Optimal Augmentation of a Submodular and Posi - modular Set Function by a Multigraph
نویسندگان
چکیده
Given a nite set V and a set function f : 2 V 7! Z, we consider the problem of constructing an undirected multigraph G = (V;E) such that the cut function c G : 2 V 7! Z of G and f together has value at least 2 for all non-empty and proper subsets of V . If f is intersecting submodular and posi-modular, and satis es the tripartite inequality, then we show that such a multigraph G with the minimum number of edges can be found in O((T f + 1)n 4 logn) time, where n = jV j and T f is the time to compute the value of f(X) for a subset X V . keywords: algorithms, submodular function, posi-modular function, minimum cut, edgeconnectivity, undirected graph, edge-splitting, graph augmentation. 1 The current address: Department of Information and Computer Sciences, Toyohashi University of Technology, Tempaku, Toyohashi, 441-8580, Japan. [email protected]
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