TY - JOUR
T1 - Persistency of linear programming relaxations for the stable set problem
AU - Rodríguez-Heck, Elisabeth
AU - Stickler, Karl
AU - Walter, Matthias
AU - Weltge, Stefan
PY - 2021/1/11
Y1 - 2021/1/11
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85099314938&partnerID=8YFLogxK
U2 - 10.1007/s10107-020-01600-3
DO - 10.1007/s10107-020-01600-3
M3 - Article
SN - 0025-5610
JO - Mathematical programming
JF - Mathematical programming
ER -