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, Mądry, 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.


Approximation algorithms traveling salesman problem bottleneck optimization 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Hyung-Chan An
    • 1
  • Robert D. Kleinberg
    • 1
  • David B. Shmoys
    • 2
  1. 1.Dept. of Computer ScienceCornell UniversityIthaca
  2. 2.School of ORIE and Dept. of Computer ScienceCornell UniversityIthaca

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