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.
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Mathematics Subject Classification (1991): 90C27
A preliminary version of this paper has appeared in Proceedings of the Tenth International Conference on Integer Programming and Combinatorial Optimization (IPCO X), LNCS 3064, Springer-Verlag, 2004, pp. 352–367.
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Iwata, S., Moriguchi, S. & Murota, K. A capacity scaling algorithm for M-convex submodular flow. Math. Program. 103, 181–202 (2005). https://doi.org/10.1007/s10107-004-0562-3
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DOI: https://doi.org/10.1007/s10107-004-0562-3