A (Slightly) Improved Approximation Algorithm for Metric TSP

TL;DR

This paper presents a randomized approximation algorithm for the metric Traveling Salesman Problem that improves upon the classic 3/2 approximation ratio by a small epsilon margin.

Contribution

It introduces a novel randomized algorithm achieving a slightly better approximation ratio than the longstanding 3/2 bound for metric TSP.

Findings

Achieves a 3/2 - epsilon approximation ratio for metric TSP.

Uses randomized techniques to improve approximation bounds.

Applicable for epsilon greater than 10^{-36}."

Abstract

For some $\epsilon > 10^{-36}$ we give a randomized $3/2-\epsilon$ approximation algorithm for metric TSP.