Bipartite graphMaximum matchingParallel algorithmTime complexitySummary: This paper shows that the maximum matching problem on bipartite graphs can be solved in $O(n(\\log\\log n)\\sp 2)$ time with $O(n\\sp 3/\\log\\log n)$ processors on a single instruction stream, multiple data ...
>>> graph = csr_matrix([[0, 0, 1], [1, 1, 0]]) 在这里,1 可以是任何东西,只要它们最终被存储为稀疏矩阵中的元素。我们现在可以计算最大匹配如下: >>> print(maximum_bipartite_matching(graph, perm_type='column')) [2 0] >>> print(maximum_bipartite_matching(graph, perm_type='row')...
内容提示: A Tight Lower Bound for the Weights ofMaximum Weight Matching in Bipartite GraphsShibsankar Das ?1,2 and Kalpesh Kapoor 21Department of MathematicsInstitute of Science, Banaras Hindu University, Varanasi - 221 005, India.2Department of MathematicsIndian Institute of Technology Guwahati, ...
The present paper shows how to construct a maximum matching in a bipartite graph with n vertices and m edges in a number of computation steps proportional to (m + n)x/. Key words, algorithm, algorithmic analysis, bipartite graphs, computational complexity, graphs, matching 1. Introduction. Sup...
All vertices in residual graph increase monotonically. Total number of iterations is O(VE) V=Vertices, E=Edges Each iteration O(E) Therefore total runtimeO(VE2) Maximum matching in bipartite graphs 二分图最大匹配 二分图:简单来说,如果图中点可以被分为两组,并且使得所有边都跨越组的边界,则这...
A graph is said to be factor-critical if G−v has a perfect matching for every v∈V(G). Clearly, any factor-critical graph has near-perfect matchings. A maximum matching of G is a matching which covers as many vertices of G as possible. Assume that G is a bipartite graph with ...
In the maximum matching problem we are asked to find a matching M of maximum size in a given input graph G = (V,E). The maximum matching problem in bipartite graphs can be easily reduced to a maximum flow problem in unit graphs that can be solved in O(m n) time using Dinic's ...
A bipartite graph G=(V,W,E) is convex if there exists an ordering of the vertices of W such that, for each v鈭圴, the neighbors of v are consecutive in W. In this work we describe a coarse grained parallel algorithm for the maximum matching problem in a convex bipartite graph. For...
1. 二分图匹配(Bipartite Matching)# 1.1 匹配(Matching)# Def. Given an undirected graph G=(V,E), subset of edges M⊆E is a matching if each node appears in at most one edge in M. 定义. 给定一个无向图G=(V,E), 如果一个边的集合M⊆E并且每个顶点最多只出现在一条M中的边中, ...
For each component l, we multiply the weight of each edge incident to a vertex of component l by γl, and denote the resulting weighted graph by G(γ). We refer to the problem of finding a maximal matching of minimum weight in a complete weighted bipartite graph as Min-Sum Weighted ...