Abstract
Algorithms for route planning in transportation networks have recently undergone a rapid development, leading to methods that are up to three million times faster than Dijkstra’s algorithm. We give an overview of the techniques enabling this development and point out frontiers of ongoing research on more challenging variants of the problem that include dynamically changing networks, time-dependent routing, and flexible objective functions.
Partially supported by DFG grants SA 933/1-3, SA 933/5-1, WA 654/16-1 and the Future and Emerging Technologies Unit of EC (IST priority – 6th FP), under contract no. FP6-021235-2 (project ARRIVAL). A preliminary version of this paper has been published in [60]
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Barrett, C., Bisset, K., Holzer, M., Konjevod, G., Marathe, M.V., Wagner, D.: Engineering Label-Constrained Shortest-Path Algorithms. In: Fleischer, R., Xu, J. (eds.) AAIM 2008. LNCS, vol. 5034, pp. 27–37. Springer, Heidelberg (2008)
Bast, H., Funke, S., Matijevic, D.: TRANSIT Ultrafast Shortest-Path Queries with Linear-Time Preprocessing. In: Demetrescu, C., Goldberg, A.V., Johnson, D.S. (eds.) Shortest Paths: Ninth DIMACS Implementation Challenge, DIMACS Book. American Mathematical Society, Providence (2008) (to appear) (accepted for publication)
Bast, H., Funke, S., Matijevic, D., Sanders, P., Schultes, D.: In Transit to Constant Shortest-Path Queries in Road Networks. In: Proceedings of the 9th Workshop on Algorithm Engineering and Experiments (ALENEX 2007), pp. 46–59. SIAM, Philadelphia (2007)
Bast, H., Funke, S., Sanders, P., Schultes, D.: Fast Routing in Road Networks with Transit Nodes. Science 316(5824), 566 (2007)
Batz, G.V., Geisberger, R., Sanders, P.: Time Dependent Contraction Hierarchies - Basic Algorithmic Ideas. Technical report, ITI Sanders, Faculty of Informatics, Universität Karlsruhe (TH) (2008), arXiv:0804.3947v1 [cs.DS]
Bauer, R., Delling, D.: SHARC: Fast and Robust Unidirectional Routing. In: Munro, I., Wagner, D. (eds.) Proceedings of the 10th Workshop on Algorithm Engineering and Experiments (ALENEX 2008), pp. 13–26. SIAM, Philadelphia (2008)
Bauer, R., Delling, D.: SHARC: Fast and Robust Unidirectional Routing. Submitted to the ACM Journal of Experimental Algorithmics (2008) (full paper)
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)
Bauer, R., Delling, D., Wagner, D.: Experimental Study on Speed-Up Techniques for Timetable Information Systems. In: Liebchen, C., Ahuja, R.K., Mesa, J.A. (eds.) Proceedings of the 7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS 2007), pp. 209–225. Internationales Begegnungs- und Forschungszentrum für Informatik (IBFI), Schloss Dagstuhl, Germany (2007)
Bingmann, T.: Visualisierung sehr großer Graphen. Student Research Project (2006)
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)
Dantzig, G.B.: Linear Programming and Extensions. Princeton University Press, Princeton (1962)
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., Holzer, M., Müller, K., Schulz, F., Wagner, D.: High-Performance Multi-Level Routing. In: Demetrescu, C., Goldberg, A.V., Johnson, D.S. (eds.) Shortest Paths: Ninth DIMACS Implementation Challenge, DIMACS Book. American Mathematical Society, Providence (2008) (to appear) (accepted for publication)
Delling, D., Nannicini, G.: Bidirectional Core-Based Routing in Dynamic Time-Dependent Road Networks. In: Proceedings of the 19th International Symposium on Algorithms and Computation (ISAAC 2008). LNCS. Springer, Heidelberg (2008) (to appear)
Delling, D., Sanders, P., Schultes, D., Wagner, D.: Highway Hierarchies Star. In: Demetrescu, et al. (eds.) [19]
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)
Demetrescu, C., Goldberg, A.V., Johnson, D.S. (eds.): 9th DIMACS Implementation Challenge - Shortest Paths (November 2006)
Dijkstra, E.W.: A Note on Two Problems in Connexion with Graphs. Numerische Mathematik 1, 269–271 (1959)
Disser, Y., Müller-Hannemann, M., Schnee, M.: Multi-Criteria Shortest Paths in Time-Dependent Train Networks. In: McGeoch, C.C. (ed.) WEA 2008. LNCS, vol. 5038, pp. 347–361. Springer, Heidelberg (2008)
