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• 10:20, 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...")
• 10:20, 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>...")
• 10:20, 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...")
• 10:20, 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...")
• 10:20, 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...")
• 10:20, 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"...")
• 10:20, 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...")
• 10:20, 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...")
• 10:20, 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%"...")
• 10:20, 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...")
• 10:20, 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...")
• 10:20, 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...")
• 10:20, 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 =...")
• 10:20, 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...")
• 10:20, 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...")
• 10:20, 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...")
• 10:20, 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...")
• 10:20, 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...")
• 10:20, 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...")
• 10:20, 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...")
• 10:20, 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...")
• 10:20, 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...")
• 10:20, 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...")
• 10:20, 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, [...")
• 10:20, 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...")
• 10:19, 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...")
• 10:19, 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-...")
• 10:19, 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...")
• 10:19, 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...")
• 10:19, 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...")
• 10:19, 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...")
• 10:19, 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...")
• 10:19, 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...")
• 10:19, 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...")
• 10:19, 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...")
• 10:19, 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...")
• 10:19, 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 ==...")
• 10:19, 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...")
• 10:19, 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...")
• 10:19, 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...")
• 10:19, 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...")
• 10:19, 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...")
• 10:19, 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,...")
• 10:19, 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...")
• 10:19, 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...")
• 10:19, 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...")
• 10:19, 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,...")
• 10:19, 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...")
• 10:19, 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...")
• 10:19, 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...")

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