Approximation algorithms for the bottleneck asymmetric traveling salesman problem

Authors:
Hyung-Chan An;Robert D. Kleinberg;David B. Shmoys
Affiliations:
Dept. of Computer Science, Cornell University, Ithaca, NY;Dept. of Computer Science, Cornell University, Ithaca, NY;School of ORIE and Dept. of Computer Science, Cornell University, Ithaca, NY
Venue:
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Year:
2010

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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(log n/ log log n) 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, Madry, 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.