An 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 $s$-$t$-path TSP by analyzing the Christofides algorithm with lonely edge deletion, enhancing understanding of the LP relaxation's approximation quality.

Contribution

It provides a refined analysis of the best-of-many Christofides algorithm with lonely edge deletion, leading to a tighter upper bound on the integrality ratio for the $s$-$t$-path TSP.

Findings

Improved upper bound on the integrality ratio for the $s$-$t$-path TSP.

Enhanced analysis of the Christofides algorithm with lonely edge deletion.

Better understanding of the LP relaxation's approximation bounds.

Abstract

We give an improved analysis of the best-of-many Christofides algorithm with lonely edge deletion, which was proposed by Seb\H{o} and van Zuylen [2016]. This implies an improved upper bound on the integrality ratio of the standard LP relaxation for the $s$-$t$-path TSP.