Persistency of linear programming relaxations for the stable set problem

• 成果类型: Article
• 署名作者: Rodriguez-Heck, Elisabeth; Stickler, Karl; Walter, Matthias; Weltge, Stefan
• 署名单位: RWTH Aachen University; University of Twente; Technical University of Munich
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-020-01600-3
• 发表日期: 2022
• 页码: 387-407
• 关键词: graphs

摘要

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.