Persistency of Linear Programming Relaxations for the Stable Set Problem
Discrete Mathematics
2020-11-25 v4 Combinatorics
Optimization and Control
Abstract
The Nemhauser-Trotter theorem states that the standard linear programming (LP) formulation for the stable set problem has a remarkable property, also known as (weak) persistency: for every optimal LP solution that assigns integer values to some variables, there exists an optimal integer solution in which these variables retain the same values. While the standard LP is defined by only non-negativity and edge constraints, a variety of other LP formulations have been studied and one may wonder whether any of them has this property as well. We show that any other formulation that satisfies mild conditions cannot have the persistency property on all graphs, unless it is always equal to the stable set polytope.
Keywords
Cite
@article{arxiv.1911.01478,
title = {Persistency of Linear Programming Relaxations for the Stable Set Problem},
author = {Elisabeth Rodríguez-Heck and Karl Stickler and Matthias Walter and Stefan Weltge},
journal= {arXiv preprint arXiv:1911.01478},
year = {2020}
}
Comments
17 pages, 6 figures