Decreasing Minimization on M-convex Sets: Algorithms and Applications
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.
Cite
@article{arxiv.2007.09618,
title = {Decreasing Minimization on M-convex Sets: Algorithms and Applications},
author = {András Frank and Kazuo Murota},
journal= {arXiv preprint arXiv:2007.09618},
year = {2021}
}
Comments
35 pages. This is a revised version of the second half of "A. Frank and K. Murota; Discrete decreasing minimization, PartI: Base-polyhedra with applications in network optimization" arXiv:1808.07600