Report on article The Travelling Salesman Problem: A Linear Programming Formulation

TL;DR

This paper presents a counterexample demonstrating the incorrectness of a linear programming formulation of the Traveling Salesman Problem, highlighting issues in the model and its potential extensions.

Contribution

It provides a counterexample that invalidates a previously proposed linear programming model for TSP, questioning its correctness and extension potential.

Findings

Counterexample shows the model is incorrect

Highlights limitations of the linear formulation

Questions the extension of the model to other problems

Abstract

This article describes counter example prepared in order to prove that linear formulation of TSP problem proposed in [arXiv:0803.4354] is incorrect (it applies also to QAP problem formulation in [arXiv:0802.4307]). Article refers not only to model itself, but also to ability of extension of proposed model to be correct.