A 3/4 Differential Approximation Algorithm for Traveling Salesman Problem

TL;DR

This paper proves that the Traveling Salesman Problem (TSP) can be approximated within a 3/4 differential ratio, improving upon the previous best bound of 3/4 - O(1/n).

Contribution

The paper establishes a new differential approximation bound of 3/4 for TSP, surpassing the previous 2008 bound, advancing the understanding of TSP approximability.

Findings

TSP is 3/4-differential approximable.

Improves previous bound of 3/4 - O(1/n).

Advances theoretical understanding of TSP approximation limits.

Abstract

In this paper, we consider differential approximability of the traveling salesman problem (TSP). We show that TSP is $3/4$-differential approximable, which improves the currently best known bound $3/4 -O(1/n)$ due to Escoffier and Monnot in 2008, where $n$ denotes the number of vertices in the given graph.