15 February 2023 Linear Programming with Reals (hist | edit) [3,212 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Linear Programming with Reals (Linear Programming)}} == Description == In this case, we allow all of the variables to be any real number. == Related Problems == Generalizations: General Linear Programming Subproblem: Integer Linear Programming Related: 0-1 Linear Programming == Parameters == <pre>n: number of variables m: number of constraints L: length of input, in bits</pre> == Table of Algorithms == {| class="wikitable sortable"...")
- 11:18, 15 February 2023 General Linear Programming (hist | edit) [3,395 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:General Linear Programming (Linear Programming)}} == Description == Linear programming (LP; also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization). == Related Problems == Subproblem: Linear Programming wi...")
- 11:18, 15 February 2023 Vandermonde Matrix (hist | edit) [1,246 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Vandermonde Matrix (Linear System)}} == Description == In this case, we restrict $A$ to be a Vandermonde matrix. == Related Problems == Generalizations: General Linear System Related: Sparse Linear System, Positive Definite, Hermitian Matrix, Non-Definite, Symmetric Matrix, Toeplitz Matrix == Parameters == <pre>n: number of variables and number of equations m: number of nonzero entries in matrix k: ratio between largest and sma...")
- 11:18, 15 February 2023 Toeplitz Matrix (hist | edit) [1,569 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Toeplitz Matrix (Linear System)}} == Description == In this case, we restrict $A$ to be a Toeplitz matrix. == Related Problems == Generalizations: General Linear System Related: Sparse Linear System, Positive Definite, Hermitian Matrix, Non-Definite, Symmetric Matrix, Vandermonde Matrix == Parameters == <pre>n: number of variables and number of equations m: number of nonzero entries in matrix k: ratio between largest and smalle...")
- 11:18, 15 February 2023 Non-Definite, Symmetric Matrix (hist | edit) [1,286 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Non-Definite, Symmetric Matrix (Linear System)}} == Description == In this case, we restrict $A$ to be non-definite and symmetric. == Related Problems == Generalizations: General Linear System Related: Sparse Linear System, Positive Definite, Hermitian Matrix, Toeplitz Matrix, Vandermonde Matrix == Parameters == <pre>n: number of variables and number of equations m: number of nonzero entries in matrix k: ratio between largest a...")
- 11:18, 15 February 2023 Positive Definite, Hermitian Matrix (hist | edit) [1,494 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Positive Definite, Hermitian Matrix (Linear System)}} == Description == In this case, we restrict $A$ to be positive definite and hermitian (or symmetric, if $A$ is real-valued). == Related Problems == Generalizations: General Linear System Related: Sparse Linear System, Non-Definite, Symmetric Matrix, Toeplitz Matrix, Vandermonde Matrix == Parameters == <pre>n: number of variables and number of equations m: number of nonzero e...")
- 11:18, 15 February 2023 Sparse Linear System (hist | edit) [1,042 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Sparse Linear System (Linear System)}} == Description == In this case, we restrict $A$ to be sparse (i.e. $A$ only has $O(n)$ nonzero entries). == Related Problems == Generalizations: General Linear System Related: Positive Definite, Hermitian Matrix, Non-Definite, Symmetric Matrix, Toeplitz Matrix, Vandermonde Matrix == Parameters == <pre>n: number of variables and number of equations m: number of nonzero entries in matrix k:...")
- 11:18, 15 February 2023 General Linear System (hist | edit) [1,592 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:General Linear System (Linear System)}} == Description == A system of linear equations (or linear system) is a collection of one or more linear equations involving the same set of variables. This is typically written in the form $Ax=b$ where $A$ is a matrix and $x, b$ are vectors. In this case, we impose no restrictions on $A$. == Related Problems == Subproblem: Sparse Linear System, Positive Definite, Hermitian Matrix, Non-Definite, Symme...")
- 11:18, 15 February 2023 $(\min, \leq)$ Product (hist | edit) [954 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:$(\min, \leq)$ Product (Matrix Product)}} == Description == Matrix product over the $(\min, \leq)$-semiring == Related Problems == Related: Matrix Multiplication, Boolean Matrix Multiplication, Boolean Matrix Multiplication (Combinatorial), Matrix Product Verification, Distance Product == Parameters == <pre>n: dimension of square matrix</pre> == Table of Algorithms == Currently no algorithms in our database for the given prob...")
- 11:18, 15 February 2023 Distance Product (hist | edit) [1,495 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Distance Product (Matrix Product)}} == Description == Matrix product over the $(\min, +)$-semiring == Related Problems == Related: Matrix Multiplication, Boolean Matrix Multiplication, Boolean Matrix Multiplication (Combinatorial), Matrix Product Verification, $(\min, \leq)$ Product == Parameters == <pre>n: dimension of square matrix</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem...")
- 11:18, 15 February 2023 Matrix Product Verification (hist | edit) [990 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Matrix Product Verification (Matrix Product)}} == Description == Given three matrices $A, B, C$, verify that $AB = C$, i.e. that $C$ is the matrix product of $A$ and $B$ == Related Problems == Generalizations: Matrix Multiplication Related: Boolean Matrix Multiplication, Boolean Matrix Multiplication (Combinatorial), Distance Product, $(\min, \leq)$ Product == Parameters == <pre>n: dimension of square matrix</pre> == Table of...")
