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Mathematical Programming

, Volume 172, Issue 1–2, pp 371–397 | Cite as

Constant factor approximation for ATSP with two edge weights

  • Ola Svensson
  • Jakub Tarnawski
  • László A. Végh
Full Length Paper Series B

Abstract

We give a constant factor approximation algorithm for the Asymmetric Traveling Salesman Problem on shortest path metrics of directed graphs with two different edge weights. For the case of unit edge weights, the first constant factor approximation was given recently by Svensson. This was accomplished by introducing an easier problem called Local-Connectivity ATSP and showing that a good solution to this problem can be used to obtain a constant factor approximation for ATSP. In this paper, we solve Local-Connectivity ATSP for two different edge weights. The solution is based on a flow decomposition theorem for solutions of the Held–Karp relaxation, which may be of independent interest.

Mathematics Subject Classification

68W25 05C85 90C05 90C27 

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Copyright information

© Springer-Verlag GmbH Germany and Mathematical Optimization Society 2017

Authors and Affiliations

  1. 1.École Polytechnique Fédérale de LausanneLausanneSwitzerland
  2. 2.London School of EconomicsLondonUK

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