Document Open Access Logo

Engineering an Approximation Scheme for Traveling Salesman in Planar Graphs

Authors Amariah Becker, Eli Fox-Epstein, Philip N. Klein, David Meierfrankenfeld

PDF
Thumbnail PDF

File

LIPIcs.SEA.2017.8.pdf
  • Filesize: 0.63 MB
  • 17 pages

Document Identifiers

Author Details

Amariah Becker
Eli Fox-Epstein
Philip N. Klein
David Meierfrankenfeld

Cite AsGet BibTex

Amariah Becker, Eli Fox-Epstein, Philip N. Klein, and David Meierfrankenfeld. Engineering an Approximation Scheme for Traveling Salesman in Planar Graphs. In 16th International Symposium on Experimental Algorithms (SEA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 75, pp. 8:1-8:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.SEA.2017.8

Abstract

We present an implementation of a linear-time approximation scheme for the traveling salesman problem on planar graphs with edge weights. We observe that the theoretical algorithm involves constants that are too large for practical use. Our implementation, which is not subject to the theoretical algorithm's guarantee, can quickly find good tours in very large planar graphs.
Keywords
  • Traveling Salesman
  • Approximation Schemes
  • Planar Graph Algorithms
  • Algorithm Engineering

Metrics

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

References

  1. D. Applegate, R. Bixby, V. Chvatal, and W. Cook. Concorde TSP solver, 2006. Google Scholar
  2. F. Barahona. Planar multicommodity flows, max cut, and the chinese postman problem. In Polyhedral Combinatorics, Proceedings of a DIMACS Workshop, Morristown, New Jersey, USA, June 12-16, 1989, pages 189-202, 1990. Google Scholar
  3. J. J. Bartholdi and L. K. Platzman. Heuristics based on spacefilling curves for combinatorial problems in euclidean space. Management Science, 34(3):291-305, 1988. Google Scholar
  4. G. Borradaile, P. N. Klein, and C. Mathieu. An O(n log n) approximation scheme for steiner tree in planar graphs. ACM Trans. Algorithms, 5(3):31:1-31:31, 2009. Google Scholar
  5. P. Chalermsook, J. Fakcharoenphol, and D. Nanongkai. A deterministic near-linear time algorithm for finding minimum cuts in planar graphs. In Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2004, New Orleans, Louisiana, USA, January 11-14, 2004, pages 828-829, 2004. Google Scholar
  6. D. Cheriton and R. E. Tarjan. Finding minimum spanning trees. SIAM Journal on Computing, 5(4):724-742, 1976. Google Scholar
  7. N. Christofides. Worst-case analysis of a new heuristic for the travelling salesman problem. Technical report, Carnegie-Mellon University, 1976. Google Scholar
  8. W. Cook and P. Seymour. Tour merging via branch-decomposition. INFORMS Journal on Computing, 15(3):233-248, 2003. Google Scholar
  9. J. Dibbelt, B. Strasser, and D. Wagner. Customizable contraction hierarchies. ACM Journal of Experimental Algorithmics, 21(1):1.5:1-1.5:49, 2016. Google Scholar
  10. R. Geisberger, P. Sanders, D. Schultes, and C. Vetter. Exact routing in large road networks using contraction hierarchies. Transportation Science, 46(3):388-404, 2012. Google Scholar
  11. Q. P. Gu and H. Tamaki. Improved bounds on the planar branchwidth with respect to the largest grid minor size. Algorithmica, 64(3):416-453, 2012. Google Scholar
  12. M. Haklay and P. Weber. Openstreetmap: User-generated street maps. IEEE Pervasive Computing, 7(4):12-18, 2008. Google Scholar
  13. K. Helsgaun. An effective implementation of the lin-kernighan traveling salesman heuristic. European Journal of Operational Research, 126(1):106-130, 2000. Google Scholar
  14. K. Helsgaun. General k-opt submoves for the Lin-Kernighan TSP heuristic. Mathematical Programming Computation, 1(2-3):119-163, 2009. Google Scholar
  15. P. N. Klein. A linear-time approximation scheme for TSP in undirected planar graphs with edge-weights. SIAM Journal on Computing, 37(6):1926-1952, 2008. Google Scholar
  16. T. Matsui. The minimum spanning tree problem on a planar graph. Discrete Applied Mathematics, 58(1):91-94, 1995. Google Scholar
  17. M. Müller-Hannemann and S. Schirra, editors. Algorithm engineering: bridging the gap between algorithm theory and practice, volume LNCS 5971. Springer, 2010. Google Scholar
  18. G. Reinelt. Fast heuristics for large geometric traveling salesman problems. ORSA Journal on Computing, 4(3):206-217, 199. Google Scholar
  19. P. Seymour and R. Thomas. Call routing and the ratcatcher. Combinatorica, 14(2):217-241, 1994. Google Scholar
  20. H. Tamaki. A linear time heuristic for the branch-decomposition of planar graphs. In Algorithms - ESA 2003, volume 2832 of Lecture Notes in Computer Science, pages 765-775. Springer, 2003. Google Scholar
  21. S. Tazari and M. Müller-Hannemann. Dealing with large hidden constants: Engineering a planar Steiner tree PTAS. Journal of Experimental Algorithmics (JEA), 16:3-6, 2011. Google Scholar
  22. Y. Xia, M. Zhu, Q. Gu, L. Zhang, and X. Li. Toward solving the steiner travelling salesman problem on urban road maps using the branch decomposition of graphs. Information Sciences, 374:164-178, 2016. Google Scholar
  23. N. E. Young. Sequential and parallel algorithms for mixed packing and covering. In 42nd Annual Symposium on Foundations of Computer Science, FOCS 2001, 14-17 October 2001, Las Vegas, Nevada, USA, pages 538-546, 2001. Google Scholar
  24. M. Zhu. Computational study on branch decompositions of planar graphs. Master’s thesis, School of Computing Science, Simon Fraser University, 2013. 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