A constant-factor approximation algorithm for the asymmetric traveling salesman problem

Svensson, Ola, Tarnawski, Jakub and Végh, László A. ORCID: 0000-0003-1152-200X (2020) A constant-factor approximation algorithm for the asymmetric traveling salesman problem. Journal of the ACM, 67 (6). ISSN 0004-5411

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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.

Item Type:	Article
Official URL:	https://dl.acm.org/journal/jacm
Additional Information:	© 2020 The Authors
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Date Deposited:	17 Sep 2020 09:18
Last Modified:	27 Sep 2024 20:18
URI:	http://eprints.lse.ac.uk/id/eprint/106582

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