A linear time approximation scheme for Euclidean TSP

Yair Bartal; Lee Ad Gottlieb

doi:10.1109/FOCS.2013.80

A linear time approximation scheme for Euclidean TSP

Yair Bartal, Lee Ad Gottlieb

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

26 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 language	English
Title of host publication	Proceedings - 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, FOCS 2013
Pages	698-706
Number of pages	9
DOIs	https://doi.org/10.1109/FOCS.2013.80
State	Published - 2013
Event	2013 IEEE 54th Annual Symposium on Foundations of Computer Science, FOCS 2013 - Berkeley, CA, United States Duration: 27 Oct 2013 → 29 Oct 2013

Publication series

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

Conference

Conference	2013 IEEE 54th Annual Symposium on Foundations of Computer Science, FOCS 2013
Country/Territory	United States
City	Berkeley, CA
Period	27/10/13 → 29/10/13

Keywords

Computations on discrete structures
Geometrical problems and computations

Access to Document

10.1109/FOCS.2013.80

Cite this

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title = "A linear time approximation scheme for Euclidean TSP",

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].",

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Bartal, Y & Gottlieb, LA 2013, A linear time approximation scheme for Euclidean TSP. in Proceedings - 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, FOCS 2013., 6686206, Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS, pp. 698-706, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, FOCS 2013, Berkeley, CA, United States, 27/10/13. https://doi.org/10.1109/FOCS.2013.80

A linear time approximation scheme for Euclidean TSP. / Bartal, Yair; Gottlieb, Lee Ad.
Proceedings - 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, FOCS 2013. 2013. p. 698-706 6686206 (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - 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].

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A linear time approximation scheme for Euclidean TSP

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