Approximation algorithms for the bottleneck asymmetric traveling salesman problem

Hyung-Chan An, Robert D. Kleinberg, David B. Shmoys

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

Abstract

We present the first nontrivial approximation algorithm for the bottleneck asymmetric traveling salesman problem. Given an asymmetric metric cost between n vertices, the problem is to find a Hamiltonian cycle that minimizes its bottleneck (or maximum-length edge) cost. We achieve an O(logn / loglogn) approximation performance guarantee by giving a novel algorithmic technique to shortcut Eulerian circuits while bounding the lengths of the shortcuts needed. This allows us to build on the recent result of Asadpour, Goemans, Ma̧dry, Oveis Gharan, and Saberi to obtain this guarantee. Furthermore, we show how our technique yields stronger approximation bounds in some cases, such as the bounded orientable genus case studied by Oveis Gharan and Saberi.

Original languageEnglish
Title of host publicationApproximation, Randomization, and Combinatorial Optimization
Subtitle of host publicationAlgorithms and Techniques - 13th International Workshop, APPROX 2010 and 14th International Workshop, RANDOM 2010, Proceedings
Pages1-11
Number of pages11
DOIs
Publication statusPublished - 2010 Nov 15
Event13th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2010 and 14th International Workshop on Randomization and Computation, RANDOM 2010 - Barcelona, Spain
Duration: 2010 Sep 12010 Sep 3

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6302 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other13th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2010 and 14th International Workshop on Randomization and Computation, RANDOM 2010
CountrySpain
CityBarcelona
Period10/9/110/9/3

Fingerprint

Asymmetric Traveling Salesman Problem
Traveling salesman problem
Approximation algorithms
Approximation Algorithms
Hamiltonians
Strong Approximation
Performance Guarantee
Hamiltonian circuit
Costs
Genus
Minimise
Metric
Networks (circuits)
Approximation

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

An, H-C., Kleinberg, R. D., & Shmoys, D. B. (2010). Approximation algorithms for the bottleneck asymmetric traveling salesman problem. In Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 13th International Workshop, APPROX 2010 and 14th International Workshop, RANDOM 2010, Proceedings (pp. 1-11). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6302 LNCS). https://doi.org/10.1007/978-3-642-15369-3_1
An, Hyung-Chan ; Kleinberg, Robert D. ; Shmoys, David B. / Approximation algorithms for the bottleneck asymmetric traveling salesman problem. Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 13th International Workshop, APPROX 2010 and 14th International Workshop, RANDOM 2010, Proceedings. 2010. pp. 1-11 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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An, H-C, Kleinberg, RD & Shmoys, DB 2010, Approximation algorithms for the bottleneck asymmetric traveling salesman problem. in Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 13th International Workshop, APPROX 2010 and 14th International Workshop, RANDOM 2010, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6302 LNCS, pp. 1-11, 13th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2010 and 14th International Workshop on Randomization and Computation, RANDOM 2010, Barcelona, Spain, 10/9/1. https://doi.org/10.1007/978-3-642-15369-3_1

Approximation algorithms for the bottleneck asymmetric traveling salesman problem. / An, Hyung-Chan; Kleinberg, Robert D.; Shmoys, David B.

Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 13th International Workshop, APPROX 2010 and 14th International Workshop, RANDOM 2010, Proceedings. 2010. p. 1-11 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6302 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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N2 - We present the first nontrivial approximation algorithm for the bottleneck asymmetric traveling salesman problem. Given an asymmetric metric cost between n vertices, the problem is to find a Hamiltonian cycle that minimizes its bottleneck (or maximum-length edge) cost. We achieve an O(logn / loglogn) approximation performance guarantee by giving a novel algorithmic technique to shortcut Eulerian circuits while bounding the lengths of the shortcuts needed. This allows us to build on the recent result of Asadpour, Goemans, Ma̧dry, Oveis Gharan, and Saberi to obtain this guarantee. Furthermore, we show how our technique yields stronger approximation bounds in some cases, such as the bounded orientable genus case studied by Oveis Gharan and Saberi.

AB - We present the first nontrivial approximation algorithm for the bottleneck asymmetric traveling salesman problem. Given an asymmetric metric cost between n vertices, the problem is to find a Hamiltonian cycle that minimizes its bottleneck (or maximum-length edge) cost. We achieve an O(logn / loglogn) approximation performance guarantee by giving a novel algorithmic technique to shortcut Eulerian circuits while bounding the lengths of the shortcuts needed. This allows us to build on the recent result of Asadpour, Goemans, Ma̧dry, Oveis Gharan, and Saberi to obtain this guarantee. Furthermore, we show how our technique yields stronger approximation bounds in some cases, such as the bounded orientable genus case studied by Oveis Gharan and Saberi.

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An H-C, Kleinberg RD, Shmoys DB. Approximation algorithms for the bottleneck asymmetric traveling salesman problem. In Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 13th International Workshop, APPROX 2010 and 14th International Workshop, RANDOM 2010, Proceedings. 2010. p. 1-11. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-15369-3_1