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

Authors Marcin Bienkowski , Hsiang-Hsuan Liu

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Author Details

Marcin Bienkowski
  • Institute of Computer Science, University of Wrocław, Poland
Hsiang-Hsuan Liu
  • Institute of Computer Science, University of Wrocław, Poland

Funding

Supported by Polish National Science Centre grant 2016/22/E/ST6/00499.

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Marcin Bienkowski and Hsiang-Hsuan Liu. An Improved Online Algorithm for the Traveling Repairperson Problem on a Line. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 6:1-6:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.MFCS.2019.6

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
  • Theory of computation → Scheduling algorithms
Keywords
  • traveling repairperson problem
  • competitive analysis
  • minimizing completion time
  • factor-revealing LP

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