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A Decomposition Theorem for Maximum Weight Bipartite Matchings | Ming-Yang Kao
; Tak-Wah Lam
; Wing-Kin Sung
; Hing-Fung Ting
; | Date: |
11 Nov 2000 | Subject: | Data Structures and Algorithms; Discrete Mathematics ACM-class: E1; F2.2 | cs.DS cs.DM | Abstract: | Let G be a bipartite graph with positive integer weights on the edges and without isolated nodes. Let n, N and W be the node count, the largest edge weight and the total weight of G. Let k(x,y) be log(x)/log(x^2/y). We present a new decomposition theorem for maximum weight bipartite matchings and use it to design an O(sqrt(n)W/k(n,W/N))-time algorithm for computing a maximum weight matching of G. This algorithm bridges a long-standing gap between the best known time complexity of computing a maximum weight matching and that of computing a maximum cardinality matching. Given G and a maximum weight matching of G, we can further compute the weight of a maximum weight matching of G-{u} for all nodes u in O(W) time. | Source: | arXiv, cs.DS/0011015 | Services: | Forum | Review | PDF | Favorites |
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