- 11:18, 15 February 2023 Boolean Matrix Multiplication (Combinatorial) (hist | edit) [2,533 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Boolean Matrix Multiplication (Combinatorial) (Matrix Product)}} == Description == Matrix multiplication of two boolean matrices (i.e. where all entries are in $F_2$ and addition is mod 2). Here, only "combinatorial" algorithms are considered. == Related Problems == Generalizations: Boolean Matrix Multiplication Related: Matrix Multiplication, Matrix Product Verification, Distance Product, $(\min, \leq)$ Product == Parameters ==...")
- 11:18, 15 February 2023 Boolean Matrix Multiplication (hist | edit) [7,916 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Boolean Matrix Multiplication (Matrix Product)}} == Description == Matrix multiplication of two boolean matrices (i.e. where all entries are in $F_2$ and addition is mod 2) == Related Problems == Generalizations: Matrix Multiplication Subproblem: Boolean Matrix Multiplication (Combinatorial) Related: Matrix Product Verification, Distance Product, $(\min, \leq)$ Product == Parameters == <pre>n: dimension of square matrix</pre>...")
- 11:18, 15 February 2023 Maximum Local Edge Connectivity (hist | edit) [6,062 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Maximum Local Edge Connectivity (Maximum Flow)}} == Description == Find the pair of nodes with the maximum number of edge-disjoint paths between them == Related Problems == Related: st-Maximum Flow, Integer Maximum Flow, Unweighted Maximum Flow, Non-integer Maximum Flow, Minimum-Cost Flow, All-Pairs Maximum Flow == Parameters == <pre>V: number of vertices E: number of edges</pre> == Table of Algorithms == {| class="wikita...")
- 11:18, 15 February 2023 All-Pairs Maximum Flow (hist | edit) [6,440 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:All-Pairs Maximum Flow (Maximum Flow)}} == Description == Find the maximum flow between all pairs of nodes == Related Problems == Related: st-Maximum Flow, Integer Maximum Flow, Unweighted Maximum Flow, Non-integer Maximum Flow, Minimum-Cost Flow, Maximum Local Edge Connectivity == Parameters == <pre>V: number of vertices E: number of edges</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:c...")
- 11:18, 15 February 2023 Minimum-Cost Flow (hist | edit) [5,740 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Minimum-Cost Flow (Maximum Flow)}} == Description == Maximum flow problems involve finding a feasible flow through a flow network that is maximum. In this variant, each edge is given a cost coefficient, and we wish to minimize total cost while reaching a threshold flow. == Related Problems == Related: st-Maximum Flow, Integer Maximum Flow, Unweighted Maximum Flow, Non-integer Maximum Flow, All-Pairs Maximum Flow, Maximum Local Ed...")
- 11:18, 15 February 2023 Non-integer Maximum Flow (hist | edit) [5,591 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Non-integer Maximum Flow (Maximum Flow)}} == Description == Maximum flow problems involve finding a feasible flow through a flow network that is maximum. In this variant, the capacities may be non-integers. == Related Problems == Subproblem: Integer Maximum Flow Related: st-Maximum Flow, Unweighted Maximum Flow, Minimum-Cost Flow, All-Pairs Maximum Flow, Maximum Local Edge Connectivity == Parameters == <pre>V: number of ver...")
- 11:18, 15 February 2023 Unweighted Maximum Flow (hist | edit) [5,622 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Unweighted Maximum Flow (Maximum Flow)}} == Description == Maximum flow problems involve finding a feasible flow through a flow network that is maximum. In this variant, all edges have unit weight. == Related Problems == Generalizations: Integer Maximum Flow Related: st-Maximum Flow, Non-integer Maximum Flow, Minimum-Cost Flow, All-Pairs Maximum Flow, Maximum Local Edge Connectivity == Parameters == <pre>V: number of vertic...")
- 11:18, 15 February 2023 Integer Maximum Flow (hist | edit) [6,683 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Integer Maximum Flow (Maximum Flow)}} == Description == Maximum flow problems involve finding a feasible flow through a flow network that is maximum. In this variant, the capacities must be integers. == Related Problems == Generalizations: Non-Integer Maximum Flow Subproblem: Unweighted Maximum Flow Related: st-Maximum Flow, Non-integer Maximum Flow, Minimum-Cost Flow, All-Pairs Maximum Flow, Maximum Local Edge Connectivity...")
- 11:18, 15 February 2023 St-Maximum Flow (hist | edit) [7,829 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:st-Maximum Flow (Maximum Flow)}} == Description == Find the maximum flow from $s$ to $t$ == Related Problems == Related: Integer Maximum Flow, Unweighted Maximum Flow, Non-integer Maximum Flow, Minimum-Cost Flow, All-Pairs Maximum Flow, Maximum Local Edge Connectivity == Parameters == <pre>V: number of vertices E: number of edges U: maximum edge capacity</pre> == Table of Algorithms == {| class="wikitable sortable" style...")
- 11:18, 15 February 2023 Longest Common Substring with don't cares (hist | edit) [1,356 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Longest Common Substring with don't cares (Longest Common Subsequence)}} == Description == Find the length of the longest common substring of two strings S and T, where S is a binary string and T is is a binary string and additional * characters that can match either 0 or 1. == Related Problems == Generalizations: Longest Common Subsequence == Parameters == <pre>$n$: length of the longer input string $m$: length of the shorter input string $r$:...")
- 11:18, 15 February 2023 Longest Common Subsequence (hist | edit) [1,377 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Longest Common Subsequence (Longest Common Subsequence)}} == Description == The longest common subsequence (LCS) problem is the problem of finding the longest subsequence common to all sequences in a set of sequences (often just two sequences). == Related Problems == Subproblem: Longest Common Substring with don't cares == Parameters == <pre>$n$: length of the longer input string $m$: length of the shorter input string $r$: length of the LCS $s...")
