A Decomposition Theorem for Maximum Weight Bipartite Matchings with Applications to Evolutionary Trees
نویسندگان
چکیده
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/y). We present a new decomposition theorem for maximum weight bipartite matchings and use it to design an O( √ nW/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.
منابع مشابه
A Decomposition Theorem for Maximum Weight Bipartite Matchings
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/y). We present a new decomposition theorem for maximum weight bipartite matchings and use it to design an O( √ nW/k(n,W/N))-time algorithm for computing a maximum weight matching of G. T...
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