The traveling salesman problem: Low-dimensionality implies a polynomial time approximation scheme

Yair Bartal*, Lee Ad Gottlieb, Robert Krauthgamer

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

31 Scopus citations

Abstract

The Traveling Salesman Problem (TSP) is among the most famous NP-hard optimization problems. We design for this problem a randomized polynomial-time algorithm that computes a (1 + ε)-approximation to the optimal tour, for any fixed ε > 0, in TSP instances that form an arbitrary metric space with bounded intrinsic dimension. The celebrated results of Arora [Aro98] and Mitchell [Mit99] prove that the above result holds in the special case of TSP in a fixed-dimensional Euclidean space. Thus, our algorithm demonstrates that the algorithmic tractability of metric TSP depends on the dimensionality of the space and not on its specific geometry. This result resolves a problem that has been open since the quasi-polynomial time algorithm of Talwar [Tal04].

Original languageEnglish
Title of host publicationSTOC '12 - Proceedings of the 2012 ACM Symposium on Theory of Computing
Pages663-672
Number of pages10
DOIs
StatePublished - 2012
Event44th Annual ACM Symposium on Theory of Computing, STOC '12 - New York, NY, United States
Duration: 19 May 201222 May 2012

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Conference

Conference44th Annual ACM Symposium on Theory of Computing, STOC '12
Country/TerritoryUnited States
CityNew York, NY
Period19/05/1222/05/12

Keywords

  • doubling metrics
  • traveling salesman problem

Fingerprint

Dive into the research topics of 'The traveling salesman problem: Low-dimensionality implies a polynomial time approximation scheme'. Together they form a unique fingerprint.

Cite this