- 11:17, 15 February 2023 Approximate MCSP (hist | edit) [1,377 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Approximate MCSP (Matrix Chain Multiplication)}} == Description == The Matrix Chain Scheduling Problem (or MCSP) is an optimization problem� where the goal is to find the product sequence for evaluating a chain of matrix products and the processor schedule for the sequence such that the evaluation time is minimized on a parallel system. In the approximation problem, the matrix multiplication carried out with the output result will use a number of opera...")
- 11:17, 15 February 2023 Matrix Chain Scheduling Problem (hist | edit) [1,194 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Matrix Chain Scheduling Problem (Matrix Chain Multiplication)}} == Description == The Matrix Chain Scheduling Problem (or MCSP) is an optimization problem� where the goal is to find the product sequence for evaluating a chain of matrix products and the processor schedule for the sequence such that the evaluation time is minimized on a parallel system. == Related Problems == Generalizations: Matrix Chain Ordering Problem Subproblem: Approximat...")
- 11:17, 15 February 2023 Approximate MCOP (hist | edit) [2,012 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Approximate MCOP (Matrix Chain Multiplication)}} == Description == Matrix chain multiplication (or Matrix Chain Ordering Problem; MCOP) is an optimization problem. Given a sequence of matrices, the goal is to find the most efficient way to multiply these matrices. In the approximation problem, the matrix multiplication carried out with the output result will use a number of operations that has some sort of upper bound based on the optimal solution. == R...")
- 11:17, 15 February 2023 Matrix Chain Ordering Problem (hist | edit) [1,541 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Matrix Chain Ordering Problem (Matrix Chain Multiplication)}} == Description == Matrix chain multiplication (or Matrix Chain Ordering Problem; MCOP) is an optimization problem. Given a sequence of matrices, the goal is to find the most efficient way to multiply these matrices. == Related Problems == Subproblem: Approximate MCOP, Matrix Chain Scheduling Problem Related: Matrix Chain Scheduling Problem, Approximate MCSP == Parameters...")
- 11:17, 15 February 2023 Kth Order Statistic (hist | edit) [1,166 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:kth Order Statistic (kth Order Statistic)}} == Description == An algorithm seeks to find the $k^{th}$ order statistic of a statistical sample, or the $k^{th}$-smallest value in a list or array. == Parameters == <pre>n: size of list</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Reference |- | Naive Selection (kth Order St...")
- 11:17, 15 February 2023 Non-Comparison Sorting (hist | edit) [2,528 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Non-Comparison Sorting (Sorting)}} == Description == A sorting algorithm is an algorithm that puts elements of a list in a certain order, not using comparisons between elements (so elements are typically integers or real numbers). == Related Problems == Generalizations: Sorting Related: Comparison Sorting == Parameters == <pre>n: size of list</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width...")
- 11:17, 15 February 2023 Comparison Sorting (hist | edit) [5,958 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Comparison Sorting (Sorting)}} == Description == A sorting algorithm is an algorithm that puts elements of a list in a certain order, using comparisons between elements. == Related Problems == Generalizations: Sorting Related: Non-Comparison Sorting == Parameters == <pre>n: size of list</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation...")
- 11:17, 15 February 2023 Sorting (hist | edit) [5,924 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Sorting (Sorting)}} == Description == A sorting algorithm is an algorithm that puts elements of a list in a certain order == Related Problems == Subproblem: Comparison Sorting, Non-Comparison Sorting Related: Non-Comparison Sorting == Parameters == <pre>n: size of list</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem. == Time Complexity graph == 1000px ==...")
- 11:17, 15 February 2023 Family:3SUM (hist | edit) [193 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:3SUM}}== Description == Currently no description in our database for the given family. == Problems Variations == * 3SUM * 3SUM' * All-Integers 3SUM * Real 3SUM")
- 11:17, 15 February 2023 Family:Dihedral Rotation Queries (hist | edit) [230 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Dihedral Rotation Queries}}== Description == Currently no description in our database for the given family. == Problems Variations == * Dynamic Dihedral Rotation Queries * Static Dihedral Rotation Queries")
- 11:17, 15 February 2023 Family:Model-Checking Problem (hist | edit) [510 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Model-Checking Problem}}== Description == Currently no description in our database for the given family. == Problems Variations == * Conjunctive Reachability Queries in MDPs * Conjunctive Safety Queries in MDPs * Disjunctive Queries of Safety in Graphs * Disjunctive Reachability Queries in MDPs * Disjunctive Safety Queries in MDPs * Disjunctive coBüchi Objectives * Generalized Büchi Games * Reachability in MDPs * Safe...")
