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A constant-factor approximation algorithm for the asymmetric traveling salesman problem

Authors:

Jakub Tarnawski,

László A. VéghAuthors Info & Claims

STOC 2018: Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing

Pages 204 - 213

https://doi.org/10.1145/3188745.3188824

Published: 20 June 2018 Publication History

Abstract

We give a constant-factor approximation algorithm for the asymmetric traveling salesman problem. Our approximation guarantee is analyzed with respect to the standard LP relaxation, and thus our result confirms the conjectured constant integrality gap of that relaxation.

Our techniques build upon the constant-factor approximation algorithm for the special case of node-weighted metrics. Specifically, we give a generic reduction to structured instances that resemble but are more general than those arising from node-weighted metrics. For those instances, we then solve Local-Connectivity ATSP, a problem known to be equivalent (in terms of constant-factor approximation) to the asymmetric traveling salesman problem.

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References

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Cited By

Saikia P(2024)An O(1)-rounds Deterministic Distributed Approximation Algorithm for the Traveling Salesman Problem in Congested Clique2024 20th International Conference on Distributed Computing in Smart Systems and the Internet of Things (DCOSS-IoT)10.1109/DCOSS-IoT61029.2024.00034(179-186)Online publication date: 29-Apr-2024
https://doi.org/10.1109/DCOSS-IoT61029.2024.00034
Khachay MNeznakhina ERyzhenko K(2023)Constant-Factor Approximation Algorithms for a Series of Combinatorial Routing Problems Based on the Reduction to the Asymmetric Traveling Salesman ProblemProceedings of the Steklov Institute of Mathematics10.1134/S0081543822060128319:S1(S140-S155)Online publication date: 16-Feb-2023
https://doi.org/10.1134/S0081543822060128
Khachay MNeznakhina KRizhenko K(2023)Prize-Collecting Asymmetric Traveling Salesman Problem Admits Polynomial Time Approximation Within a Constant RatioOptimization and Applications10.1007/978-3-031-22543-7_6(81-90)Online publication date: 3-Jan-2023
https://doi.org/10.1007/978-3-031-22543-7_6
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Index Terms

A constant-factor approximation algorithm for the asymmetric traveling salesman problem
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Paths and connectivity problems
2. Theory of computation
  1. Design and analysis of algorithms

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cover image ACM Conferences

STOC 2018: Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing

June 2018

1332 pages

ISBN:9781450355599

DOI:10.1145/3188745

General Chairs:
Ilias Diakonikolas
University of Southern California, USA
,
David Kempe
University of Southern California, USA
,
Program Chair:
Monika Henzinger
University of Vienna, Austria

Copyright © 2018 ACM.

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SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

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Published: 20 June 2018

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European Research Council
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STOC '18

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STOC '18: Symposium on Theory of Computing

June 25 - 29, 2018

CA, Los Angeles, USA

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Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Cited By

Saikia P(2024)An O(1)-rounds Deterministic Distributed Approximation Algorithm for the Traveling Salesman Problem in Congested Clique2024 20th International Conference on Distributed Computing in Smart Systems and the Internet of Things (DCOSS-IoT)10.1109/DCOSS-IoT61029.2024.00034(179-186)Online publication date: 29-Apr-2024
https://doi.org/10.1109/DCOSS-IoT61029.2024.00034
Khachay MNeznakhina ERyzhenko K(2023)Constant-Factor Approximation Algorithms for a Series of Combinatorial Routing Problems Based on the Reduction to the Asymmetric Traveling Salesman ProblemProceedings of the Steklov Institute of Mathematics10.1134/S0081543822060128319:S1(S140-S155)Online publication date: 16-Feb-2023
https://doi.org/10.1134/S0081543822060128
Khachay MNeznakhina KRizhenko K(2023)Prize-Collecting Asymmetric Traveling Salesman Problem Admits Polynomial Time Approximation Within a Constant RatioOptimization and Applications10.1007/978-3-031-22543-7_6(81-90)Online publication date: 3-Jan-2023
https://doi.org/10.1007/978-3-031-22543-7_6
Agarwal SAkella S(2023)The single robot line coverage problem: Theory, algorithms, and experimentsNetworks10.1002/net.2217182:4(479-505)Online publication date: 25-Jul-2023
https://doi.org/10.1002/net.22171
Ghuge RNagarajan V(2022)Quasi-Polynomial Algorithms for Submodular Tree Orienteering and Directed Network Design ProblemsMathematics of Operations Research10.1287/moor.2021.118147:2(1612-1630)Online publication date: May-2022
https://doi.org/10.1287/moor.2021.1181
Bérczi KMnich MVincze R(2022)A 3/2-Approximation for the Metric Many-Visits Path TSPSIAM Journal on Discrete Mathematics10.1137/22M148341436:4(2995-3030)Online publication date: 8-Dec-2022
https://doi.org/10.1137/22M1483414
Wang Y(2022)The Polynomial Randomized Algorithm to Compute Bounded Degree Graph for TSP Based on Frequency QuadrilateralsTheoretical Computer Science10.1007/978-981-19-8152-4_5(77-95)Online publication date: 10-Dec-2022
https://doi.org/10.1007/978-981-19-8152-4_5
Garg NKhanna SKumar AMarx D(2021)Hardness of approximation for orienteering with multiple time windowsProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458241(2977-2990)Online publication date: 10-Jan-2021
https://dl.acm.org/doi/10.5555/3458064.3458241
Tarnawski J(2021)New graph algorithms via polyhedral techniquesit - Information Technology10.1515/itit-2021-001463:3(177-182)Online publication date: 15-Apr-2021
https://doi.org/10.1515/itit-2021-0014
Friggstad ZSwamy C(2021)A constant-factor approximation for directed latency in quasi-polynomial timeJournal of Computer and System Sciences10.1016/j.jcss.2021.12.001Online publication date: Dec-2021
https://doi.org/10.1016/j.jcss.2021.12.001
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