TY - JOUR

T1 - The Graphical Traveling Salesperson Problem has no integer programming formulation in the original space

AU - Walter, Matthias

N1 - We thank R. Carr and N. Simonetti for stimulating discussions on the challenge of Naddef as well as an anonymous referee whose comments led to an improved presentation of the material.
Publisher Copyright:
© 2021

PY - 2021/7

Y1 - 2021/7

N2 - The Graphical Traveling Salesperson Problem is the problem of assigning, for a given weighted graph, a nonnegative number xe to each edge e such that the induced multi-subgraph is of minimum weight among those that are spanning, connected and Eulerian. Known MIP formulations are based on integer variables xe. Carr and Simonetti (IPCO 2021) showed that unless NP=coNP, no (reasonable) formulation can have integrality constraints only on x-variables, a challenge posed by Denis Naddef. We establish the same result unconditionally.

AB - The Graphical Traveling Salesperson Problem is the problem of assigning, for a given weighted graph, a nonnegative number xe to each edge e such that the induced multi-subgraph is of minimum weight among those that are spanning, connected and Eulerian. Known MIP formulations are based on integer variables xe. Carr and Simonetti (IPCO 2021) showed that unless NP=coNP, no (reasonable) formulation can have integrality constraints only on x-variables, a challenge posed by Denis Naddef. We establish the same result unconditionally.

KW - Formulation

KW - Graphical Traveling Salesperson Problem

KW - Integer programming

UR - http://www.scopus.com/inward/record.url?scp=85109083298&partnerID=8YFLogxK

U2 - 10.1016/j.orl.2021.06.015

DO - 10.1016/j.orl.2021.06.015

M3 - Article

AN - SCOPUS:85109083298

VL - 49

SP - 623

EP - 624

JO - Operations research letters

JF - Operations research letters

SN - 0167-6377

IS - 4

ER -