Abstract
In a recent work [1], we proposed a point-to-point shortest paths algorithm which applies bidirectional search on time-dependent road networks. The algorithm is based on A ∗ and runs a backward search in order to bound the set of nodes that have to be explored by the forward search. In this paper we extend the bidirectional time-dependent search algorithm in order to allow core routing, which is a very effective technique introduced for static graphs that consists in carrying out most of the search on a subset of the original node set. Moreover, we tackle the dynamic scenario where the piecewise linear time-dependent arc cost functions are not fixed, but can have their coefficients updated. We provide extensive computational results to show that our approach is a significant speed-up with respect to the original algorithm, and it is able to deal with the dynamic scenario requiring only a small computational effort to update the cost functions and related data structures.
Partially supported by the DFG (project WA 654/16-1) and the EU under grant ARRIVAL (contract no. FP6-021235-2).
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References
Nannicini, G., Delling, D., Liberti, L., Schultes, D.: Bidirectional A* search for time-dependent fast paths. In: [22], pp. 334–346
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)
Bauer, R., Delling, D., Sanders, P., Schieferdecker, D., Schultes, D., Wagner, D.: Combining hierarchical and goal-directed speed-up techniques for dijkstra’s algorithm. In: [22], pp. 303–318
Cooke, K., Halsey, E.: The shortest route through a network with time-dependent internodal transit times. J. of Math. Analysis and Applications 14, 493–498 (1966)
Dijkstra, E.: A note on two problems in connexion with graphs. Numerische Mathematik 1, 269–271 (1959)
Dreyfus, S.: An appraisal of some shortest-path algorithms. Operations Research 17(3), 395–412 (1969)
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)
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)
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)
Goldberg, A., Harrelson, C.: Computing the shortest path: A ∗ meets graph theory. In: Proceedings of SODA 2005, pp. 156–165. SIAM, Philadelphia (2005)
Goldberg, A., Kaplan, H., Werneck, R.: Reach for A ∗ : Efficient point-to-point shortest path algorithms. In: Proceedings of ALENEX 2006. LNCS, pp. 129–143. Springer, Heidelberg (2006)
Delling, D., Wagner, D.: Landmark-based routing in dynamic graphs. In: [21], pp. 52–65
Chabini, I., Lan, S.: 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)
Bauer, R., Delling, D.: SHARC: Fast and Robust Unidirectional Routing. In: Proceedings of the ALENEX 2008, pp. 13–26. SIAM, Philadelphia (2008)
Möhring, R.H., Schilling, H., Schütz, B., Wagner, D., Willhalm, T.: Partitioning graphs to speed up dijkstra’s algorithm. In: Nikoletseas, S.E. (ed.) WEA 2005. LNCS, vol. 3503, pp. 189–202. Springer, Heidelberg (2005)
Delling, D.: Time-Dependent SHARC-Routing. In: Halperin, D., Mehlhorn, K. (eds.) Esa 2008. LNCS, vol. 5193, pp. 332–343. Springer, Heidelberg (2008)
Goldberg, A., Werneck, R.: Computing point-to-point shortest paths from external memory. In: Demetrescu, C., Sedgewick, R., Tamassia, R. (eds.) Proceedings of ALENEX 2005, pp. 26–40. SIAM, Philadelphia (2005)
Geisberger, R., Sanders, P., Schultes, D., Delling, D.: Contraction hierarchies: Faster and simpler hierarchical routing in road networks. In: [22], pp. 319–333
Goldberg, A., Kaplan, H., Werneck, R.: Better landmarks within reach. In: [21], pp. 38–51
Delling, D., Sanders, P., Schultes, D., Wagner, D.: Highway Hierarchies Star. In: Shortest Paths: Ninth DIMACS Implementation Challenge. DIMACS Book. American Mathematical Society (to appear, 2008)
Demetrescu, C. (ed.): WEA 2007. LNCS, vol. 4525. Springer, Heidelberg (2007)
McGeoch, C.C. (ed.): WEA 2008. LNCS, vol. 5038. Springer, Heidelberg (2008)
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Delling, D., Nannicini, G. (2008). Bidirectional Core-Based Routing in Dynamic Time-Dependent Road Networks. In: Hong, SH., Nagamochi, H., Fukunaga, T. (eds) Algorithms and Computation. ISAAC 2008. Lecture Notes in Computer Science, vol 5369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92182-0_71
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