Fully Dynamic Maintenance of Arc-Flags in Road Networks

  • Gianlorenzo D’Angelo
  • Mattia D’Emidio
  • Daniele Frigioni
  • Camillo Vitale
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7276)

Abstract

The problem of finding best routes in road networks can be solved by applying Dijkstra’s shortest paths algorithm. Unfortunately, road networks deriving from real-world applications are huge yielding unsustainable times to compute shortest paths. For this reason, great research efforts have been done to accelerate Dijkstra’s algorithm on road networks. These efforts have led to the development of a number of speed-up techniques, as for example Arc-Flags, whose aim is to compute additional data in a preprocessing phase in order to accelerate the shortest paths queries in an on-line phase. The main drawback of most of these techniques is that they do not work well in dynamic scenarios.

In this paper we propose a new algorithm to update the Arc-Flags of a graph subject to edge weight decrease operations. To check the practical performances of the new algorithm we experimentally analyze it, along with a previously known algorithm for edge weight increase operations, on real-world road networks subject to fully dynamic sequences of operations. Our experiments show a significant speed-up in the updating phase of the Arc-Flags, at the cost of a small space and time overhead in the preprocessing phase.

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References

  1. 1.
    Berger, A., Grimmer, M., Müller-Hannemann, M.: Fully Dynamic Speed-Up Techniques for Multi-criteria Shortest Path Searches in Time-Dependent Networks. In: Festa, P. (ed.) SEA 2010. LNCS, vol. 6049, pp. 35–46. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  2. 2.
    Berrettini, E., D’Angelo, G., Delling, D.: Arc-flags in dynamic graphs. In: Proc. of the 9th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS 2009), Schloss Dagstuhl, Germany (2009)Google Scholar
  3. 3.
    D’Angelo, G., Frigioni, D., Vitale, C.: Dynamic Arc-Flags in Road Networks. In: Pardalos, P.M., Rebennack, S. (eds.) SEA 2011. LNCS, vol. 6630, pp. 88–99. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  4. 4.
    Delling, D., Goldberg, A.V., Pajor, T., Werneck, R.F.: Customizable Route Planning. In: Pardalos, P.M., Rebennack, S. (eds.) SEA 2011. LNCS, vol. 6630, pp. 376–387. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  5. 5.
    Delling, D., Sanders, P., Schultes, D., Wagner, D.: Engineering Route Planning Algorithms. In: Lerner, J., Wagner, D., Zweig, K.A. (eds.) Algorithmics. LNCS, vol. 5515, pp. 117–139. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  6. 6.
    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
  7. 7.
    Goldberg, A.V., Harrelson, C.: Computing the Shortest Path: A* Search Meets Graph Theory. In: 16th Annual ACM–SIAM Symp. on Discrete Algorithms (SODA 2005), pp. 156–165 (2005)Google Scholar
  8. 8.
    Karypis, G.: METIS - A Family of Multilevel Partitioning Algorithms (2007)Google Scholar
  9. 9.
    Lauther, U.: An extremely fast, exact algorithm for finding shortest paths. Static Networks with Geographical Background 22, 219–230 (2004)Google Scholar
  10. 10.
    Möhring, R.H., Schilling, H., Schütz, B., Wagner, D., Willhalm, T.: Partitioning Graphs to Speedup Dijkstra’s Algorithm. ACM J. Exp. Algorithmics 11, 2.8 (2006)Google Scholar
  11. 11.
    PTV AG - Planung Transport Verkehr (2008),http://www.ptv.de
  12. 12.
    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
  13. 13.
    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
  14. 14.
    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
  15. 15.
    Wagner, D., Willhalm, T., Zaroliagis, C.: Geometric Containers for Efficient Shortest-Path Computation. ACM J. Exp. Algorithmics 10, 1.3 (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Gianlorenzo D’Angelo
    • 1
  • Mattia D’Emidio
    • 2
  • Daniele Frigioni
    • 2
  • Camillo Vitale
    • 2
  1. 1.MASCOTTE ProjectI3S(CNRS/UNSA)/INRIAFrance
  2. 2.Dept. of Electrical and Information EngineeringUniversity of L’AquilaItaly

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