Deineko, Vladimir G. and Tiskin, Alexander (2009) Min-weight double-tree shortcutting for metric TSP : bounding the approximation ratio. Electronic Notes in Discrete Mathematics, Volume 32 . pp. 19-26. doi:10.1016/j.endm.2009.02.004

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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:	Journal Article
Subjects:	Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions:	Faculty of Science, Engineering and Medicine > Science > Computer Science Faculty of Social Sciences > Warwick Business School
Journal or Publication Title:	Electronic Notes in Discrete Mathematics
Publisher:	Elsevier
ISSN:	1571-0653
Official Date:	15 March 2009
Dates:	Date Event 15 March 2009 Published
Volume:	Volume 32
Page Range:	pp. 19-26
DOI:	10.1016/j.endm.2009.02.004
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC), University of Warwick. Centre for Discrete Mathematics and Its Applications (DIMAP)

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