Deineko, V. and Tiskin, A. (2009) Min-Weight Double-Tree Shortcutting for Metric TSP: Bounding the Approximation Ratio. Electronic Notes in Discrete Mathematics, 32. pp. 19-26. ISSN 1571-0653

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Abstract

The Metric Traveling Salesman Problem (TSP) is a classical NP-hard optimization problem. The double-tree shortcutting method for Metric TSP yields an exponentially-sized space of TSP tours, each of which approximates the optimal solution within at most a factor of 2. We consider the problem of finding among these tours the one that gives the closest approximation, i.e. the minimum-weight double-tree shortcutting. Previously, we gave an efficient algorithm for this problem, and carried out its experimental analysis. In this paper, we address the related question of the worst-case approximation ratio for the minimum-weight double-tree shortcutting method. In particular, we give lower bounds on the approximation ratio in some specific metric spaces: the ratio of 2 in the discrete shortest path metric, 1.622 in the planar Euclidean metric, and 1.666 in the planar Minkowski metric. The first of these lower bounds is tight; we conjecture that the other two bounds are also tight, and in particular that the minimum-weight double-tree method provides a 1.622-approximation for planar Euclidean TSP.

Item Type:	Article
Uncontrolled Keywords:	focs approximation algorithms metric TSP double tree shortcutting
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions:	Faculty of Science > Computer Science
Depositing User:	Ms Saima Arif
Date Deposited:	13 Dec 2010 10:52
Last Modified:	26 Jul 2011 11:15
URI:	http://eprints.dcs.warwick.ac.uk/id/eprint/437

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