- 11:17, 15 February 2023 Family:Vertex Reachability (hist | edit) [360 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Vertex Reachability}}== Description == Currently no description in our database for the given family. == Problems Variations == * #SSR * 1-sensitive incremental ss-reach * 2-sensitive incremental st-reach * ST-Reach * ap-reach * constant sensitivity incremental ST-Reach * sensitive incremental #SSR * st-Reach")
- 11:17, 15 February 2023 Family:Matrix-Vector Multiplication (hist | edit) [245 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Matrix-Vector Multiplication}}== Description == Currently no description in our database for the given family. == Problems Variations == * Online Matrix-Vector Multiplication * Online Vector-Matrix-Vector Multiplication")
- 11:17, 15 February 2023 Family:Graph Cycles (hist | edit) [182 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Graph Cycles}}== Description == Currently no description in our database for the given family. == Problems Variations == * Shortest Cycle * Shortest k-Cycle")
- 11:17, 15 February 2023 Family:Minimum Witness (hist | edit) [203 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Minimum Witness}}== Description == Currently no description in our database for the given family. == Problems Variations == * All Pairs Minimum Witness * Minimum Witness Finding")
- 11:17, 15 February 2023 Family:Local Alignment (hist | edit) [194 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Local Alignment}}== Description == Currently no description in our database for the given family. == Problems Variations == * Local Alignment * Multiple Local Alignment")
- 11:17, 15 February 2023 Family:Motion Planning Problems (hist | edit) [204 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Motion Planning Problems}}== Description == Currently no description in our database for the given family. == Problems Variations == * 3D Motion Planning * Planar Motion Planning")
- 11:17, 15 February 2023 Family:Geometric Visibility Problems (hist | edit) [243 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Geometric Visibility Problems}}== Description == Currently no description in our database for the given family. == Problems Variations == * Visibility Between Segments * Visibility From Infinity * Visible Triangle")
- 11:17, 15 February 2023 Family:Geometric Covering Problems (hist | edit) [319 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Geometric Covering Problems}}== Description == Currently no description in our database for the given family. == Problems Variations == * Hole in Union * Max-Weight Rectangle * Point Covering * Strips Cover Box * Triangle Measure * Triangles Cover Triangle * Weighted Depth")
- 11:17, 15 February 2023 Family:Geometric Separator Problems (hist | edit) [188 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Geometric Separator Problems}}== Description == Currently no description in our database for the given family. == Problems Variations == * Separator1 * Separator2")
- 11:17, 15 February 2023 Family:Geometric Incidence Problems (hist | edit) [200 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Geometric Incidence Problems}}== Description == Currently no description in our database for the given family. == Problems Variations == * 3 Points on Line * Point on 3 Lines")
- 11:17, 15 February 2023 Family:Graph Triangle Problems (hist | edit) [385 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Graph Triangle Problems}}== Description == Currently no description in our database for the given family. == Problems Variations == * Minimum Triangle * Negative Triangle Detection * Negative Triangle Listing * Negative Triangle Search * Nondecreasing Triangle * Triangle Collection* * Triangle Detection * Triangle in Unweighted Graph")
- 11:17, 15 February 2023 Family:Vertex Centrality (hist | edit) [560 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Vertex Centrality}}== Description == Currently no description in our database for the given family. == Problems Variations == * All-Nodes Median Parity * Approximate Betweenness Centrality * Approximate Reach Centrality * Betweenness Centrality * Directed All-Nodes Positive Betweenness Centrality * Directed All-Nodes Reach Centrality * Eccentricity * Positive Betweenness Centrality * Reach Centrality * Undirected Al...")
- 11:17, 15 February 2023 Family:Graph Metrics (hist | edit) [501 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Graph Metrics}}== Description == Currently no description in our database for the given family. == Problems Variations == * 1-sensitive (4/3)-approximate decremental diameter * 1-sensitive (4/3)-approximate decremental eccentricity * 1-sensitive decremental diameter * Approximate Diameter * Decremental Diameter * Diameter * Diameter 2 vs 3 * Diameter 3 vs 7 * Median * Radius * constant sensitivity (4/3)-approxim...")
- 11:17, 15 February 2023 Family:Orthogonal Vectors (hist | edit) [195 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Orthogonal Vectors}}== Description == Currently no description in our database for the given family. == Problems Variations == * 3-OV * OV * Unbalanced OV * k-OV")
- 11:17, 15 February 2023 Family:Boolean Satisfiability (hist | edit) [577 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Boolean Satisfiability}}== Description == Currently no description in our database for the given family. == Problems Variations == * 1-in-3SAT * 2SAT * 3SAT * 3SAT-5 * 4SAT * All-Equal-SAT * Conjunctive Normal Form SAT * Disjunctive Normal Form SAT * Dual-Horn SAT * Horn SAT * MaxSAT * Monotone 1-in-3SAT * Monotone 3SAT * Monotone Not-All-Equal 3-SAT (Monotone NAE 3SAT) * Monotone Not-Exactly-1-i...")
