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.
This research was partially supported by the Ministry of Education, Science, Sports and Culture (MEXT), Japan.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network flows: theory, algorithms, and applications. Prentice-Hall (1993)
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)
Cooke, K.L., Halsey, E.: The shortest route through a network with time-dependent internodal transit. J. Math. Anal. Appl. 14, 493–498 (1996)
Dijkstra, E.W.: A note on two problems in connexion with graphs. Operations Research 17(3), 395–412 (1969)
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)
Dreyfus, S.E.: An appraisal of some shortest-path algorithm. Operations Research 17(3), 395–412 (1969)
Goldberg, A.V., Harrelson, C.: Computing the shortest path: A* search meets graph theory. In: Proc. SODA 2005, pp. 156–165 (2005)
Halpern, H.J.: Shortest route with time dependent length of edges and limited delay possibilities in nodes. Operation Research 21, 117–124 (1997)
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)
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)
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)
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)
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)
Orda, A., Rom, R.: Shortest-path and minimum-delay algorithms in networks with time-dependent edge-length. J. ACM 37(3), 607–625 (1990)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ohshima, T., Eumthurapojn, P., Zhao, L., Nagamochi, H. (2011). An A* Algorithm Framework for the Point-to-Point Time-Dependent Shortest Path Problem. In: Akiyama, J., Bo, J., Kano, M., Tan, X. (eds) Computational Geometry, Graphs and Applications. CGGA 2010. Lecture Notes in Computer Science, vol 7033. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24983-9_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-24983-9_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24982-2
Online ISBN: 978-3-642-24983-9
eBook Packages: Computer ScienceComputer Science (R0)