Constant factor approximation for ATSP with two edge weights

Svensson, Ola, Tarnawski, Jakub and Végh, László A. ORCID: 0000-0003-1152-200X (2018) Constant factor approximation for ATSP with two edge weights. Mathematical Programming, 172 (1-2). pp. 371-397. ISSN 0025-5610

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Abstract

We give a constant factor approximation algorithm for the Asymmetric Traveling Salesman Problem on shortest path metrics of directed graphs with two different edge weights. For the case of unit edge weights, the first constant factor approximation was given recently by Svensson. Thiswas accomplished by introducing an easier problem called Local-Connectivity ATSP and showing that a good solution to this problem can be used to obtain a constant factor approximation for ATSP. In this paper, we solve Local-Connectivity ATSP for two different edge weights. The solution is based on a flow decomposition theorem for solutions of the Held–Karp relaxation, which may be of independent interest.

Item Type:	Article
Official URL:	https://link.springer.com/journal/10107
Additional Information:	© 2017 Springer-Verlag GmbH Germany and Mathematical Optimization Society
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	13 Nov 2017 12:28
Last Modified:	16 Nov 2024 20:09
Projects:	335288-OptApprox, EP/M02797X/1
Funders:	ERC Starting Grant, EPSRC First Gran
URI:	http://eprints.lse.ac.uk/id/eprint/85331

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