- 11:17, 15 February 2023 Family:Graph Coloring (hist | edit) [398 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Graph Coloring}}== Description == Currently no description in our database for the given family. == Problems Variations == * #2-Graph Coloring * #3-Graph Coloring * #4-Graph Coloring * #5-Graph Coloring * #k-Graph Coloring * 2-Graph Coloring * 3-Graph Coloring * 4-Graph Coloring * 5-Graph Coloring * Chromatic Number * k-Graph Coloring")
- 11:16, 15 February 2023 Family:Recovery (hist | edit) [178 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Recovery}}== Description == Currently no description in our database for the given family. == Problems Variations == * No-Steal/Force * Steal/No-Force")
- 11:16, 15 February 2023 Family:Page Replacements (hist | edit) [170 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Page Replacements}}== Description == Currently no description in our database for the given family. == Problems Variations == * Offline * Online")
- 11:16, 15 February 2023 Family:Deadlock Avoidance (hist | edit) [203 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Deadlock Avoidance}}== Description == Currently no description in our database for the given family. == Problems Variations == * Deadlock Avoidance * Dining Philosophers Problem")
- 11:16, 15 February 2023 Family:Interval Scheduling (hist | edit) [288 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Interval Scheduling}}== Description == Currently no description in our database for the given family. == Problems Variations == * Unweighted Interval Scheduling * Weighted Interval Schedule Maximization Problem (ISMP)")
- 11:16, 15 February 2023 Family:One-Way Hash Functions (hist | edit) [204 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:One-Way Hash Functions}}== Description == Currently no description in our database for the given family. == Problems Variations == * Keyed Hash Functions * Unkeyed Hash Functions")
- 11:16, 15 February 2023 Family:Integral Equations (hist | edit) [194 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Integral Equations}}== Description == Currently no description in our database for the given family. == Problems Variations == * Fredholm Equations * Volterra Equations")
- 11:16, 15 February 2023 Family:Median String Problem (hist | edit) [301 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Median String Problem}}== Description == Currently no description in our database for the given family. == Problems Variations == * Median String Problem with Binary Alphabets * Median String Problem with Bounded Alphabets * Median String Problem with Unbounded Alphabets")
- 11:16, 15 February 2023 Family:n-Queens Problem (hist | edit) [222 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:n-Queens Problem}}== Description == Currently no description in our database for the given family. == Problems Variations == * Constructing Solutions * Counting Solutions * n-Queens Completion")
- 11:16, 15 February 2023 Family:Integer Relation (hist | edit) [215 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Integer Relation}}== Description == Currently no description in our database for the given family. == Problems Variations == * Integer Relation Among Integers * Integer Relation Among Reals")
- 11:16, 15 February 2023 Family:Wiener Index (hist | edit) [207 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Wiener Index}}== Description == Currently no description in our database for the given family. == Problems Variations == * Minimum Wiener Connector Problem * Undirected Wiener Index")
- 11:16, 15 February 2023 Family:Texture Mapping (hist | edit) [218 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Texture Mapping}}== Description == Currently no description in our database for the given family. == Problems Variations == * Diffuse Reflection * Environment Mapping * Specular Reflection")
- 11:15, 15 February 2023 Family:Link Analysis (hist | edit) [183 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Link Analysis}}== Description == Currently no description in our database for the given family. == Problems Variations == * InDegree Analysis * Link Analysis")
- 11:15, 15 February 2023 Family:The Set-Covering Problem (hist | edit) [208 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:The Set-Covering Problem}}== Description == Currently no description in our database for the given family. == Problems Variations == * Unweighted Set-Covering * Weighted Set-Covering")
- 11:15, 15 February 2023 Family:Feature Detection (hist | edit) [187 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Feature Detection}}== Description == Currently no description in our database for the given family. == Problems Variations == * Blob Detection * Corner Detection")
- 11:15, 15 February 2023 Family:Graph Realization Problems (hist | edit) [216 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Graph Realization Problems}}== Description == Currently no description in our database for the given family. == Problems Variations == * DAG Realization Problem * Digraph Realization Problem")
- 11:15, 15 February 2023 Family:Graph Isomorphism Problem (hist | edit) [403 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Graph Isomorphism Problem}}== Description == Currently no description in our database for the given family. == Problems Variations == * Graph Isomorphism, Bounded Number of Vertices of Each Color * Graph Isomorphism, Bounded Vertex Valences * Graph Isomorphism, General Graphs * Graph Isomorphism, Trivalent Graphs * Largest Common Subtree * Subtree Isomorphism")
- 11:15, 15 February 2023 Family:AST to Code Translation (hist | edit) [219 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:AST to Code Translation}}== Description == Currently no description in our database for the given family. == Problems Variations == * AST to Code Translation * Arithmetic Expression Binary Tree")
- 11:15, 15 February 2023 Family:Maximum Subarray Problem (hist | edit) [255 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Maximum Subarray Problem}}== Description == Currently no description in our database for the given family. == Problems Variations == * 1D Maximum Subarray * 2D Maximum Subarray * Maximum Square Subarray * Maximum Subarray")
- 11:15, 15 February 2023 Family:Stable Matching Problem (hist | edit) [351 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Stable Matching Problem}}== Description == Currently no description in our database for the given family. == Problems Variations == * Almost Stable Marriage Problem * Boolean d-Attribute Stable Matching * Stable Marriage Problem * Stable Matching Verification * Stable Pair Checking * Stable Roommates Problem")
- 11:15, 15 February 2023 Family:Data Compression (hist | edit) [193 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Data Compression}}== Description == Currently no description in our database for the given family. == Problems Variations == * Lossless Compression * Lossy Compression")
- 11:15, 15 February 2023 Family:CFG Problems (hist | edit) [178 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:CFG Problems}}== Description == Currently no description in our database for the given family. == Problems Variations == * CFG Parsing * CFG Recognition")
- 11:15, 15 February 2023 Family:The Vertex Cover Problem (hist | edit) [234 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:The Vertex Cover Problem}}== Description == Currently no description in our database for the given family. == Problems Variations == * The Vertex Cover Problem * The Vertex Cover Problem, Degrees Bounded By 3")
- 11:15, 15 February 2023 Family:4NF Decomposition (hist | edit) [296 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:4NF Decomposition}}== Description == Currently no description in our database for the given family. == Problems Variations == * 4NF Decomposition * 4NF Decomposition for Conflict-Free Dependency Sets * 4NF Decomposition for Functional and Multivalued Dependency Sets")
- 11:15, 15 February 2023 Family:BCNF Decomposition (hist | edit) [191 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:BCNF Decomposition}}== Description == Currently no description in our database for the given family. == Problems Variations == * BCNF Decomposition * Decisional BCNF")
