New Inapproximability Bounds for TSP

TL;DR

This paper advances the understanding of the metric Traveling Salesman Problem by establishing new inapproximability bounds, improving previous results and introducing novel reduction techniques and constructions.

Contribution

It presents improved explicit inapproximability bounds for metric TSP and introduces new bounded occurrence CSP reductions and a bounded degree wheel amplifier.

Findings

Improved symmetric TSP inapproximability bound to 123/122.

Enhanced asymmetric TSP inapproximability bound to 75/74.

First improvement in over a decade for asymmetric TSP bounds.

Abstract

In this paper, we study the approximability of the metric Traveling Salesman Problem (TSP) and prove new explicit inapproximability bounds for that problem. The best up to now known hardness of approximation bounds were 185/184 for the symmetric case (due to Lampis) and 117/116 for the asymmetric case (due to Papadimitriou and Vempala). We construct here two new bounded occurrence CSP reductions which improve these bounds to 123/122 and 75/74, respectively. The latter bound is the first improvement in more than a decade for the case of the asymmetric TSP. One of our main tools, which may be of independent interest, is a new construction of a bounded degree wheel amplifier used in the proof of our results.