An LP-based 3/2-approximation algorithm for the graphic s-t path TSP

TL;DR

This paper introduces a novel linear programming-based algorithm for the graphic s-t path TSP, achieving a 1.5 approximation factor by leveraging narrow cuts, thus advancing the approximation algorithms for this problem.

Contribution

It presents the first LP-based 3/2-approximation algorithm for the graphic s-t path TSP, partially resolving an open question in the field.

Findings

Achieves a 1.5 approximation ratio for the problem.

Utilizes narrow cuts technique to improve approximation.

Advances understanding of LP-based approaches for TSP.

Abstract

We design a new LP-based algorithm for the graphic $s$-$t$ path Traveling Salesman Problem (TSP), which achieves the best approximation factor of 1.5. The algorithm is based on the idea of narrow cuts due to An, Kleinberg, and Shmoys. It partly answers an open question of Seb\H{o}.