Fakcharoenphol, J., Rao, S.: Planar Graphs, Negative Weight Edges, Shortest Paths, and near Linear Time. Journal of Computer and System Sciences 72(5), 868–889 (2006)
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.: Personal communication (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., Kaplan, H., Werneck, R.F.: Reach for A*: Efficient Point-to-Point Shortest Path Algorithms. In: Proceedings of the 8th Workshop on Algorithm Engineering and Experiments (ALENEX 2006), pp. 129–143. SIAM, Philadelphia (2006)
Goldberg, A.V., Kaplan, H., Werneck, R.F.: Better Landmarks Within Reach. In: Demetrescu, C. (ed.) WEA 2007. LNCS, vol. 4525, pp. 38–51. Springer, Heidelberg (2007)
Goldberg, A.V., Kaplan, H., Werneck, R.F.: Reach for A*: Shortest Path Algorithms with Preprocessing. In: Demetrescu, C., Goldberg, A.V., Johnson, D.S. (eds.) Shortest Paths: Ninth DIMACS Implementation Challenge, DIMACS Book. American Mathematical Society, Providence (2008) (to appear) (accepted for publication)
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)
Gunkel, T., Müller-Hannemann, M., Schnee, M.: Improved Search for Night Train Connections. In: Liebchen, C., Ahuja, R.K., Mesa, J.A. (eds.) Proceedings of the 7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS 2007), pp. 243–258. Internationales Begegnungs- und Forschungszentrum für Informatik (IBFI), Schloss Dagstuhl, Germany (2007)
Gutman, R.J.: Reach-Based Routing: A New Approach to Shortest Path Algorithms Optimized for Road Networks. In: Proceedings of the 6th Workshop on Algorithm Engineering and Experiments (ALENEX 2004), pp. 100–111. SIAM, Philadelphia (2004)
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 Paths: Ninth DIMACS Implementation Challenge, DIMACS Book. American Mathematical Society, Providence (2008) (to appear)
Holzer, M.: Engineering Planar-Separator and Shortest-Path Algorithms. Ph.D thesis, Universität Karlsruhe (TH), Fakultät für Informatik (2008)
Holzer, M., Schulz, F., Wagner, D.: Engineering Multi-Level Overlay Graphs for Shortest-Path Queries. In: Proceedings of the 8th Workshop on Algorithm Engineering and Experiments (ALENEX 2006). SIAM, Philadelphia (2006)
Holzer, M., Schulz, F., Wagner, D.: Engineering Multi-Level Overlay Graphs for Shortest-Path Queries. ACM Journal of Experimental Algorithmics (2008) (to appear)
Holzer, M., Schulz, F., Wagner, D., Willhalm, T.: Combining Speed-up Techniques for Shortest-Path Computations. ACM Journal of Experimental Algorithmics 10 (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)
Ishikawa, K., Ogawa, M., Azuma, M., Ito, T.: Map Navigation Software of the Electro-Multivision of the 91 Toyoto Soarer. In: Proceedings of the Vehicle Navigation and Information Systems Conference (VNIS 1991), pp. 463–473. IEEE Computer Society, Los Alamitos (1991)
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)
Klein, P.N.: Multiple-Source Shortest Paths in Planar Graphs. In: Proceedings of the 16th Annual ACM–SIAM Symposium on Discrete Algorithms (SODA 2005), pp. 146–155 (2005)
Knopp, S., Sanders, P., Schultes, D., Schulz, F., Wagner, D.: Computing Many-to-Many Shortest Paths Using Highway Hierarchies. In: Proceedings of the 9th Workshop on Algorithm Engineering and Experiments (ALENEX 2007), pp. 36–45. SIAM, Philadelphia (2007)
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 Paths: Ninth DIMACS Implementation Challenge, DIMACS Book. American Mathematical Society, Providence (2008) (to appear)
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. 316–327. Springer, Heidelberg (2006)
Meyer, U.: Single-Source Shortest-Paths on Arbitrary Directed Graphs in Linear Average-Case Time. In: Proceedings of the 12th Annual ACM–SIAM Symposium on Discrete Algorithms (SODA 2001), pp. 797–806 (2001)
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)
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)
Müller, K.: Berechnung kürzester Pfade unter Beachtung von Abbiegeverboten. Student Research Project (2005)
Müller, K.: Design and Implementation of an Efficient Hierarchical Speed-up Technique for Computation of Exact Shortest Paths in Graphs. Master’s thesis, Universität Karlsruhe (TH), Fakultät für Informatik (June 2006)
