Augmenting a Submodular and Posi-modular Set Function by a Multigraph

Hiroshi Nagamochi (), Takashi Shiraki () and Toshihide Ibaraki ()
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Hiroshi Nagamochi: Toyohashi University of Technology
Takashi Shiraki: NEC Networks Abiko
Toshihide Ibaraki: Kyoto University

Journal of Combinatorial Optimization, 2001, vol. 5, issue 2, No 3, 175-212

Abstract: Abstract Given a finite set V and a set function $$f:2^V \mapsto Z$$ , we consider the problem of constructing an undirected multigraph G = (V,E) such that the cut function $$C_G :2^V \mapsto Z{\text{ of }}G{\text{ and }}f$$ together has value at least 2 for all non-empty and proper subsets of V. If f is intersecting submodular and posi-modular, and satisfies the tripartite inequality, then we show that such a multigraph G with the minimum number of edges can be found in $$O\left( {\left( {T_f + 1} \right)n^4 \log n} \right)$$ time, where $$n = \left| V \right|{\text{ and }}T_f$$ is the time to compute the value of f(X) for a subset $$X \subset V$$ .

Keywords: algorithms; submodular function; posi-modular function; minimum cut; edge-connectivity; undirected graph; edge-splitting; graph augmentation (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1011409332456

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