License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018.3
URN: urn:nbn:de:0030-drops-94075
URL: https://drops.dagstuhl.de/opus/volltexte/2018/9407/
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Becker, Amariah

A Tight 4/3 Approximation for Capacitated Vehicle Routing in Trees

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Abstract

Given a set of clients with demands, the Capacitated Vehicle Routing problem is to find a set of tours that collectively cover all client demand, such that the capacity of each vehicle is not exceeded and such that the sum of the tour lengths is minimized. In this paper, we provide a 4/3-approximation algorithm for Capacitated Vehicle Routing on trees, improving over the previous best-known approximation ratio of (sqrt{41}-1)/4 by Asano et al.[Asano et al., 2001], while using the same lower bound. Asano et al. show that there exist instances whose optimal cost is 4/3 times this lower bound. Notably, our 4/3 approximation ratio is therefore tight for this lower bound, achieving the best-possible performance.

BibTeX - Entry

@InProceedings{becker:LIPIcs:2018:9407,
  author =	{Amariah Becker},
  title =	{{A Tight 4/3 Approximation for Capacitated Vehicle Routing in Trees}},
  booktitle =	{Approximation, Randomization, and Combinatorial  Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{3:1--3:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-085-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{116},
  editor =	{Eric Blais and Klaus Jansen and Jos{\'e} D. P. Rolim and David Steurer},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9407},
  URN =		{urn:nbn:de:0030-drops-94075},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.3},
  annote =	{Keywords: Approximation algorithms, Graph algorithms, Capacitated vehicle routing}
}

Keywords: Approximation algorithms, Graph algorithms, Capacitated vehicle routing
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)
Issue Date: 2018
Date of publication: 13.08.2018


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