Improved Approximations for Cubic and Cubic Bipartite TSP

TL;DR

This paper presents improved approximation algorithms for the Traveling Salesman Problem on cubic and cubic bipartite graphs, achieving tighter bounds on tour lengths through novel algorithmic techniques.

Contribution

It introduces a simple local improvement algorithm for cubic bipartite graphs and combines existing methods to enhance approximation guarantees for 2-connected cubic graphs.

Findings

Tour length at most 5/4 n - 2 for cubic bipartite graphs

Tour length at most (4/3 - 1/8754) n for 2-connected cubic graphs

Improved approximation bounds over previous results

Abstract

We show improved approximation guarantees for the traveling salesman problem on cubic graphs, and cubic bipartite graphs. For cubic bipartite graphs with n nodes, we improve on recent results of Karp and Ravi (2014) by giving a simple "local improvement" algorithm that finds a tour of length at most 5/4 n - 2. For 2-connected cubic graphs, we show that the techniques of Moemke and Svensson (2011) can be combined with the techniques of Correa, Larre and Soto (2012), to obtain a tour of length at most (4/3-1/8754)n.