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• 10:19, 15 February 2023 Admin talk contribs created page Directed (Optimum Branchings), General MST (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 Admin talk contribs created page Undirected, Integer Weights MST (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 Admin talk contribs created page Undirected, Planar MST (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 Admin talk contribs created page Undirected, Dense MST (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 Admin talk contribs created page Undirected, General MST (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 Admin talk contribs created page ConnSub (Redirected page to Connected Subgraph) Tag: New redirect
• 10:19, 15 February 2023 Admin talk contribs created page Connected Subgraph (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 Admin talk contribs created page SC2 (Redirected page to 2 Strong Components (dynamic)) Tag: New redirect
• 10:19, 15 February 2023 Admin talk contribs created page 2 Strong Components (dynamic) (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 Admin talk contribs created page Strong Connectivity (dynamic) (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 Admin talk contribs created page MaxSCC (Redirected page to Maximum Strongly Connected Component) Tag: New redirect
• 10:19, 15 February 2023 Admin talk contribs created page Maximum Strongly Connected Component (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...")
• 10:19, 15 February 2023 Admin talk contribs created page Transitive Closure (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...")
• 10:19, 15 February 2023 Admin talk contribs created page SCCs (Redirected page to Strongly Connected Components) Tag: New redirect
• 10:19, 15 February 2023 Admin talk contribs created page 2-dimensional Convex Hull, Dynamic (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...")
• 10:19, 15 February 2023 Admin talk contribs created page 2-dimensional Convex Hull, Online (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</...")
• 10:19, 15 February 2023 Admin talk contribs created page D-dimensional Convex Hull (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...")
• 10:19, 15 February 2023 Admin talk contribs created page 3-dimensional Convex Hull (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...")
• 10:19, 15 February 2023 Admin talk contribs created page 2-dimensional Convex Hull (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...")
• 10:19, 15 February 2023 Admin talk contribs created page Counting number of intersection points, line segments (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...")
• 10:18, 15 February 2023 Admin talk contribs created page Reporting all intersection points, general polygons (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...")
• 10:18, 15 February 2023 Admin talk contribs created page Reporting all intersection points, convex polygons (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...")
• 10:18, 15 February 2023 Admin talk contribs created page Reporting all intersection points, generalized segments (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...")
• 10:18, 15 February 2023 Admin talk contribs created page Reporting all intersection points, line segments (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...")
• 10:18, 15 February 2023 Admin talk contribs created page 0-1 Linear Programming (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...")
• 10:18, 15 February 2023 Admin talk contribs created page ILP (Redirected page to Integer Linear Programming) Tag: New redirect
• 10:18, 15 February 2023 Admin talk contribs created page Integer Linear Programming (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...")
• 10:18, 15 February 2023 Admin talk contribs created page Linear Programming with Reals (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"...")
• 10:18, 15 February 2023 Admin talk contribs created page General Linear Programming (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...")
• 10:18, 15 February 2023 Admin talk contribs created page Vandermonde Matrix (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...")
• 10:18, 15 February 2023 Admin talk contribs created page Toeplitz Matrix (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...")
• 10:18, 15 February 2023 Admin talk contribs created page Non-Definite, Symmetric Matrix (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...")
• 10:18, 15 February 2023 Admin talk contribs created page Positive Definite, Hermitian Matrix (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...")
• 10:18, 15 February 2023 Admin talk contribs created page Sparse Linear System (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:...")
• 10:18, 15 February 2023 Admin talk contribs created page General Linear System (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...")
• 10:18, 15 February 2023 Admin talk contribs created page $(\min, \leq)$ Matrix Multiplication (Redirected page to $(\min, \leq)$ Product) Tag: New redirect
• 10:18, 15 February 2023 Admin talk contribs created page $(\min, \leq)$ Product (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...")
• 10:18, 15 February 2023 Admin talk contribs created page Funny Matrix Multiplication (Redirected page to Distance Product) Tag: New redirect
• 10:18, 15 February 2023 Admin talk contribs created page $(\min, +)$ Matrix Product (Redirected page to Distance Product) Tag: New redirect
• 10:18, 15 February 2023 Admin talk contribs created page $(\min, +)$ Matrix Multiplication (Redirected page to Distance Product) Tag: New redirect
• 10:18, 15 February 2023 Admin talk contribs created page Distance Product (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...")
• 10:18, 15 February 2023 Admin talk contribs created page Matrix Product Verification (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...")
• 10:18, 15 February 2023 Admin talk contribs created page BMM (Combinatorial) (Redirected page to Boolean Matrix Multiplication (Combinatorial)) Tag: New redirect
• 10:18, 15 February 2023 Admin talk contribs created page Boolean Matrix Multiplication (Combinatorial) (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 ==...")
• 10:18, 15 February 2023 Admin talk contribs created page And-or Matrix Product (Redirected page to Boolean Matrix Multiplication) Tag: New redirect
• 10:18, 15 February 2023 Admin talk contribs created page BMM (Redirected page to Boolean Matrix Multiplication) Tag: New redirect
• 10:18, 15 February 2023 Admin talk contribs created page Boolean Matrix Multiplication (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>...")
• 10:18, 15 February 2023 Admin talk contribs created page Maximum Local Edge Connectivity (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...")
• 10:18, 15 February 2023 Admin talk contribs created page All-Pairs Maximum Flow (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...")
• 10:18, 15 February 2023 Admin talk contribs created page MCF (Redirected page to Minimum-Cost Flow) Tag: New redirect

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