Muller, L.F., Zachariasen, M.: Fast and Compact Oracles for Approximate Distances in Planar Graphs. In: Arge, L., Hoffmann, M., Welzl, E. (eds.) ESA 2007. LNCS, vol. 4698, pp. 657–668. Springer, Heidelberg (2007)
Müller-Hannemann, M., Schnee, M.: Finding All Attractive Train Connections by Multi-Criteria Pareto Search. In: Geraets, F., Kroon, L.G., Schoebel, A., Wagner, D., Zaroliagis, C.D. (eds.) Railway Optimization 2004. LNCS, vol. 4359, pp. 246–263. Springer, Heidelberg (2007)
Müller-Hannemann, M., Schulz, F., Wagner, D., Zaroliagis, C.: Timetable Information: Models and Algorithms. In: Geraets, F., Kroon, L.G., Schoebel, A., Wagner, D., Zaroliagis, C.D. (eds.) Railway Optimization 2004. LNCS, vol. 4359, pp. 67–90. Springer, Heidelberg (2007)
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)
Sanders, P., Schultes, D.: Engineering Highway Hierarchies. In: Azar, Y., Erlebach, T. (eds.) ESA 2006. LNCS, vol. 4168, pp. 804–816. Springer, Heidelberg (2006)
Sanders, P., Schultes, D.: Engineering Fast Route Planning Algorithms. In: Demetrescu, C. (ed.) WEA 2007. LNCS, vol. 4525, pp. 23–36. Springer, Heidelberg (2007)
Sanders, P., Schultes, D.: Robust, Almost Constant Time Shortest-Path Queries in Road Networks. In: Demetrescu, C., Goldberg, A.V., Johnson, D.S. (eds.) Shortest Paths: Ninth DIMACS Implementation Challenge, DIMACS Book. American Mathematical Society, Providence (2008) (to appear) (accepted for publication)
Sanders, P., Schultes, D., Vetter, C.: Mobile Route Planning. In: Halperin, D., Mehlhorn, K. (eds.) ESA 2008. LNCS, vol. 5193, pp. 732–743. Springer, Heidelberg (2008)
Schilling, H.: Route Assignment Problems in Large Networks. Ph.D thesis, Technische Universität Berlin (2006)
Schultes, D.: Route Planning in Road Networks. Ph.D thesis, Universität Karlsruhe (TH), Fakultät für Informatik (February 2008)
Schultes, D., Sanders, P.: Dynamic Highway-Node Routing. In: Demetrescu, C. (ed.) WEA 2007. LNCS, vol. 4525, pp. 66–79. Springer, Heidelberg (2007)
Schulz, F.: Timetable Information and Shortest Paths. Ph.D thesis, Universität Karlsruhe (TH), Fakultät für Informatik (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)
Schulz, F., Wagner, D., Weihe, K.: Dijkstra’s Algorithm On-Line: An Empirical Case Study from Public Railroad Transport. ACM Journal of Experimental Algorithmics 5 (2000)
Schulz, F., Wagner, D., Zaroliagis, C.: Using Multi-Level Graphs for Timetable Information in Railway Systems. In: Mount, D.M., Stein, C. (eds.) ALENEX 2002. LNCS, vol. 2409, pp. 43–59. Springer, Heidelberg (2002)
Thorup, M.: Compact Oracles for Reachability and Approximate Distances in Planar Digraphs. In: Proceedings of the 42nd Annual IEEE Symposium on Foundations of Computer Science (FOCS 2001), pp. 242–251. IEEE Computer Society Press, Los Alamitos (2001)
Thorup, M.: Integer Priority Queues with Decrease Key in Constant Time and the Single Source Shortest Paths Problem. In: Proceedings of the 35th Annual ACM Symposium on the Theory of Computing (STOC 2003), June 2003, pp. 149–158 (2003)
U.S. Census Bureau, Washington, DC. UA Census 2000 TIGER/Line Files (2002), http://www.census.gov/geo/www/tiger/tigerua/ua_tgr2k.html
Volker, L.: Route planning in road networks with turn costs. Studienarbeit, Universität Karlsruhe, Institut für theoretische Informatik (2008)
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)
Wagner, D., Willhalm, T., Zaroliagis, C.: Geometric Containers for Efficient Shortest-Path Computation. ACM Journal of Experimental Algorithmics 10, 1.3 (2005)
Willhalm, T.: Engineering Shortest Paths and Layout Algorithms for Large Graphs. Ph.D thesis, Universität Karlsruhe (TH), Fakultät für Informatik (2005)
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Delling, D., Sanders, P., Schultes, D., Wagner, D. (2009). Engineering Route Planning Algorithms. In: Lerner, J., Wagner, D., Zweig, K.A. (eds) Algorithmics of Large and Complex Networks. Lecture Notes in Computer Science, vol 5515. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02094-0_7
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