Slightly Improved Upper Bound on the Integrality Ratio for the $s-t$ Path TSP

TL;DR

This paper improves the upper bound on the integrality ratio for the metric s-t Path TSP LP relaxation to 1.5273 by refining the analysis with a better auxiliary function.

Contribution

It provides a near-optimal choice of an auxiliary function that tightens the known upper bound on the integrality ratio for the s-t Path TSP.

Findings

Upper bound on integrality ratio improved to 1.5273

Refined analysis using a better auxiliary function

Advances theoretical understanding of LP relaxations for Path TSP

Abstract

In this paper we investigate the integrality ratio of the standard LP relaxation for the metric $s-t$ Path TSP. We make a near-optimal choice for an auxiliary function used in the analysis of Traub and Vygen which leads to an improved upper bound on the integrality ratio of 1.5273.