A near-optimal approximation algorithm for Asymmetric TSP on embedded graphs

Jeff Erickson, Anastasios Sidiropoulos

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

Abstract

We present a near-optimal polynomial-time approximation algorithm for the asymmetric traveling salesman problem for graphs of bounded orientable or non-orientable genus. Given any algorithm that achieves an approximation ratio of f (n) on arbitrary n-vertex graphs as a black box, our algorithm achieves an approximation factor of O( f (g)) on graphs with genus g. In particular, the O(log n= log log n)-approximation algorithm for general graphs by Asadpour et al. [SODA 2010] immediately implies an O(log g= log log g)-approximation algorithm for genus-g graphs. Moreover, recent results on approximating the genus of graphs imply that our O(log g= log log g)-approximation algorithm can be applied to bounded-degree graphs even if no genus-g embedding of the graph is given. Our result improves and generalizes the O(√g log g)-approximation algorithm of Oveis Gharan and Saberi [SODA 2011], which applies only to graphs with orientable genus g and requires a genus-g embedding as part of the input, even for bounded-degree graphs. Finally, our techniques yield a O(1)-approximation algorithm for ATSP on graphs of genus g with running time 2O(g)· nO(1)

Original languageEnglish (US)
Title of host publicationProceedings of the 30th Annual Symposium on Computational Geometry, SoCG 2014
PublisherAssociation for Computing Machinery
Pages130-135
Number of pages6
ISBN (Print)9781450325943
DOIs
StatePublished - Jan 1 2014
Event30th Annual Symposium on Computational Geometry, SoCG 2014 - Kyoto, Japan
Duration: Jun 8 2014Jun 11 2014

Publication series

NameProceedings of the Annual Symposium on Computational Geometry

Other

Other30th Annual Symposium on Computational Geometry, SoCG 2014
CountryJapan
CityKyoto
Period6/8/146/11/14

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Keywords

  • Approximation algorithms
  • Topological graph algorithms
  • Traveling salesman

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics

Cite this

Erickson, J., & Sidiropoulos, A. (2014). A near-optimal approximation algorithm for Asymmetric TSP on embedded graphs. In Proceedings of the 30th Annual Symposium on Computational Geometry, SoCG 2014 (pp. 130-135). (Proceedings of the Annual Symposium on Computational Geometry). Association for Computing Machinery. https://doi.org/10.1145/2582112.2582136