Every rational polyhedron has finite split rank: new proof
Optimization and Control
2016-11-21 v2
Abstract
Split rank of a rational polyhedron is finite. The well known proof of this is based on the fact that split closure is stronger than the Chv\'{a}tal closure, and the Chv\'{a}tal rank of a rational polyhedron is finite due to the result of Chv\'{a}tal and Schrijver. In this note we provide an independent proof for the fact that every rational polyhedron has finite split rank. In principal, we construct a nonnegative potential function which decreases by at least one with "every" second split closure unless the integer hull of the polyhedron is reached.
Keywords
Cite
@article{arxiv.1606.05811,
title = {Every rational polyhedron has finite split rank: new proof},
author = {Kanstantsin Pashkovich},
journal= {arXiv preprint arXiv:1606.05811},
year = {2016}
}