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• 10:28, 15 February 2023 Admin talk contribs created page Diameter 3 vs 7 (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, ...")
• 10:28, 15 February 2023 Admin talk contribs created page 4/3-Diameter (Redirected page to Diameter 2 vs 3) Tag: New redirect
• 10:28, 15 February 2023 Admin talk contribs created page Diameter 2 vs 3 (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, ...")
• 10:28, 15 February 2023 Admin talk contribs created page Diameter (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...")
• 10:28, 15 February 2023 Admin talk contribs created page Radius (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...")
• 10:27, 15 February 2023 Admin talk contribs created page Median (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...")
• 10:27, 15 February 2023 Admin talk contribs created page UOV (Redirected page to Unbalanced OV) Tag: New redirect
• 10:27, 15 February 2023 Admin talk contribs created page Unbalanced OV (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...")
• 10:27, 15 February 2023 Admin talk contribs created page 3-OV (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...")
• 10:27, 15 February 2023 Admin talk contribs created page K-OV (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; $d = omega(log(n))$...")
• 10:27, 15 February 2023 Admin talk contribs created page 2-OV (Redirected page to OV) Tag: New redirect
• 10:27, 15 February 2023 Admin talk contribs created page OV (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...")
• 10:27, 15 February 2023 Admin talk contribs created page MAX-CNF-SAT (Redirected page to MaxSAT) Tag: New redirect
• 10:27, 15 February 2023 Admin talk contribs created page MaxSAT (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...")
• 10:27, 15 February 2023 Admin talk contribs created page Renamable Horn (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,...")
• 10:27, 15 February 2023 Admin talk contribs created page Dual-Horn SAT (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)]...")
• 10:27, 15 February 2023 Admin talk contribs created page Horn SAT (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...")
• 10:27, 15 February 2023 Admin talk contribs created page XOR-SAT (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,...")
• 10:27, 15 February 2023 Admin talk contribs created page Monotone 3SAT (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...")
• 10:27, 15 February 2023 Admin talk contribs created page 4-SAT (Redirected page to 4SAT) Tag: New redirect
• 10:27, 15 February 2023 Admin talk contribs created page 4SAT (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]...")
• 10:27, 15 February 2023 Admin talk contribs created page 3-SAT-5 (Redirected page to 3SAT-5) Tag: New redirect
• 10:27, 15 February 2023 Admin talk contribs created page 3SAT-5 (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), ...")
• 10:27, 15 February 2023 Admin talk contribs created page 3-SAT (Redirected page to 3SAT) Tag: New redirect
• 10:27, 15 February 2023 Admin talk contribs created page 3SAT (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...")
• 10:27, 15 February 2023 Admin talk contribs created page 2-SAT (Redirected page to 2SAT) Tag: New redirect
• 10:27, 15 February 2023 Admin talk contribs created page 2SAT (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]...")
• 10:27, 15 February 2023 Admin talk contribs created page K-SAT (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...")
• 10:27, 15 February 2023 Admin talk contribs created page Monotone Not-All-Equal 3-SAT (Monotone NAE 3SAT) (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,...")
• 10:27, 15 February 2023 Admin talk contribs created page Not-All-Equal 3-SAT (NAE 3SAT) (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, [...")
• 10:27, 15 February 2023 Admin talk contribs created page All-Equal-SAT (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...")
• 10:27, 15 February 2023 Admin talk contribs created page Monotone Not-Exactly-1-in-3SAT (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...")
• 10:27, 15 February 2023 Admin talk contribs created page Monotone 1-in-3SAT (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...")
• 10:27, 15 February 2023 Admin talk contribs created page 1-in-3SAT (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,...")
• 10:27, 15 February 2023 Admin talk contribs created page DNF-SAT (Redirected page to Disjunctive Normal Form SAT) Tag: New redirect
• 10:27, 15 February 2023 Admin talk contribs created page Disjunctive Normal Form SAT (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...")
• 10:27, 15 February 2023 Admin talk contribs created page CNF-SAT (Redirected page to Conjunctive Normal Form SAT) Tag: New redirect
• 10:27, 15 February 2023 Admin talk contribs created page Conjunctive Normal Form SAT (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...")
• 10:27, 15 February 2023 Admin talk contribs created page Boolean Satisfiability (Redirected page to SAT) Tag: New redirect
• 10:27, 15 February 2023 Admin talk contribs created page SAT (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), [...")
• 10:27, 15 February 2023 Admin talk contribs created page Chromatic Polynomial (Created page with "#REDIRECT #k-Graph Coloring")
• 10:26, 15 February 2023 Admin talk contribs created page 5-Graph Coloring (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...")
• 10:26, 15 February 2023 Admin talk contribs created page 4-Graph Coloring (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...")
• 10:26, 15 February 2023 Admin talk contribs created page 3-Graph Coloring (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...")
• 10:26, 15 February 2023 Admin talk contribs created page 2-Graph Coloring (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...")
• 10:26, 15 February 2023 Admin talk contribs created page Chromatic Number (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...")
• 10:26, 15 February 2023 Admin talk contribs created page K-Graph Coloring (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...")
• 10:26, 15 February 2023 Admin talk contribs created page Link Analysis (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...")
• 10:26, 15 February 2023 Admin talk contribs created page No-Steal/Force (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.")
• 10:26, 15 February 2023 Admin talk contribs created page Steal/No-Force (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...")

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