- 11:15, 15 February 2023 Family:Dependency Inference Problem (hist | edit) [247 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Dependency Inference Problem}}== Description == Currently no description in our database for the given family. == Problems Variations == * Functional Dependency Inference Problem * Multivalued Dependency Inference Problem")
- 11:15, 15 February 2023 Family:Poisson Problem (hist | edit) [213 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Poisson Problem}}== Description == Currently no description in our database for the given family. == Problems Variations == * 2-Dimensional Poisson Problem * 3-Dimensional Poisson Problem")
- 11:14, 15 February 2023 Family:The Traveling-Salesman Problem (hist | edit) [214 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:The Traveling-Salesman Problem}}== Description == Currently no description in our database for the given family. == Problems Variations == * Approximate TSP * Maximum TSP * Minimum TSP")
- 11:14, 15 February 2023 Family:Clique Problems (hist | edit) [280 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Clique Problems}}== Description == Currently no description in our database for the given family. == Problems Variations == * Enumerating Maximal Cliques, arbitrary graph * Exact k-Clique * Max-Weight k-Clique * Min-Weight k-Clique * k-Clique")
- 11:14, 15 February 2023 Family:Graph Edit Distance Computation (hist | edit) [191 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Graph Edit Distance Computation}}== Description == Currently no description in our database for the given family. == Problems Variations == * Exact GED * Inexact GED")
- 11:14, 15 February 2023 Family:Lowest Common Ancestor (hist | edit) [407 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Lowest Common Ancestor}}== Description == Currently no description in our database for the given family. == Problems Variations == * Lowest Common Ancestor * Lowest Common Ancestor with Linking * Lowest Common Ancestor with Linking Roots * Lowest Common Ancestor with Static Trees * Lowest Common Ancestors with Linking and Cutting * Off-Line Lowest Common Ancestor")
- 11:14, 15 February 2023 Family:DFA Minimization (hist | edit) [242 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:DFA Minimization}}== Description == Currently no description in our database for the given family. == Problems Variations == * Acyclic DFA Minimization * Cyclic Nontrivial SCCs DFA Minimization * DFA Minimization")
- 11:14, 15 February 2023 Family:Register Allocation (hist | edit) [210 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Register Allocation}}== Description == Currently no description in our database for the given family. == Problems Variations == * Global Register Allocation * Local Register Allocation")
- 11:14, 15 February 2023 Family:Nearest Neighbor Search (hist | edit) [279 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Nearest Neighbor Search}}== Description == Currently no description in our database for the given family. == Problems Variations == * k Approximate Nearest Neighbors Search * k Nearest Neighbors Search")
- 11:14, 15 February 2023 Family:Root Computation (hist | edit) [229 bytes] Admin (talk | contribs) (Redirected page to Root Computation) Tag: New redirect
- 11:14, 15 February 2023 Family:Eigenvalues (Iterative Methods) (hist | edit) [315 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Eigenvalues (Iterative Methods)}}== Description == Currently no description in our database for the given family. == Problems Variations == * All Eigenpairs * All Eigenvalues * Any Eigenpair * Any Eigenvalue * Eigenpair closest to mu * Eigenpair with the Largest Eigenvalue")
- 11:14, 15 February 2023 Family:Polygon Clipping (hist | edit) [249 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Polygon Clipping}}== Description == Currently no description in our database for the given family. == Problems Variations == * Polygon Clipping with Arbitrary Clipping Polygon * Polygon Clipping with Convex Clipping Polygon")
- 11:14, 15 February 2023 Family:Maximum-Weight Matching (hist | edit) [219 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Maximum-Weight Matching}}== Description == Currently no description in our database for the given family. == Problems Variations == * Bipartite Maximum-Weight Matching * Maximum-Weight Matching")
- 11:14, 15 February 2023 Family:Nash Equilibria (hist | edit) [171 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Nash Equilibria}}== Description == Currently no description in our database for the given family. == Problems Variations == * 2-Player * n-Player")
- 11:14, 15 February 2023 Family:Optimal Binary Search Trees (hist | edit) [270 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Optimal Binary Search Trees}}== Description == Currently no description in our database for the given family. == Problems Variations == * Alphabetic Tree Problem * Approximate OBST * Huffman Encoding * Optimal Binary Search Tree Problem")
- 11:14, 15 February 2023 Family:Generating Random Permutations (hist | edit) [209 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Generating Random Permutations}}== Description == Currently no description in our database for the given family. == Problems Variations == * Cyclic Permutations * General Permutations")
- 11:14, 15 February 2023 Family:SDD Systems Solvers (hist | edit) [205 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:SDD Systems Solvers}}== Description == Currently no description in our database for the given family. == Problems Variations == * Exact Laplacian Solver * Inexact Laplacian Solver")
- 11:14, 15 February 2023 Family:Maximum Cardinality Matching (hist | edit) [250 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Maximum Cardinality Matching}}== Description == Currently no description in our database for the given family. == Problems Variations == * Bipartite Graph MCM * General Graph MCM * Planar Bipartite Graph Perfect Matching")
- 11:14, 15 February 2023 Family:Line Clipping (hist | edit) [225 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Line Clipping}}== Description == Currently no description in our database for the given family. == Problems Variations == * Convex Polygonal Window * Convex Polyhedral Window * Rectangular Window")
- 11:14, 15 February 2023 Family:Sequence Alignment (hist | edit) [232 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Sequence Alignment}}== Description == Currently no description in our database for the given family. == Problems Variations == * Edit Distance, constant-size alphabet * Edit Sequence, constant-size alphabet")
- 11:14, 15 February 2023 Family:String Search (hist | edit) [195 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:String Search}}== Description == Currently no description in our database for the given family. == Problems Variations == * Multiple String Search * Single String Search")
- 11:13, 15 February 2023 Family:LU Decomposition (hist | edit) [221 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:LU Decomposition}}== Description == Currently no description in our database for the given family. == Problems Variations == * Rectangular Matrix LU Decomposition * Square Matrix LU Decomposition")
- 11:13, 15 February 2023 Family:Integer Factoring (hist | edit) [189 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Integer Factoring}}== Description == Currently no description in our database for the given family. == Problems Variations == * Integer Factoring * Smallest Factor")
- 11:13, 15 February 2023 Family:All-Pairs Shortest Paths (APSP) (hist | edit) [827 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:All-Pairs Shortest Paths (APSP)}}== Description == Currently no description in our database for the given family. == Problems Variations == * (5/3)-approximate ap-shortest paths * APSP * APSP on Dense Directed Graphs with Arbitrary Weights * APSP on Dense Directed Unweighted Graphs * APSP on Dense Undirected Graphs with Arbitrary Weights * APSP on Dense Undirected Graphs with Positive Integer Weights * APSP on Dense Undirected...")
