License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC BY-NC-ND 3.0)
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DOI: 10.4230/LIPIcs.FSTTCS.2012.325
URN: urn:nbn:de:0030-drops-38707
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2012/3870/
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Bhattacharya, Binay ; Hu, Yuzhuang

k-delivery traveling salesman problem on tree networks

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Abstract

In this paper we study the k-delivery traveling salesman problem (TSP)on trees, a variant of the non-preemptive capacitated vehicle routing problem with pickups and deliveries. We are given n pickup locations and n delivery locations on trees, with exactly one item at each pickup location. The k-delivery TSP is to find a minimum length tour by a vehicle of finite capacity k to pick up and deliver exactly one item to each delivery location. We show that an optimal solution for the k-delivery TSP on paths can be found that allows succinct representations of the routes. By exploring the symmetry inherent in the k-delivery TSP, we design a 5/3-approximation algorithm for the k-delivery TSP on trees of arbitrary heights. The ratio can be improved to (3/2 - 1/2k) for the problem on trees of height 2. The developed algorithms are based on the following observation: under certain conditions, it makes sense for a non-empty vehicle to turn around and pick up additional loads.

BibTeX - Entry

@InProceedings{bhattacharya_et_al:LIPIcs:2012:3870,
  author =	{Binay  Bhattacharya and Yuzhuang Hu},
  title =	{{k-delivery traveling salesman problem on tree networks}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012) },
  pages =	{325--336},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-47-7},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{18},
  editor =	{Deepak D'Souza and Telikepalli Kavitha and Jaikumar Radhakrishnan},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2012/3870},
  URN =		{urn:nbn:de:0030-drops-38707},
  doi =		{10.4230/LIPIcs.FSTTCS.2012.325},
  annote =	{Keywords: k-delivery traveling salesman problem, approximation algorithms}
}

Keywords: k-delivery traveling salesman problem, approximation algorithms
Collection: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)
Issue Date: 2012
Date of publication: 14.12.2012

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