New inapproximability bounds for TSP

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 ca...

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Bibliographic Details
Published in:	Journal of computer and system sciences Vol. 81; no. 8; pp. 1665 - 1677
Main Authors:	Karpinski, Marek, Lampis, Michael, Schmied, Richard
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01.12.2015
Subjects:	Hardness of approximation Travelling Salesman Problem Hardness of approximation Travelling Salesman Problem
ISSN:	0022-0000, 1090-2724
Online Access:	Get full text
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Summary:	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.
ISSN:	0022-0000 1090-2724
DOI:	10.1016/j.jcss.2015.06.003