Bidirectional A ∗  Search for Time-Dependent Fast Paths

  • Giacomo Nannicini
  • Daniel Delling
  • Leo Liberti
  • Dominik Schultes
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5038)

Abstract

The computation of point-to-point shortest paths on time-dependent road networks has many practical applications, but there have been very few works that propose efficient algorithms for large graphs. One of the difficulties of route planning on time-dependent graphs is that we do not know the exact arrival time at the destination, hence applying bidirectional search is not straightforward; we propose a novel approach based on A ∗  with landmarks (ALT) that starts a search from both the source and the destination node, where the backward search is used to bound the set of nodes that have to be explored by the forward search. Extensive computational results show that this approach is very effective in practice if we are willing to accept a small approximation factor, resulting in a speed-up of several times with respect to Dijkstra’s algorithm while finding only slightly suboptimal solutions.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Wagner, D., Willhalm, T.: Speed-up techniques for shortest-path computations. In: Thomas, W., Weil, P. (eds.) STACS 2007. LNCS, vol. 4393, pp. 23–36. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  2. 2.
    Sanders, P., Schultes, D.: Engineering fast route planning algorithms. In: Demetrescu, C. (ed.) WEA 2007. LNCS, vol. 4525, pp. 23–36. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  3. 3.
    Bast, H., Funke, S., Sanders, P., Schultes, D.: Fast routing in road networks with transit nodes. Science 316(5824), 566 (2007)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Delling, D., Wagner, D.: Landmark-based routing in dynamic graphs. In: Demetrescu, C. (ed.) WEA 2007. LNCS, vol. 4525, Springer, Heidelberg (2007)CrossRefGoogle Scholar
  5. 5.
    Sanders, P., Schultes, D.: Dynamic highway-node routing. In: Demetrescu, C. (ed.) WEA 2007. LNCS, vol. 4525, pp. 66–79. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  6. 6.
    Wagner, D., Willhalm, T., Zaroliagis, C.: Geometric containers for efficient shortest-path computation. ACM Journal of Experimental Algorithmics 10, 1–30 (2005)MathSciNetGoogle Scholar
  7. 7.
    Cooke, K., Halsey, E.: The shortest route through a network with time-dependent internodal transit times. Journal of Mathematical Analysis and Applications 14, 493–498 (1966)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Dreyfus, S.: An appraisal of some shortest-path algorithms. Operations Research 17(3), 395–412 (1969)MATHCrossRefGoogle Scholar
  9. 9.
    Dijkstra, E.: A note on two problems in connexion with graphs. Numerische Mathematik 1, 269–271 (1959)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Kaufman, D.E., Smith, R.L.: Fastest paths in time-dependent networks for intelligent vehicle-highway systems application. Journal of Intelligent Transportation Systems 1(1), 1–11 (1993)CrossRefGoogle Scholar
  11. 11.
    Orda, A., Rom, R.: Shortest-path and minimum delay algorithms in networks with time-dependent edge-length. Journal of the ACM 37(3), 607–625 (1990)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Daganzo, C.: Reversibility of time-dependent shortest path problem. Technical report, Institute of Transportation Studies, University of California, Berkeley (1998)Google Scholar
  13. 13.
    Hart, E., Nilsson, N., Raphael, B.: A formal basis for the heuristic determination of minimum cost paths. IEEE Transactions on Systems, Science and Cybernetics SSC-4(2), 100–107 (1968)Google Scholar
  14. 14.
    Goldberg, A., Harrelson, C.: Computing the shortest path: A  ∗  meets graph theory. In: Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2005), SIAM (2005)Google Scholar
  15. 15.
    Goldberg, A., Kaplan, H., Werneck, R.: Reach for A  ∗ : Efficient point-to-point shortest path algorithms. In: Demetrescu, C., Sedgewick, R., Tamassia, R. (eds.) Proceedings of the 7th Workshop on Algorithm Engineering and Experimentation (ALENEX 2005), SIAM (2005)Google Scholar
  16. 16.
    Chabini, I., Shan, L.: Adaptations of the A  ∗  algorithm for the computation of fastest paths in deterministic discrete-time dynamic networks. IEEE Transactions on Intelligent Transportation Systems 3(1), 60–74 (2002)CrossRefGoogle Scholar
  17. 17.
    Bauer, R., Delling, D.: SHARC: Fast and Robust Unidirectional Routing. In: Proceedings of the 10th Workshop on Algorithm Engineering and Experiments (ALENEX 2008), SIAM (to appear, 2008)Google Scholar
  18. 18.
    Ikeda, T., Tsu, M., Imai, H., Nishimura, S., Shimoura, H., Hashimoto, T., Tenmoku, K., Mitoh, K.: A fast algorithm for finding better routes by ai search techniques. In: Proceedings for the IEEE Vehicle Navigation and Information Systems Conference, pp. 291–296 (2004)Google Scholar
  19. 19.
    Goldberg, A., Werneck, R.: An efficient external memory shortest path algorithm. In: Demetrescu, C., Sedgewick, R., Tamassia, R. (eds.) Proceedings of the 7th Workshop on Algorithm Engineering and Experimentation (ALENEX 2005), pp. 26–40. SIAM (2005)Google Scholar
  20. 20.
    Sanders, P., Schultes, D.: Highway hierarchies hasten exact shortest path queries. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 568–579. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  21. 21.
    Kerner, B.S.: The Physics of Traffic. Springer, Berlin (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Giacomo Nannicini
    • 1
    • 2
  • Daniel Delling
    • 3
  • Leo Liberti
    • 1
  • Dominik Schultes
    • 3
  1. 1.LIXÉcole PolytechniquePalaiseauFrance
  2. 2.MediamobileParisFrance
  3. 3.Universität Karlsruhe (TH)KarlsruheGermany

Personalised recommendations