Document Open Access Logo

A PTAS for Capacitated Vehicle Routing on Trees

Authors Claire Mathieu, Hang Zhou

PDF
Thumbnail PDF

File

LIPIcs.ICALP.2022.95.pdf
  • Filesize: 0.78 MB
  • 20 pages

Document Identifiers

Author Details

Claire Mathieu
  • CNRS Paris, France
Hang Zhou
  • École Polytechnique, Institut Polytechnique de Paris, France

Funding

This work was partially funded by the grant ANR-19-CE48-0016 from the French National Research Agency (ANR).

Cite AsGet BibTex

Claire Mathieu and Hang Zhou. A PTAS for Capacitated Vehicle Routing on Trees. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 95:1-95:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.ICALP.2022.95

Abstract

We give a polynomial time approximation scheme (PTAS) for the unit demand capacitated vehicle routing problem (CVRP) on trees, for the entire range of the tour capacity. The result extends to the splittable CVRP.

Subject Classification

ACM Subject Classification
  • Theory of computation → Routing and network design problems
Keywords
  • approximation algorithms
  • capacitated vehicle routing
  • graph algorithms
  • combinatorial optimization

Metrics

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

Related Versions

References

  1. Anna Adamaszek, Artur Czumaj, and Andrzej Lingas. PTAS for k-tour cover problem on the plane for moderately large values of k. International Journal of Foundations of Computer Science, 21(06):893-904, 2010. Google Scholar
  2. Kemal Altinkemer and Bezalel Gavish. Heuristics for delivery problems with constant error guarantees. Transportation Science, 24(4):294-297, 1990. Google Scholar
  3. S. P. Anbuudayasankar, K. Ganesh, and Sanjay Mohapatra. Models for practical routing problems in logistics. Springer, 2016. Google Scholar
  4. Tetsuo Asano, Naoki Katoh, and Kazuhiro Kawashima. A new approximation algorithm for the capacitated vehicle routing problem on a tree. Journal of Combinatorial Optimization, 5(2):213-231, 2001. Google Scholar
  5. Tetsuo Asano, Naoki Katoh, Hisao Tamaki, and Takeshi Tokuyama. Covering points in the plane by k-tours: towards a polynomial time approximation scheme for general k. In Proceedings of the twenty-ninth annual ACM symposium on Theory of computing, pages 275-283, 1997. Google Scholar
  6. Amariah Becker. A tight 4/3 approximation for capacitated vehicle routing in trees. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM), volume 116 of LIPIcs, pages 3:1-3:15, Dagstuhl, Germany, 2018. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik. Google Scholar
  7. Amariah Becker, Philip N. Klein, and David Saulpic. A quasi-polynomial-time approximation scheme for vehicle routing on planar and bounded-genus graphs. In 25th Annual European Symposium on Algorithms (ESA 2017). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2017. Google Scholar
  8. Amariah Becker, Philip N. Klein, and David Saulpic. Polynomial-time approximation schemes for k-center, k-median, and capacitated vehicle routing in bounded highway dimension. In 26th Annual European Symposium on Algorithms (ESA 2018). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2018. Google Scholar
  9. Amariah Becker, Philip N. Klein, and Aaron Schild. A PTAS for bounded-capacity vehicle routing in planar graphs. In Workshop on Algorithms and Data Structures, pages 99-111. Springer, 2019. Google Scholar
  10. Amariah Becker and Alice Paul. A framework for vehicle routing approximation schemes in trees. In Workshop on Algorithms and Data Structures, pages 112-125. Springer, 2019. Google Scholar
  11. Jannis Blauth, Vera Traub, and Jens Vygen. Improving the approximation ratio for capacitated vehicle routing. In International Conference on Integer Programming and Combinatorial Optimization, pages 1-14. Springer, 2021. Google Scholar
  12. Agustín Bompadre, Moshe Dror, and James B. Orlin. Improved bounds for vehicle routing solutions. Discrete Optimization, 3(4):299-316, 2006. Google Scholar
  13. Vincent Cohen-Addad, Arnold Filtser, Philip N. Klein, and Hung Le. On light spanners, low-treewidth embeddings and efficient traversing in minor-free graphs. In 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS), pages 589-600. IEEE, 2020. Google Scholar
  14. Teodor G. Crainic and Gilbert Laporte. Fleet management and logistics. Springer Science & Business Media, 2012. Google Scholar
  15. George B. Dantzig and John H. Ramser. The truck dispatching problem. Management Science, 6(1):80-91, 1959. Google Scholar
  16. Aparna Das and Claire Mathieu. A quasipolynomial time approximation scheme for Euclidean capacitated vehicle routing. Algorithmica, 73(1):115-142, 2015. Google Scholar
  17. Zachary Friggstad, Ramin Mousavi, Mirmahdi Rahgoshay, and Mohammad R. Salavatipour. Improved approximations for CVRP with unsplittable demands. arXiv preprint, 2021. URL: http://arxiv.org/abs/2111.08138.
  18. Bruce Golden, S. Raghavan, and Edward Wasil. The vehicle routing problem: latest advances and new challenges, volume 43 of Operations Research/Computer Science Interfaces Series. Springer, 2008. Google Scholar
  19. Bruce L. Golden and Richard T. Wong. Capacitated arc routing problems. Networks, 11(3):305-315, 1981. Google Scholar
  20. Mordecai Haimovich and Alexander H. G. Rinnooy Kan. Bounds and heuristics for capacitated routing problems. Mathematics of Operations Research, 10(4):527-542, 1985. Google Scholar
  21. Shin-ya Hamaguchi and Naoki Katoh. A capacitated vehicle routing problem on a tree. In International Symposium on Algorithms and Computation, pages 399-407. Springer, 1998. Google Scholar
  22. Aditya Jayaprakash and Mohammad R. Salavatipour. Approximation schemes for capacitated vehicle routing on graphs of bounded treewidth, bounded doubling, or highway dimension. In ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 877-893, 2022. Google Scholar
  23. Michael Khachay and Roman Dubinin. PTAS for the Euclidean capacitated vehicle routing problem in ℝ^d. In International Conference on Discrete Optimization and Operations Research, pages 193-205. Springer, 2016. Google Scholar
  24. Martine Labbé, Gilbert Laporte, and Hélene Mercure. Capacitated vehicle routing on trees. Operations Research, 39(4):616-622, 1991. Google Scholar
  25. Claire Mathieu and Hang Zhou. A tight (1.5 + ε)-approximation for unsplittable capacitated vehicle routing on trees, 2022. URL: http://arxiv.org/abs/2202.05691.
  26. Paolo Toth and Daniele Vigo. The Vehicle Routing Problem. Society for Industrial and Applied Mathematics, 2002. Google Scholar
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 Imprint Privacy Contact