Abstract
In this paper, we present an overview over existing speed-up techniques for time-dependent route planning. Apart from only explaining each technique one by one, we follow a more systematic approach. We identify basic ingredients of these recent techniques and show how they need to be augmented to guarantee correctness in time-dependent networks. With the ingredients adapted, three efficient speed-up techniques can be set up: Core-ALT, SHARC, and Contraction Hierarchies. Experiments on real-world data deriving from road networks and public transportation confirm that these techniques allow the fast computation of time-dependent shortest paths.
Partially supported by the Future and Emerging Technologies Unit of EC (IST priority – 6th FP), under contract no. FP6-021235-2 (project ARRIVAL) and the DFG (project WA 654/16-1).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Batz, V., Delling, D., Sanders, P., Vetter, C.: Time-Dependent Contraction Hierarchies. In: Proceedings of the 11th Workshop on Algorithm Engineering and Experiments (ALENEX 2009), pp. 97–105. SIAM, Philadelphia (2009)
Bauer, R., Delling, D.: SHARC: Fast and Robust Unidirectional Routing. ACM Journal of Experimental Algorithmics, 2.4-2.29 14 (2009); special Section on Selected Papers from ALENEX 2008
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: McGeoch, C.C. (ed.) WEA 2008. LNCS, vol. 5038, pp. 303–318. Springer, Heidelberg (2008)
Cooke, K., Halsey, E.: The Shortest Route Through a Network with Time-Dependent Intermodal Transit Times. Journal of Mathematical Analysis and Applications 14, 493–498 (1966)
Dean, B.C.: Continuous-Time Dynamic Shortest Path Algorithms. Master’s thesis, Massachusetts Institute of Technology (1999)
Delling, D.: Time-Dependent SHARC-Routing. In: Halperin, D., Mehlhorn, K. (eds.) Esa 2008. LNCS, vol. 5193, pp. 332–343. Springer, Heidelberg (2008)
Delling, D.: Engineering and Augmenting Route Planning Algorithms. PhD thesis, Universität Karlsruhe (TH), Fakultät für Informatik (2009)
Delling, D.: Time-Dependent SHARC-Routing. Algorithmica, July 2009. Special Issue: European Symposium on Algorithms (2008)
Delling, D., Nannicini, G.: Bidirectional Core-Based Routing in Dynamic Time-Dependent Road Networks. In: Hong, S.-H., Nagamochi, H., Fukunaga, T. (eds.) ISAAC 2008. LNCS, vol. 5369, pp. 812–824. Springer, Heidelberg (2008)
Delling, D., Sanders, P., Schultes, D., Wagner, D.: Engineering Route Planning Algorithms. In: Lerner, J., Wagner, D., Zweig, K.A. (eds.) Algorithmics of Large and Complex Networks. LNCS, vol. 5515, pp. 117–139. Springer, Heidelberg (2009)
Delling, D., Wagner, D.: Landmark-Based Routing in Dynamic Graphs. In: Demetrescu, C. (ed.) WEA 2007. LNCS, vol. 4525, pp. 52–65. Springer, Heidelberg (2007)
Delling, D., Wagner, D.: Pareto Paths with SHARC. In: Vahrenhold, J. (ed.) SEA 2009. LNCS, vol. 5526, pp. 125–136. Springer, Heidelberg (2009)
Dijkstra, E.W.: A Note on Two Problems in Connexion with Graphs. Numerische Mathematik 1, 269–271 (1959)
Geisberger, R., Sanders, P., Schultes, D., Delling, D.: Contraction Hierarchies: Faster and Simpler Hierarchical Routing in Road Networks. In: McGeoch, C.C. (ed.) WEA 2008. LNCS, vol. 5038, pp. 319–333. Springer, Heidelberg (2008)
Goldberg, A.V., Harrelson, C.: Computing the Shortest Path: A* Search Meets Graph Theory. In: Proceedings of the 16th Annual ACM–SIAM Symposium on Discrete Algorithms (SODA 2005), pp. 156–165 (2005)
