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Erschienen in:
2010 | OriginalPaper | Buchkapitel
Approximation Algorithms for the Bottleneck Asymmetric Traveling Salesman Problem
verfasst von : Hyung-Chan An, Robert D. Kleinberg, David B. Shmoys
Erschienen in: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Verlag: Springer Berlin Heidelberg
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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
/ loglog
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, 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.