- 11:13, 15 February 2023 Family:Shortest Path (Directed Graphs) (hist | edit) [532 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Shortest Path (Directed Graphs)}}== Description == Currently no description in our database for the given family. == Problems Variations == * 1-sensitive (3/2)-approximate ss-shortest paths * 1-sensitive decremental st-shortest paths * 2-sensitive (7/5)-approximate st-shortest paths * 2-sensitive decremental st-shortest paths * General Weights * Nonnegative Integer Weights * Nonnegative Weights * Replacement Paths Problem...")
- 11:13, 15 February 2023 Family:Closest Pair Problem (hist | edit) [339 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Closest Pair Problem}}== Description == Currently no description in our database for the given family. == Problems Variations == * 2-dimensional array representation * 2-dimensional space, $l_m$ (or $l_\infty$) norm * 2-dimensional space, Euclidean metric * k-dimensional space, $l_m$ (or $l_\infty$) norm")
- 11:12, 15 February 2023 Family:Minimum Spanning Tree (MST) (hist | edit) [380 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Minimum Spanning Tree (MST)}}== Description == Currently no description in our database for the given family. == Problems Variations == * Directed (Optimum Branchings), General MST * Directed (Optimum Branchings), Super Dense MST * Undirected, Dense MST * Undirected, General MST * Undirected, Integer Weights MST * Undirected, Planar MST")
- 11:12, 15 February 2023 Family:Strongly Connected Components (hist | edit) [356 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Strongly Connected Components}}== Description == Currently no description in our database for the given family. == Problems Variations == * 2 Strong Components (dynamic) * Connected Subgraph * Maximum Strongly Connected Component * Strong Connectivity (dynamic) * Strongly Connected Components * Transitive Closure")
- 11:12, 15 February 2023 Family:Convex Hull (hist | edit) [314 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Convex Hull}}== Description == Currently no description in our database for the given family. == Problems Variations == * 2-dimensional Convex Hull * 2-dimensional Convex Hull, Dynamic * 2-dimensional Convex Hull, Online * 3-dimensional Convex Hull * d-dimensional Convex Hull")
- 11:12, 15 February 2023 Family:Line segment intersection (hist | edit) [443 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Line segment intersection}}== Description == Currently no description in our database for the given family. == Problems Variations == * Counting number of intersection points, line segments * Reporting all intersection points, convex polygons * Reporting all intersection points, general polygons * Reporting all intersection points, generalized segments * Reporting all intersection points, line segments")
- 11:12, 15 February 2023 Family:Linear Programming (hist | edit) [275 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Linear Programming}}== Description == Currently no description in our database for the given family. == Problems Variations == * 0-1 Linear Programming * General Linear Programming * Integer Linear Programming * Linear Programming with Reals")
- 11:12, 15 February 2023 Family:Linear System (hist | edit) [320 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Linear System}}== Description == Currently no description in our database for the given family. == Problems Variations == * General Linear System * Non-Definite, Symmetric Matrix * Positive Definite, Hermitian Matrix * Sparse Linear System * Toeplitz Matrix * Vandermonde Matrix")
- 11:12, 15 February 2023 Family:Matrix Product (hist | edit) [342 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Matrix Product}}== Description == Currently no description in our database for the given family. == Problems Variations == * $(\min, \leq)$ Product * Boolean Matrix Multiplication * Boolean Matrix Multiplication (Combinatorial) * Distance Product * Matrix Multiplication * Matrix Product Verification")
- 11:12, 15 February 2023 Family:Maximum Flow (hist | edit) [339 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Maximum Flow}}== Description == Currently no description in our database for the given family. == Problems Variations == * All-Pairs Maximum Flow * Integer Maximum Flow * Maximum Local Edge Connectivity * Minimum-Cost Flow * Non-integer Maximum Flow * Unweighted Maximum Flow * st-Maximum Flow")
- 11:12, 15 February 2023 Family:Longest Common Subsequence (hist | edit) [233 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Longest Common Subsequence}}== Description == Currently no description in our database for the given family. == Problems Variations == * Longest Common Subsequence * Longest Common Substring with don't cares")
- 11:12, 15 February 2023 Family:Matrix Chain Multiplication (hist | edit) [273 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Matrix Chain Multiplication}}== Description == Currently no description in our database for the given family. == Problems Variations == * Approximate MCOP * Approximate MCSP * Matrix Chain Ordering Problem * Matrix Chain Scheduling Problem")
- 11:11, 15 February 2023 Family:Sorting (hist | edit) [201 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Sorting}}== Description == Currently no description in our database for the given family. == Problems Variations == * Comparison Sorting * Non-Comparison Sorting * Sorting")
- 11:11, 15 February 2023 Domain:Cryptography (hist | edit) [3,125 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Cryptography}}== Description == Cryptography is the practice and study of techniques for secure communication in the presence of adversarial behavior. More generally, cryptography is about constructing and analyzing protocols that prevent third parties or the public from reading private messages; various aspects in information security such as data confidentiality, data integrity, authentication, and non-repudiation are central to modern cryptography. Mod...")
