Affiliation:
1. École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
2. London School of Economics and Political Science, London, United Kingdom
Abstract
We give a constant-factor approximation algorithm for the asymmetric traveling salesman problem (ATSP). Our approximation guarantee is analyzed with respect to the standard LP relaxation, and thus our result confirms the conjectured constant integrality gap of that relaxation.
The main idea of our approach is a reduction to Subtour Partition Cover, an easier problem obtained by significantly relaxing the general connectivity requirements into local connectivity conditions. We first show that any algorithm for Subtour Partition Cover can be turned into an algorithm for ATSP while only losing a small constant factor in the performance guarantee. Next, we present a reduction from general ATSP instances to structured instances, on which we then solve Subtour Partition Cover, yielding our constant-factor approximation algorithm for ATSP.
Funder
European Research Council
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
Engineering and Physical Sciences Research Council
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Cited by
29 articles.
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