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Improved approximations for ordered TSP on near-metricgraphs∗∗∗
Published online by Cambridge University Press: 06 November 2014
Abstract
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The traveling salesman problem is one of the most important problems in operationsresearch, especially when additional precedence constraints are considered. Here, weconsider the well-known variant where a linear order on k special vertices is giventhat has to be preserved in any feasible Hamiltonian cycle. This problem is called OrderedTSP and we consider it on input instances where the edge-cost function satisfies aβ-relaxedtriangle inequality, i.e., where the length of a direct edge cannotexceed the cost of any detour via a third vertex by more than a factor ofβ> 1. Wedesign two new polynomial-time approximation algorithms for this problem. The firstalgorithm essentially improves over the best previously known algorithm for almost allvalues of kand β<1.087889. The second algorithm gives a further improvement for2n ≥ 11k +7 and β< √34/3 , where n is the number of vertices in the graph.
Information
- Type
- Research Article
- Information
- RAIRO - Theoretical Informatics and Applications , Volume 48 , Issue 5 , December 2014, pp. 479 - 494
- Copyright
- © EDP Sciences 2014
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