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Min-weight double-tree shortcutting for metric TSP : bounding the approximation ratio
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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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Official URL: http://dx.doi.org/10.1016/j.endm.2009.02.004
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 | ||||
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| Subjects: | Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software | ||||
| Divisions: | Faculty of Science > Computer Science Faculty of Social Sciences > Warwick Business School |
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| Journal or Publication Title: | Electronic Notes in Discrete Mathematics | ||||
| Publisher: | Elsevier | ||||
| ISSN: | 1571-0653 | ||||
| Official Date: | 15 March 2009 | ||||
| Dates: |
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| 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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