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.MFCS.2019.6
URN: urn:nbn:de:0030-drops-109503
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10950/
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Bienkowski, Marcin ; Liu, Hsiang-Hsuan

An Improved Online Algorithm for the Traveling Repairperson Problem on a Line

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LIPIcs-MFCS-2019-6.pdf (0.4 MB)

Abstract

In the online variant of the traveling repairperson problem (TRP), requests arrive in time at points of a metric space X and must be eventually visited by a server. The server starts at a designated point of X and travels at most at unit speed. Each request has a given weight and once the server visits its position, the request is considered serviced; we call such time completion time of the request. The goal is to minimize the weighted sum of completion times of all requests.
In this paper, we give a 5.429-competitive deterministic algorithm for line metrics improving over 5.829-competitive solution by Krumke et al. (TCS 2003). Our result is obtained by modifying the schedule by serving requests that are close to the origin first. To compute the competitive ratio of our approach, we use a charging scheme, and later evaluate its properties using a factor-revealing linear program which upper-bounds the competitive ratio.

BibTeX - Entry

@InProceedings{bienkowski_et_al:LIPIcs:2019:10950,
  author =	{Marcin Bienkowski and Hsiang-Hsuan Liu},
  title =	{{An Improved Online Algorithm for the Traveling Repairperson Problem on a Line}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{6:1--6:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Peter Rossmanith and Pinar Heggernes and Joost-Pieter Katoen},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10950},
  URN =		{urn:nbn:de:0030-drops-109503},
  doi =		{10.4230/LIPIcs.MFCS.2019.6},
  annote =	{Keywords: traveling repairperson problem, competitive analysis, minimizing completion time, factor-revealing LP}
}

Keywords: traveling repairperson problem, competitive analysis, minimizing completion time, factor-revealing LP
Collection: 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)
Issue Date: 2019
Date of publication: 20.08.2019

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