Abstract
Algorithms for route planning in transportation networks have recently undergone a rapid development, leading to methods that are up to one million times faster than Dijkstra’s algorithm. We outline ideas, algorithms, implementations, and experimental methods behind this development. We also explain why the story is not over yet because dynamically changing networks, flexible objective functions, and new applications pose a lot of interesting challenges.
Partially supported by DFG grant SA 933/1-3.
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
Dijkstra, E.W.: A note on two problems in connexion with graphs. Numerische Mathematik 1, 269–271 (1959)
Thorup, M.: Integer priority queues with decrease key in constant time and the single source shortest paths problem. In: 35th ACM Symposium on Theory of Computing, pp. 149–158. ACM Press, New York (2003)
Meyer, U.: Single-source shortest-paths on arbitrary directed graphs in linear average-case time. In: 12th Symposium on Discrete Algorithms. pp. 797–806 (2001)
Dantzig, G.B.: Linear Programming and Extensions. Princeton University Press, Princeton (1962)
Hart, P.E., Nilsson, N.J., Raphael, B.: A formal basis for the heuristic determination of minimum cost paths. IEEE Transactions on System Science and Cybernetics 4(2), 100–107 (1968)
Goldberg, A.V., Harrelson, C.: Computing the shortest path: A * meets graph theory. In: 16th ACM-SIAM Symposium on Discrete Algorithms, pp. 156–165. ACM Press, New York (2005)
Ishikawa, K., Ogawa, M., Azume, S., Ito, T.: Map Navigation Software of the Electro Multivision of the ’91 Toyota Soarer. In: IEEE Int. Conf. Vehicle Navig, pp. 463–473. IEEE Computer Society Press, Los Alamitos (1991)
Fakcharoenphol, J., Rao, S.: Planar graphs, negative weight edges, shortest paths, and near linear time. J. Comput. Syst. Sci. 72(5), 868–889 (2006)
Klein, P.: Multiple-source shortest paths in planar graphs. In: 16th ACM-SIAM Symposium on Discrete Algorithms, SIAM, pp. 146–155 (2005)
Thorup, M.: Compact oracles for reachability and approximate distances in planar digraphs. In: 42nd IEEE Symposium on Foundations of Computer Science, pp. 242–251. IEEE Computer Society Press, Los Alamitos (2001)
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)
Gutman, R.: Reach-based routing: A new approach to shortest path algorithms optimized for road networks. In: 6th Workshop on Algorithm Engineering and Experiments. pp. 100–111 (2004)
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)
Sanders, P., Schultes, D.: Engineering highway hierarchies. In: Azar, Y., Erlebach, T. (eds.) ESA 2006. LNCS, vol. 4168, pp. 804–816. Springer, Heidelberg (2006)
Goldberg, A., Kaplan, H., Werneck, R.: Reach for A *: Efficient point-to-point shortest path algorithms. In: Workshop on Algorithm Engineering & Experiments, Miami, pp. 129–143 (2006)
Schultes, D., Sanders, P.: Dynamic highway-node routing. In: 6th Workshop on Experimental Algorithms (2007)
Bast, H., Funke, S., Matijevic, D., Sanders, P., Schultes, D.: In transit to constant time shortest-path queries in road networks. In: Workshop on Algorithm Engineering and Experiments (2007)
Bast, H., Funke, S., Sanders, P., Schultes, D.: Fast routing in road networks with transit nodes. Science (to appear 2007)
Wagner, D., Willhalm, T.: Geometric speed-up techniques for finding shortest paths in large sparse graphs. In: Di Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 776–787. Springer, Heidelberg (2003)
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, Institut für Geoinformatik, Münster (2004)
Köhler, E., Möhring, R.H., Schilling, H.: Acceleration of shortest path and constrained shortest path computation. In: 4th International Workshop on Efficient and Experimental Algorithms (2005)
Möhring, R.H., Schilling, H., Schütz, B., Wagner, D., Willhalm, T.: Partitioning graphs to speed up Dijkstra’s algorithm. In: 4th International Workshop on Efficient and Experimental Algorithms. pp. 189–202 (2005)
Köhler, E., Möhring, R.H., Schilling, H.: Fast point-to-point shortest path computations with arc-flags. In: 9th DIMACS Implementation Challenge [29] (2006)
Goldberg, A.V., Werneck, R.F.: An efficient external memory shortest path algorithm. In: Workshop on Algorithm Engineering and Experimentation. pp. 26–40 (2005)
Maue, J., Sanders, P., Matijevic, D.: Goal directed shortest path queries using Precomputed Cluster Distances. In: Àlvarez, C., Serna, M. (eds.) WEA 2006. LNCS, vol. 4007, pp. 316–328. Springer, Heidelberg (2006)
Holzer, M., Schulz, F., Willhalm, T.: Combining speed-up techniques for shortest-path computations. In: Ribeiro, C.C., Martins, S.L. (eds.) WEA 2004. LNCS, vol. 3059, pp. 269–284. Springer, Heidelberg (2004)
Willhalm, T.: Engineering Shortest Path and Layout Algorithms for Large Graphs. PhD thesis, Universität Karlsruhe (TH), Fakultät für Informatik (2005)
Delling, D., Sanders, P., Schultes, D., Wagner, D.: Highway hierarchies star. In: 9th DIMACS Implementation Challenge [29] (2006)
9th DIMACS Implementation Challenge: Shortest Paths. http://www.dis.uniroma1.it/~challenge9 (2006)
Holzer, M., Schulz, F., Wagner, D.: Engineering multi-level overlay graphs for shortest-path queries. invited for ACM Journal of Experimental Algorithmics (special issue Alenex 2006) (2007)
Lauther, U.: An experimental evaluation of point-to-point shortest path calculation on roadnetworks with precalculated edge-flags. In: 9th DIMACS Implementation Challenge [29] (2006)
Goldberg, A.V., Kaplan, H., Werneck, R.F.: Better landmarks within reach. In: 9th DIMACS Implementation Challenge [29] (2006)
Müller, K.: Design and implementation of an efficient hierarchical speed-up technique for computation of exact shortest paths in graphs. Master’s thesis, Universtät Karlsruhe supervised by Delling, D., Holzer, M., Schulz, F., Wagner, D.: (2006)
Delling, D., Holzer, M., Müller, K., Schulz, F., Wagner, D.: High-performance multi-level graphs. In: 9th DIMACS Implementation Challenge [29] (2006)
Knopp, S., Sanders, P., Schultes, D., Schulz, F., Wagner, D.: Computing many-to-many shortest paths using highway hierarchies. In: Workshop on Algorithm Engineering and Experiments (2007)
Delling, D., Wagner, D.: Landmark-based routing in dynamic graphs. In: 6th Workshop on Experimental Algorithms (2007)
Bingmann, T.: Visualisierung sehr großer Graphen. Student Research Project, Universität Karlsruhe, supervised by Sanders, P., Schultes, D.: (2006)
U.S. Census Bureau, Washington, DC: UA Census 2000 TIGER/Line Files. http://www.census.gov/geo/www/ tiger/tigerua/ua_tgr2k.html (2002)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Sanders, P., Schultes, D. (2007). Engineering Fast Route Planning Algorithms. In: Demetrescu, C. (eds) Experimental Algorithms. WEA 2007. Lecture Notes in Computer Science, vol 4525. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72845-0_2
Download citation
DOI: https://doi.org/10.1007/978-3-540-72845-0_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72844-3
Online ISBN: 978-3-540-72845-0
eBook Packages: Computer ScienceComputer Science (R0)