Document Open Access Logo

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

Authors Marcin Bienkowski , Hsiang-Hsuan Liu

PDF
Thumbnail PDF

File

LIPIcs.MFCS.2019.6.pdf
  • Filesize: 408 kB
  • 12 pages

Document Identifiers

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.

Cite As Get BibTex

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

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. Foto N. Afrati, Stavros S. Cosmadakis, Christos H. Papadimitriou, George Papageorgiou, and Nadia Papakostantinou. The Complexity of the Travelling Repairman Problem. Informat. Theor. Appl., 20(1):79-87, 1986. URL: https://doi.org/10.1051/ita/1986200100791.
  2. Aaron Archer and Anna Blasiak. Improved Approximation Algorithms for the Minimum Latency Problem via Prize-Collecting Strolls. In Proc. 21st ACM-SIAM Symp. on Discrete Algorithms (SODA), pages 429-447, 2010. URL: https://doi.org/10.1137/1.9781611973075.36.
  3. Norbert Ascheuer, Sven Oliver Krumke, and Jörg Rambau. Online Dial-a-Ride Problems: Minimizing the Completion Time. In Proc. 17th Symp. on Theoretical Aspects of Computer Science (STACS), pages 639-650, 2000. URL: https://doi.org/10.1007/s10951-005-6811-3.
  4. Giorgio Ausiello, Esteban Feuerstein, Stefano Leonardi, Leen Stougie, and Maurizio Talamo. Serving Requests with On-line Routing. In Proc. 4th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT), pages 37-48, 1994. URL: https://doi.org/10.1007/3-540-58218-5_4.
  5. Giorgio Ausiello, Esteban Feuerstein, Stefano Leonardi, Leen Stougie, and Maurizio Talamo. Competitive Algorithms for the On-line Traveling Salesman. In Proc. 4th Int. Workshop on Algorithms and Data Structures (WADS), pages 206-217, 1995. URL: https://doi.org/10.1007/3-540-60220-8_63.
  6. Giorgio Ausiello, Esteban Feuerstein, Stefano Leonardi, Leen Stougie, and Maurizio Talamo. Algorithms for the On-Line Travelling Salesman. Algorithmica, 29(4):560-581, 2001. URL: https://doi.org/10.1007/s004530010071.
  7. Ricardo A. Baeza-Yates, Joseph C. Culberson, and Gregory J. E. Rawlins. Searching in the Plane. Information and Computation, 106(2):234-252, 1993. URL: https://doi.org/10.1006/inco.1993.1054.
  8. Alexander Birx and Yann Disser. Tight Analysis of the Smartstart Algorithm for Online Dial-a-Ride on the Line. In Proc. 36th Symp. on Theoretical Aspects of Computer Science (STACS), pages 15:1-15:17, 2019. URL: https://doi.org/10.4230/LIPIcs.STACS.2019.15.
  9. Antje Bjelde, Yann Disser, Jan Hackfeld, Christoph Hansknecht, Maarten Lipmann, Julie Meißner, Kevin Schewior, Miriam Schlöter, and Leen Stougie. Tight Bounds for Online TSP on the Line. In Proc. 28th ACM-SIAM Symp. on Discrete Algorithms (SODA), pages 994-1005, 2017. URL: https://doi.org/10.1137/1.9781611974782.63.
  10. Vincenzo Bonifaci and Leen Stougie. Online k-Server Routing Problems. Theory of Computing Systems, 45(3):470-485, 2009. URL: https://doi.org/10.1007/s00224-008-9103-4.
  11. Allan Borodin and Ran El-Yaniv. Online Computation and Competitive Analysis. Cambridge University Press, 1998. Google Scholar
  12. Kamalika Chaudhuri, Brighten Godfrey, Satish Rao, and Kunal Talwar. Paths, Trees, and Minimum Latency Tours. In Proc. 44th IEEE Symp. on Foundations of Computer Science (FOCS), pages 36-45, 2003. URL: https://doi.org/10.1109/SFCS.2003.1238179.
  13. Esteban Feuerstein and Leen Stougie. On-line single-server dial-a-ride problems. Theoretical Computer Science, 268(1):91-105, 2001. URL: https://doi.org/10.1016/S0304-3975(00)00261-9.
  14. Irene Fink, Sven Oliver Krumke, and Stephan Westphal. New lower bounds for online k-server routing problems. Information Processing Letters, 109(11):563-567, 2009. URL: https://doi.org/10.1016/j.ipl.2009.01.024.
  15. Michel X. Goemans and Jon M. Kleinberg. An improved approximation ratio for the minimum latency problem. Math. Program., 82:111-124, 1998. URL: https://doi.org/10.1007/BF01585867.
  16. Dietrich Hauptmeier, Sven Oliver Krumke, and Jörg Rambau. The Online Dial-a-Ride Problem under Reasonable Load. In Proc. 4th Int. Conf. on Algorithms and Complexity (CIAC), pages 125-136, 2000. URL: https://doi.org/10.1007/3-540-46521-9_11.
  17. Sven Oliver Krumke, Willem de Paepe, Diana Poensgen, Maarten Lipmann, Alberto Marchetti-Spaccamela, and Leen Stougie. On Minimizing the Maximum Flow Time in the Online Dial-a-Ride Problem. In Proc. 3rd Workshop on Approximation and Online Algorithms (WAOA), pages 258-269, 2005. URL: https://doi.org/10.1007/11671411_20.
  18. Sven Oliver Krumke, Willem de Paepe, Diana Poensgen, and Leen Stougie. News from the online traveling repairman. Theoretical Computer Science, 295:279-294, 2003. URL: https://doi.org/10.1016/S0304-3975(02)00409-7.
  19. Sven Oliver Krumke, Luigi Laura, Maarten Lipmann, Alberto Marchetti-Spaccamela, Willem de Paepe, Diana Poensgen, and Leen Stougie. Non-abusiveness Helps: An O(1)-Competitive Algorithm for Minimizing the Maximum Flow Time in the Online Traveling Salesman Problem. In Proc. 5th Int. Workshop on Approximation Algorithms for Combinatorial Optimization (APPROX), pages 200-214, 2002. URL: https://doi.org/10.1007/3-540-45753-4_18.
  20. René Sitters. The Minimum Latency Problem Is NP-Hard for Weighted Trees. In Proc. 9th Int. Conf. on Integer Programming and Combinatorial Optimization (IPCO), pages 230-239, 2002. URL: https://doi.org/10.1007/3-540-47867-1_17.
  21. René Sitters. Polynomial time approximation schemes for the traveling repairman and other minimum latency problems. In Proc. 25th ACM-SIAM Symp. on Discrete Algorithms (SODA), pages 604-616, 2014. URL: https://doi.org/10.1137/1.9781611973402.46.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact