Engineering Route Planning Algorithms

  • Daniel Delling
  • Peter Sanders
  • Dominik Schultes
  • Dorothea Wagner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5515)

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    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)CrossRefGoogle Scholar
  2. 2.
    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)Google Scholar
  3. 3.
    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)CrossRefGoogle Scholar
  4. 4.
    Bast, H., Funke, S., Sanders, P., Schultes, D.: Fast Routing in Road Networks with Transit Nodes. Science 316(5824), 566 (2007)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    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]Google Scholar
  6. 6.
    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)CrossRefGoogle Scholar
  7. 7.
    Bauer, R., Delling, D.: SHARC: Fast and Robust Unidirectional Routing. Submitted to the ACM Journal of Experimental Algorithmics (2008) (full paper)Google Scholar
  8. 8.
    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)CrossRefGoogle Scholar
  9. 9.
    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)Google Scholar
  10. 10.
    Bingmann, T.: Visualisierung sehr großer Graphen. Student Research Project (2006)Google Scholar
  11. 11.
    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)Google Scholar
  12. 12.
    Dantzig, G.B.: Linear Programming and Extensions. Princeton University Press, Princeton (1962)MATHGoogle Scholar
  13. 13.
    Dean, B.C.: Continuous-Time Dynamic Shortest Path Algorithms. Master’s thesis, Massachusetts Institute of Technology (1999)Google Scholar
  14. 14.
    Delling, D.: Time-Dependent SHARC-Routing. In: Halperin, D., Mehlhorn, K. (eds.) ESA 2008. LNCS, vol. 5193, pp. 332–343. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  15. 15.
    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)Google Scholar
  16. 16.
    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)Google Scholar
  17. 17.
    Delling, D., Sanders, P., Schultes, D., Wagner, D.: Highway Hierarchies Star. In: Demetrescu, et al. (eds.) [19]Google Scholar
  18. 18.
    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)CrossRefGoogle Scholar
  19. 19.
    Demetrescu, C., Goldberg, A.V., Johnson, D.S. (eds.): 9th DIMACS Implementation Challenge - Shortest Paths (November 2006)Google Scholar
  20. 20.
    Dijkstra, E.W.: A Note on Two Problems in Connexion with Graphs. Numerische Mathematik 1, 269–271 (1959)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    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)CrossRefGoogle Scholar
  22. 22.
    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)MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    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)CrossRefGoogle Scholar
  24. 24.
    Goldberg, A.: Personal communication (2008)Google Scholar
  25. 25.
    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)Google Scholar
  26. 26.
    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)CrossRefGoogle Scholar
  27. 27.
    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)CrossRefGoogle Scholar
  28. 28.
    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) Google Scholar
  29. 29.
    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)Google Scholar
  30. 30.
    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)Google Scholar
  31. 31.
    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)Google Scholar
  32. 32.
    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)CrossRefGoogle Scholar
  33. 33.
    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)Google Scholar
  34. 34.
    Holzer, M.: Engineering Planar-Separator and Shortest-Path Algorithms. Ph.D thesis, Universität Karlsruhe (TH), Fakultät für Informatik (2008)Google Scholar
  35. 35.
    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)Google Scholar
  36. 36.
    Holzer, M., Schulz, F., Wagner, D.: Engineering Multi-Level Overlay Graphs for Shortest-Path Queries. ACM Journal of Experimental Algorithmics (2008) (to appear)Google Scholar
  37. 37.
    Holzer, M., Schulz, F., Wagner, D., Willhalm, T.: Combining Speed-up Techniques for Shortest-Path Computations. ACM Journal of Experimental Algorithmics 10 (2006)Google Scholar
  38. 38.
    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)CrossRefGoogle Scholar
  39. 39.
    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)Google Scholar
  40. 40.
    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)Google Scholar
  41. 41.
    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)Google Scholar
  42. 42.
    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)CrossRefGoogle Scholar
  43. 43.
    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)CrossRefGoogle Scholar
  44. 44.
    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)Google Scholar
  45. 45.
    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)Google Scholar
  46. 46.
    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)CrossRefGoogle Scholar
  47. 47.
    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)Google Scholar
  48. 48.
    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)CrossRefGoogle Scholar
  49. 49.
    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)Google Scholar
  50. 50.
    Müller, K.: Berechnung kürzester Pfade unter Beachtung von Abbiegeverboten. Student Research Project (2005)Google Scholar
  51. 51.
    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)Google Scholar
  52. 52.
    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)CrossRefGoogle Scholar
  53. 53.
    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)CrossRefGoogle Scholar
  54. 54.
    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)CrossRefGoogle Scholar
  55. 55.
    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)CrossRefGoogle Scholar
  56. 56.
    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)MathSciNetCrossRefMATHGoogle Scholar
  57. 57.
    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)Google Scholar
  58. 58.
    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)CrossRefGoogle Scholar
  59. 59.
    Sanders, P., Schultes, D.: Engineering Highway Hierarchies. In: Azar, Y., Erlebach, T. (eds.) ESA 2006. LNCS, vol. 4168, pp. 804–816. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  60. 60.
    Sanders, P., Schultes, D.: Engineering Fast Route Planning Algorithms. In: Demetrescu, C. (ed.) WEA 2007. LNCS, vol. 4525, pp. 23–36. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  61. 61.
    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)Google Scholar
  62. 62.
    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)CrossRefGoogle Scholar
  63. 63.
    Schilling, H.: Route Assignment Problems in Large Networks. Ph.D thesis, Technische Universität Berlin (2006)Google Scholar
  64. 64.
    Schultes, D.: Route Planning in Road Networks. Ph.D thesis, Universität Karlsruhe (TH), Fakultät für Informatik (February 2008)Google Scholar
  65. 65.
    Schultes, D., Sanders, P.: Dynamic Highway-Node Routing. In: Demetrescu, C. (ed.) WEA 2007. LNCS, vol. 4525, pp. 66–79. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  66. 66.
    Schulz, F.: Timetable Information and Shortest Paths. Ph.D thesis, Universität Karlsruhe (TH), Fakultät für Informatik (2005)Google Scholar
  67. 67.
    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)CrossRefGoogle Scholar
  68. 68.
    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)Google Scholar
  69. 69.
    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)CrossRefGoogle Scholar
  70. 70.
    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)Google Scholar
  71. 71.
    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)Google Scholar
  72. 72.
    U.S. Census Bureau, Washington, DC. UA Census 2000 TIGER/Line Files (2002), http://www.census.gov/geo/www/tiger/tigerua/ua_tgr2k.html
  73. 73.
    Volker, L.: Route planning in road networks with turn costs. Studienarbeit, Universität Karlsruhe, Institut für theoretische Informatik (2008)Google Scholar
  74. 74.
    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)CrossRefGoogle Scholar
  75. 75.
    Wagner, D., Willhalm, T., Zaroliagis, C.: Geometric Containers for Efficient Shortest-Path Computation. ACM Journal of Experimental Algorithmics 10, 1.3 (2005)Google Scholar
  76. 76.
    Willhalm, T.: Engineering Shortest Paths and Layout Algorithms for Large Graphs. Ph.D thesis, Universität Karlsruhe (TH), Fakultät für Informatik (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Daniel Delling
    • 1
  • Peter Sanders
    • 1
  • Dominik Schultes
    • 1
  • Dorothea Wagner
    • 1
  1. 1.Universität Karlsruhe (TH)KarlsruheGermany

Personalised recommendations