Fair Integral Submodular Flows
Abstract
Integer-valued elements of an integral submodular flow polyhedron are investigated which are decreasingly minimal (dec-min) in the sense that their largest component is as small as possible, within this, the second largest component is as small as possible, and so on. As a main result, we prove that the set of dec-min integral elements of is the set of integral elements of another integral submodular flow polyhedron arising from by intersecting a face of with a box. Based on this description, we develop a strongly polynomial algorithm for computing not only a dec-min integer-valued submodular flow but even a cheapest one with respect to a linear cost-function. A special case is the problem of finding a strongly connected (or -edge-connected) orientation of a mixed graph whose in-degree vector is decreasingly minimal.
Cite
@article{arxiv.2012.07325,
title = {Fair Integral Submodular Flows},
author = {András Frank and Kazuo Murota},
journal= {arXiv preprint arXiv:2012.07325},
year = {2022}
}
Comments
27 pages. arXiv admin note: text overlap with arXiv:1907.02673