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• 10:23, 15 February 2023 Admin talk contribs created page 2D Maximum Subarray (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...")
• 10:23, 15 February 2023 Admin talk contribs created page Maximum Subsequence (Redirected page to 1D Maximum Subarray) Tag: New redirect
• 10:23, 15 February 2023 Admin talk contribs created page 1D Maximum Subarray (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...")
• 10:23, 15 February 2023 Admin talk contribs created page Maximum Subarray (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...")
• 10:23, 15 February 2023 Admin talk contribs created page Longest Path on Interval Graphs (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...")
• 10:23, 15 February 2023 Admin talk contribs created page Stable Pair Checking (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...")
• 10:23, 15 February 2023 Admin talk contribs created page Stable Matching Verification (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...")
• 10:23, 15 February 2023 Admin talk contribs created page Boolean d-Attribute Stable Matching (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...")
• 10:23, 15 February 2023 Admin talk contribs created page SRP (Redirected page to Stable Roommates Problem) Tag: New redirect
• 10:23, 15 February 2023 Admin talk contribs created page Stable Roommates Problem (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...")
• 10:23, 15 February 2023 Admin talk contribs created page Almost Stable Marriage Problem (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...")
• 10:23, 15 February 2023 Admin talk contribs created page Stable Matching Problem, SMP (Redirected page to Stable Marriage Problem) Tag: New redirect
• 10:23, 15 February 2023 Admin talk contribs created page Stable Marriage Problem (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: ...")
• 10:23, 15 February 2023 Admin talk contribs created page Factorization of Polynomials Over Finite Fields (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 (...")
• 10:23, 15 February 2023 Admin talk contribs created page Lossless Compression (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....")
• 10:23, 15 February 2023 Admin talk contribs created page Lossy Compression (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...")
• 10:23, 15 February 2023 Admin talk contribs created page Finding Association Rules (Redirected page to Finding Frequent Itemsets) Tag: New redirect
• 10:23, 15 February 2023 Admin talk contribs created page Finding Frequent Itemsets (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...")
• 10:23, 15 February 2023 Admin talk contribs created page CFG Recognition (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...")
• 10:23, 15 February 2023 Admin talk contribs created page CFG Parsing (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...")
• 10:23, 15 February 2023 Admin talk contribs created page 3DVC (Redirected page to The Vertex Cover Problem, Degrees Bounded By 3) Tag: New redirect
• 10:23, 15 February 2023 Admin talk contribs created page The Vertex Cover Problem, Degrees Bounded By 3 (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...")
• 10:23, 15 February 2023 Admin talk contribs created page VC (Redirected page to The Vertex Cover Problem) Tag: New redirect
• 10:23, 15 February 2023 Admin talk contribs created page The Vertex Cover Problem (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...")
• 10:23, 15 February 2023 Admin talk contribs created page 4NF Decomposition for Conflict-Free Dependency Sets (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...")
• 10:23, 15 February 2023 Admin talk contribs created page 4NF Decomposition for Functional and Multivalued Dependency Sets (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 $R^*$,...")
• 10:23, 15 February 2023 Admin talk contribs created page Fourth Normal Form Decomposition (Redirected page to 4NF Decomposition) Tag: New redirect
• 10:23, 15 February 2023 Admin talk contribs created page 4NF Decomposition (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...")
• 10:23, 15 February 2023 Admin talk contribs created page Decisional Boyce-Codd Normal Form (Redirected page to Decisional BCNF) Tag: New redirect
• 10:23, 15 February 2023 Admin talk contribs created page Decisional BCNF (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...")
• 10:22, 15 February 2023 Admin talk contribs created page Boyce-Codd Normal Form Decomposition (Redirected page to BCNF Decomposition) Tag: New redirect
• 10:22, 15 February 2023 Admin talk contribs created page Multivalued Dependency Inference Problem (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...")
• 10:22, 15 February 2023 Admin talk contribs created page Functional Dependency Inference Problem (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...")
• 10:22, 15 February 2023 Admin talk contribs created page Subset Sum (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...")
• 10:22, 15 February 2023 Admin talk contribs created page De Novo Genome Assembly (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...")
• 10:22, 15 February 2023 Admin talk contribs created page Delaunay Triangulation (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...")
• 10:22, 15 February 2023 Admin talk contribs created page 3-Dimensional Poisson Problem (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...")
• 10:22, 15 February 2023 Admin talk contribs created page Two-dimensional elliptic partial differential equations (Redirected page to 2-Dimensional Poisson Problem) Tag: New redirect
• 10:22, 15 February 2023 Admin talk contribs created page 2-Dimensional Poisson Problem (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 |- | ...")
• 10:22, 15 February 2023 Admin talk contribs created page Approximate TSP (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....")
• 10:22, 15 February 2023 Admin talk contribs created page Maximum TSP (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...")
• 10:22, 15 February 2023 Admin talk contribs created page TSP (Redirected page to Minimum TSP) Tag: New redirect
• 10:22, 15 February 2023 Admin talk contribs created page Minimum TSP (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...")
• 10:22, 15 February 2023 Admin talk contribs created page Max-Weight k-Clique (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...")
• 10:22, 15 February 2023 Admin talk contribs created page Min-Weight k-Clique (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...")
• 10:22, 15 February 2023 Admin talk contribs created page Exact k-Clique (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.")
• 10:22, 15 February 2023 Admin talk contribs created page K-Clique (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...")
• 10:22, 15 February 2023 Admin talk contribs created page Enumerating Maximal Cliques, arbitrary graph (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...")
• 10:22, 15 February 2023 Admin talk contribs created page Inexact GED (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...")
• 10:22, 15 February 2023 Admin talk contribs created page GED Computation (Redirected page to Exact GED) Tag: New redirect

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