Advertisement

An A* Algorithm Framework for the Point-to-Point Time-Dependent Shortest Path Problem

  • Tatsuya Ohshima
  • Pipaporn Eumthurapojn
  • Liang Zhao
  • Hiroshi Nagamochi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7033)

Abstract

Given a directed graph, a nonnegative transit-time function c e (t) for each edge e (where t denotes departure time at the tail of e), a source vertex s, a destination vertex d and a departure time t 0, the point-to-point time-dependent shortest path problem (TDSPP) asks to find an s,d-path that leaves s at time t 0 and minimizes the arrival time at d. This formulation generalizes the classical shortest path problem in which c e are all constants.

This paper presents a novel generalized A* algorithm framework by introducing time-dependent estimator functions. This framework generalizes previous proposals that work with static estimator functions. We provide sufficient conditions on the time-dependent estimator functions for the correctness. As an application, we design a practical algorithm which generalizes the ALT algorithm for the classical problem (Goldberg and Harrelson, SODA05). Finally experimental results on several road networks are shown.

Keywords

Road Network Estimator Function Short Path Problem Algorithm Framework Fast Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network flows: theory, algorithms, and applications. Prentice-Hall (1993)Google Scholar
  2. 2.
    Chabini, I., Shan, L.: Adaptations of the A* algorithm for computation of fastest paths in deterministic discrete-time dynamic networks. IEEE Transactions on Intelligent Transportation Systems 3(1), 60–74 (2002)CrossRefGoogle Scholar
  3. 3.
    Cooke, K.L., Halsey, E.: The shortest route through a network with time-dependent internodal transit. J. Math. Anal. Appl. 14, 493–498 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Dijkstra, E.W.: A note on two problems in connexion with graphs. Operations Research 17(3), 395–412 (1969)CrossRefGoogle Scholar
  5. 5.
    Ding, B., Xu, J.X., Qin, L.: Finding time-dependent shortest paths over large graphs. In: Proc. EDBT 2008, ACM Intl., Conf. Proc., vol. 261, pp. 205–216 (2008)Google Scholar
  6. 6.
    Dreyfus, S.E.: An appraisal of some shortest-path algorithm. Operations Research 17(3), 395–412 (1969)CrossRefzbMATHGoogle Scholar
  7. 7.
    Goldberg, A.V., Harrelson, C.: Computing the shortest path: A* search meets graph theory. In: Proc. SODA 2005, pp. 156–165 (2005)Google Scholar
  8. 8.
    Halpern, H.J.: Shortest route with time dependent length of edges and limited delay possibilities in nodes. Operation Research 21, 117–124 (1997)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Hart, P.E., Nilsson, N.J., Raphael, B.: A formal basis for the heuristic determination of minimum cost paths. IEEE Transactions Systems Science and Cybernetics 4(2), 100–107 (1968)CrossRefGoogle Scholar
  10. 10.
    Kanoulas, E., Du, Y., Xia, T., Zhang, D.: Finding fastest paths on a road network with speed patterns. In: Proc. ICDE 2006, pp. 10–19 (2006)Google Scholar
  11. 11.
    Kaufman, D.E., Smith, R.L.: Fastest paths in time-dependent networks for intelligent vehicle-highway systems application. J. Intelligent Transportation Systems 1(1), 1–11 (1993)Google Scholar
  12. 12.
    Nannicini, G., et al.: Bidirectional A* Search for Time-Dependent Fast Paths. In: McGeoch, C.C. (ed.) WEA 2008. LNCS, vol. 5038, pp. 334–346. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  13. 13.
    Orda, A., Rom, R.: Traveling without waiting in time-dependent networks is NP-hard. Manuscript, Dept. Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel (1989)Google Scholar
  14. 14.
    Orda, A., Rom, R.: Shortest-path and minimum-delay algorithms in networks with time-dependent edge-length. J. ACM 37(3), 607–625 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    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

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Tatsuya Ohshima
    • 1
  • Pipaporn Eumthurapojn
    • 2
  • Liang Zhao
    • 2
  • Hiroshi Nagamochi
    • 2
  1. 1.JFE Steel CorporationKurashikiJapan
  2. 2.Graduate School of InformaticsKyoto UniversityJapan

Personalised recommendations