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arXiv · 2007.09618

Decreasing Minimization on M-convex Sets: Algorithms and Applications

András Frank·Kazuo Murota
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Abstract

This paper is concerned with algorithms and applications of decreasing minimization on an M-convex set, which is the set of integral elements of an integral base-polyhedron. Based on a recent characterization of decreasingly minimal (dec-min) elements, we develop a strongly polynomial algorithm for computing a dec-min element of an M-convex set. The matroidal feature of the set of dec-min elements makes it possible to compute a minimum cost dec-min element, as well. Our second goal is to exhibit various applications in matroid and network optimization, resource allocation, and (hyper)graph orientation. We extend earlier results on semi-matchings to a large degree by developing a structural description of dec-min in-degree bounded orientations of a graph. This characterization gives rise to a strongly polynomial algorithm for finding a minimum edge-cost dec-min orientation.

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András Frank, Kazuo Murota. 2021-07-16. Decreasing Minimization on M-convex Sets: Algorithms and Applications. https://arxiv.org/abs/2007.09618

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