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A Quasi-Polynomial-Time Approximation Scheme for Vehicle Routing on Planar and Bounded-Genus Graphs

Authors Amariah Becker, Philip N. Klein, David Saulpic

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Amariah Becker
Philip N. Klein
David Saulpic

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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). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.ESA.2017.12

Abstract

The Capacitated Vehicle Routing problem is a generalization of the Traveling Salesman problem in which a set of clients must be visited by a collection of capacitated tours. Each tour can visit at most Q clients and must start and end at a specified depot. We present the first approximation scheme for Capacitated Vehicle Routing for non-Euclidean metrics. Specifically we give a quasi-polynomial-time approximation scheme for Capacitated Vehicle Routing with fixed capacities on planar graphs. We also show how this result can be extended to bounded-genus graphs and polylogarithmic capacities, as well as to variations of the problem that include multiple depots and charging penalties for unvisited clients.
Keywords
  • Capacitated Vehicle Routing
  • Approximation Algorithms
  • Planar Graphs

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References

  1. Anna Adamaszek, Artur Czumaj, and Andrzej Lingas. PTAS for k-tour cover problem on the plane for moderately large values of k. Algorithms and Computation, pages 994-1003, 2009. Google Scholar
  2. Sanjeev Arora, M. Grigni, D. R. Karger, Philip N. Klein, and A. Woloszyn. A polynomial-time approximation scheme for weighted planar graph TSP. In Proceedings of the 9th Symposium on Discrete Algorithms, pages 33-41, 1998. Google Scholar
  3. 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
  4. Tetsuo Asano, Naoki Katoh, Hisao Tamaki, and Takeshi Tokuyama. Covering points in the plane by k-tours: a polynomial approximation scheme for fixed k. IBM Tokyo Research Laboratory Research Report RT0162, 1996. 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. ACM, 1997. Google Scholar
  6. Vincent Cohen-Addad, Éric Colin de Verdière, Philip N. Klein, Claire Mathieu, and David Meierfrankenfeld. Approximating connectivity domination in weighted bounded-genus graphs. In Proceedings of the 48th Annual ACMSymposium on Theory of Computing (STOC, pages 584-597, 2016. URL: http://dx.doi.org/10.1145/2897518.2897635.
  7. Aparna Das and Claire Mathieu. A quasipolynomial time approximation scheme for euclidean capacitated vehicle routing. Algorithmica, 73(1):115-142, 2015. Google Scholar
  8. David Eisenstat, Philip N. Klein, and Claire Mathieu. Approximating k-center in planar graphs. In Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 617-627. Society for Industrial and Applied Mathematics, 2014. Google Scholar
  9. David Eppstein. Dynamic generators of topologically embedded graphs. In Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms, pages 599-608. Society for Industrial and Applied Mathematics, 2003. Google Scholar
  10. Bruce L. Golden and Richard T. Wong. Capacitated arc routing problems. Networks, 11(3):305-315, 1981. Google Scholar
  11. M. Grigni, E. Koutsoupias, and C. Papadimitriou. An approximation scheme for planar graph TSP. In Proceedings of the 36th Annual Symposium on Foundations of Computer Science, pages 640-645, 1995. Google Scholar
  12. Mark Haimovich and A. H. G. Rinnooy Kan. Bounds and heuristics for capacitated routing problems. Mathematics of operations Research, 10(4):527-542, 1985. Google Scholar
  13. 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
  14. Stefan Irnich, Paolo Toth, and Daniele Vigo. Chapter 1: The family of vehicle routing problems. In Paolo Toh and Daniele Vigo, editors, Vehicle Routing: Problems, Methods, and Applications. SIAM, 2014. Google Scholar
  15. Michael Khachay and Roman Dubinin. PTAS for the Euclidean Capacitated Vehicle Routing Problem in R^d. In Proceedings of the 9th International Conference on Discrete Optimization and Operations Research (DOOR 2016), pages 193-205. Springer, 2016. Google Scholar
  16. Michael Khachay and Helen Zaytseva. Polynomial time approximation scheme for single-depot euclidean capacitated vehicle routing problem. In Combinatorial Optimization and Applications, pages 178-190. Springer, 2015. Google Scholar
  17. Mikkel Thorup. Compact oracles for reachability and approximate distances in planar digraphs. Journal of the ACM, 51(6):993-1024, 2004. Google Scholar
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