A linear time approximation scheme for Euclidean TSP

Yair Bartal, Lee Ad Gottlieb

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

21 Scopus citations

Abstract

The Traveling Salesman Problem (TSP) is among the most famous NP-hard optimization problems. The special case of TSP in bounded-dimensional Euclidean spaces has been a particular focus of research: The celebrated results of Arora [Aro98] and Mitchell [Mit99] - Along with subsequent improvements of Rao and Smith [RS98] - demonstrated a polynomial time approximation scheme for this problem, ultimately achieving a runtime of Od,ε(n log n). In this paper, we present a linear time approximation scheme for Euclidean TSP, with runtime Od,ε(n). This improvement resolves a 15 year old conjecture of Rao and Smith, and matches for Euclidean spaces the bound known for a broad class of planar graphs [Kle08].

Original languageAmerican English
Title of host publicationProceedings - 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, FOCS 2013
Pages698-706
Number of pages9
DOIs
StatePublished - 2013
Event2013 IEEE 54th Annual Symposium on Foundations of Computer Science, FOCS 2013 - Berkeley, CA, United States
Duration: 27 Oct 201329 Oct 2013

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)0272-5428

Conference

Conference2013 IEEE 54th Annual Symposium on Foundations of Computer Science, FOCS 2013
Country/TerritoryUnited States
CityBerkeley, CA
Period27/10/1329/10/13

Keywords

  • Computations on discrete structures
  • Geometrical problems and computations

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