Approximation Algorithms for the Bottleneck Asymmetric Traveling Salesman Problem

摘要

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 Hamilto-nian cycle that minimizes its bottleneck (or maximum-length edge) cost. We achieve an O(logn/log logn) 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 Gha-ran, 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.