by Takashi Shiraki, Toshihide Ibaraki
http://www.kuamp.kyoto-u.ac.jp/labs/or/members/naga/TC/99002.ps
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Abstract:
Abstract 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 satises 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 log n) time, where n = jV j and T f is the time to compute the value of f(X) for a subset X V.
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