- 11:11, 15 February 2023 Domain:Statistics (hist | edit) [1,551 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Statistics}}== Description == Machine learning (ML) is the study of computer algorithms that can improve automatically through experience and by the use of data. It is seen as a part of artificial intelligence. Machine learning algorithms build a model based on sample data, known as "training data", in order to make predictions or decisions without being explicitly programmed to do so. Machine learning algorithms are used in a wide variety of applications...")
- 11:11, 15 February 2023 Domain:Robotics (hist | edit) [2,546 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Robotics}}== Description == Robotics is an interdisciplinary field that integrates computer science and engineering. Robotics involves design, construction, operation, and use of robots. The goal of robotics is to design machines that can help and assist humans. Robotics integrates fields of mechanical engineering, electrical engineering, information engineering, mechatronics, electronics, bioengineering, computer engineering, control engineering, softwar...")
- 11:11, 15 February 2023 Domain:Operating Systems (hist | edit) [2,630 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Operating Systems}}== Description == An operating system (OS) is system software that manages computer hardware, software resources, and provides common services for computer programs. Time-sharing operating systems schedule tasks for efficient use of the system and may also include accounting software for cost allocation of processor time, mass storage, printing, and other resources. For hardware functions such as input and output and memory allocation...")
- 11:11, 15 February 2023 Domain:Numerical Analysis (hist | edit) [3,113 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Numerical Analysis}}== Description == Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts. Current growth in computi...")
- 11:11, 15 February 2023 Domain:Image Processing (hist | edit) [2,251 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Image Processing}}== Description == Digital image processing is the use of a digital computer to process digital images through an algorithm. As a subcategory or field of digital signal processing, digital image processing has many advantages over analog image processing. It allows a much wider range of algorithms to be applied to the input data and can avoid problems such as the build-up of noise and distortion during processing. Since images are defined...")
- 11:11, 15 February 2023 Domain:Databases (hist | edit) [1,423 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Databases}}== Description == In computing, a database is an organized collection of data stored and accessed electronically from a computer system. Where databases are more complex they are often developed using formal design and modeling techniques. The database management system (DBMS) is the software that interacts with end users, applications, and the database itself to capture and analyze the data. The DBMS software additionally encompasses the core...")
- 11:11, 15 February 2023 Domain:Combinatorics (hist | edit) [5,333 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Combinatorics}}== Description == == Problems Within Domain == * #2-Graph Coloring * #3-Graph Coloring * #4-Graph Coloring * #5-Graph Coloring * #k-Graph Coloring * $(\min, \leq)$ Product * (5/3)-approximate ap-shortest paths * 1-sensitive (3/2)-approximate ss-shortest paths * 1-sensitive decremental st-shortest paths * 1D Maximum Subarray * 2 Strong Components (dynamic) * 2-Graph Coloring * 2-sensitive...")
- 11:11, 15 February 2023 Domain:Bioinformatics (hist | edit) [1,524 bytes] Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Bioinformatics}}== Description == Bioinfromatics an interdisciplinary field that develops methods and software tools for understanding biological data, in particular when the data sets are large and complex. As an interdisciplinary field of science, bioinformatics combines biology, computer science, information engineering, mathematics and statistics to analyze and interpret the biological data. Bioinformatics has been used for in silico analyses of biolo...")
- 11:11, 15 February 2023 List:Domains (hist | edit) [437 bytes] Admin (talk | contribs) (Created page with "* Bioinformatics * Combinatorics * Databases * Image Processing * Numerical Analysis * Operating Systems * Robotics * Signal Processing * Statistics * Cryptography")
- 11:11, 15 February 2023 List:Hypotheses (hist | edit) [1,697 bytes] Admin (talk | contribs) (Created page with "* Exponential Time Hypothesis (ETH) * Strong Exponential Time Hypothesis (SETH) * Orthogonal Vectors Hypothesis (OVH) * Unbalanced Orthogonal Vectors Hypothesis (UOVH) * k-OV Hypothesis * k-Clique Hypothesis * 3SUM Hypothesis (3-SUM Hypothes...")
- 11:11, 15 February 2023 List:Problem Families (hist | edit) [10,798 bytes] Admin (talk | contribs) (Created page with "== Bioinformatics == <ul style="display: grid; grid-template-columns: repeat(2, minmax(0, 1fr));"> <li> All Maximal Non-Branching Paths in a Graph</li> <li> Cyclic Peptide Sequencing Problem</li> <li> De Novo Genome Assembly</li> <li> Motif Search</li> <li>Family:Sequence Alignme...")