A capacity scaling algorithm for M-convex submodular flow

Authors:
Satoru Iwata;Satoko Moriguchi;Kazuo Murota
Affiliations:
Graduate School of Information Science and Technology, University of Tokyo, 113-8656, Tokyo, Japan;CREST, Japan Science and Technology Agency, 332-0012, Saitama, Japan;Graduate School of Information Science and Technology, University of Tokyo, 113-8656, Tokyo, Japan and PRESTO JST,
Venue:
Mathematical Programming: Series A and B
Year:
2005

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Abstract

This paper presents a faster algorithm for the M-convex submodular flow problem, which is a generalization of the minimum-cost flow problem with an M-convex cost function for the flow-boundary, where an M-convex function is a nonlinear nonseparable discrete convex function on integer points. The algorithm extends the capacity scaling approach for the submodular flow problem by Fleischer, Iwata and McCormick (2002) with the aid of a novel technique of changing the potential by solving maximum submodular flow problems.