Goldberg, A.V., Werneck, R.F.: Computing Point-to-Point Shortest Paths from External Memory. In: Proceedings of the 7th Workshop on Algorithm Engineering and Experiments (ALENEX 2005), pp. 26–40. SIAM, Philadelphia (2005)
Hart, P.E., Nilsson, N., Raphael, B.: A Formal Basis for the Heuristic Determination of Minimum Cost Paths. IEEE Transactions on Systems Science and Cybernetics 4, 100–107 (1968)
Hilger, M., Köhler, E., Möhring, R.H., Schilling, H.: Fast Point-to-Point Shortest Path Computations with Arc-Flags. In: Demetrescu, C., Goldberg, A.V., Johnson, D.S. (eds.) Shortest Path Computations: Ninth DIMACS Challenge. DIMACS Book, vol. 24. American Mathematical Society (to appear, 2009)
Ikeda, T., Hsu, M.-Y., 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 of the Vehicle Navigation and Information Systems Conference (VNSI 1994), pp. 291–296. ACM Press, New York (1994)
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)
Köhler, E., Möhring, R.H., Schilling, H.: Acceleration of Shortest Path and Constrained Shortest Path Computation. In: Nikoletseas, S.E. (ed.) WEA 2005. LNCS, vol. 3503, pp. 126–138. Springer, Heidelberg (2005)
Lauther, U.: An Extremely Fast, Exact Algorithm for Finding Shortest Paths in Static Networks with Geographical Background. In: Geoinformation und Mobilität - von der Forschung zur praktischen Anwendung, vol. 22, pp. 219–230. IfGI prints (2004)
Lauther, U.: An Experimental Evaluation of Point-To-Point Shortest Path Calculation on Roadnetworks with Precalculated Edge-Flags. In: Demetrescu, C., Goldberg, A.V., Johnson, D.S. (eds.) Shortest Path Computations: Ninth DIMACS Challenge. DIMACS Book, vol. 24, American Mathematical Society(to appear, 2009)
Möhring, R.H., Schilling, H., Schütz, B., Wagner, D., Willhalm, T.: artitioning Graphs to Speed Up Dijkstra’s Algorithm. In: Nikoletseas, S.E. (ed.) WEA 2005. LNCS, vol. 3503, pp. 189–202. Springer, Heidelberg (2005)
Möhring, R.H., Schilling, H., Schütz, B., Wagner, D., Willhalm, T.: Partitioning Graphs to Speedup Dijkstra’s Algorithm. ACM Journal of Experimental Algorithmics 11, 2.8 (2006)
Nannicini, G., Delling, D., Liberti, L., Schultes, D.: 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.: Shortest-Path and Minimum Delay Algorithms in Networks with Time-Dependent Edge-Length. Journal of the ACM 37(3), 607–625 (1990)
Pyrga, E., Schulz, F., Wagner, D., Zaroliagis, C.: Efficient Models for Timetable Information in Public Transportation Systems. ACM Journal of Experimental Algorithmics 12, Article 2.4 (2007)
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)
Schulz, F., Wagner, D., Weihe, K.: Dijkstra’s Algorithm On-Line: An Empirical Case Study from Public Railroad Transport. In: Vitter, J.S., Zaroliagis, C.D. (eds.) WAE 1999. LNCS, vol. 1668, pp. 110–123. Springer, Heidelberg (1999)
Sedgewick, R., Vitter, J.S.: Shortest Paths in Euclidean Graphs. Algorithmica 1(1), 31–48 (1986)
Wagner, D., Willhalm, T.: Drawing Graphs to Speed Up Shortest-Path Computations. In: Proceedings of the 7th Workshop on Algorithm Engineering and Experiments (ALENEX 2005), pp. 15–24. SIAM, Philadelphia (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Delling, D., Wagner, D. (2009). Time-Dependent Route Planning. In: Ahuja, R.K., Möhring, R.H., Zaroliagis, C.D. (eds) Robust and Online Large-Scale Optimization. Lecture Notes in Computer Science, vol 5868. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05465-5_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-05465-5_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05464-8
Online ISBN: 978-3-642-05465-5
eBook Packages: Computer ScienceComputer Science (R0)