Dynamic Arc-Flags in Road Networks

  • Gianlorenzo D’Angelo
  • Daniele Frigioni
  • Camillo Vitale
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6630)

Abstract

In this work we introduce a new data structure, named Road-Signs, which allows us to efficiently update the Arc-Flags of a graph in a dynamic scenario. Road-Signs can be used to compute Arc-Flags, can be efficiently updated and do not require large space consumption for many real-world graphs like, e.g., graphs arising from road networks. In detail, we define an algorithm to preprocess Road-Signs and an algorithm to update them each time that a weight increase operation occurs on an edge of the network. We also experimentally analyze the proposed algorithms in real-world road networks showing that they yields a significant speed-up in the updating phase of Arc-Flags, at the cost of a very small space and time overhead in the preprocessing phase.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Berrettini, E., D’Angelo, G., Delling, D.: Arc-flags in dynamic graphs. In: 9th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS 2009). Schloss Dagstuhl–Leibniz-Zentrum für Informatik, Germany (2009)Google Scholar
  2. 2.
    Bruera, F., Cicerone, S., D’Angelo, G., Stefano, G.D., Frigioni, D.: Dynamic multi-level overlay graphs for shortest paths. Mathematics in Computer Science 1(4), 709–736 (2008)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Delling, D., Hoffmann, R., Kandyba, M., Schulze, A.: Chapter 9. Case Studies. In: Müller-Hannemann, M., Schirra, S. (eds.) Algorithm Engineering. LNCS, vol. 5971, pp. 389–445. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  4. 4.
    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)CrossRefGoogle Scholar
  5. 5.
    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
  6. 6.
    Dijkstra, E.W.: A note on two problems in connexion with graphs. Numerische Mathematik 1, 269–271 (1959)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Frigioni, D., Marchetti-Spaccamela, A., Nanni, U.: Fully dynamic algorithms for maintaining shortest paths trees. Journal of Algorithms 34(2), 251–281 (2000)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Goldberg, A.V., Harrelson, C.: Computing the Shortest Path: A* Search Meets Graph Theory. In: 16th Annual ACM–SIAM Symposium on Discrete Algorithms (SODA 2005), pp. 156–165 (2005)Google Scholar
  9. 9.
    Hilger, M., Köhler, E., Möhring, R.H., Schilling, H.: Fast Point-to-Point Shortest Path Computations with Arc-Flags. In: Shortest Path Computations: Ninth DIMACS Challenge. DIMACS Book, vol. 24 (2009)Google Scholar
  10. 10.
    Karypis, G.: METIS - A Family of Multilevel Partitioning Algorithms (2007)Google Scholar
  11. 11.
    Lauther, U.: An extremely fast, exact algorithm for finding shortest paths. Static Networks with Geographical Background 22, 219–230 (2004)Google Scholar
  12. 12.
    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
  13. 13.
    PTV AG - Planung Transport Verkehr (2008), http://www.ptv.de
  14. 14.
    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
  15. 15.
    Sanders, P., Schultes, D.: Dynamic Highway-Node Routing. In: Demetrescu, C. (ed.) WEA 2007. LNCS, vol. 4525, pp. 66–79. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  16. 16.
    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
  17. 17.
    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
  18. 18.
    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 2011

Authors and Affiliations

  • Gianlorenzo D’Angelo
    • 1
  • Daniele Frigioni
    • 1
  • Camillo Vitale
    • 1
  1. 1.Department of Electrical and Information EngineeringUniversity of L’AquilaL’AquilaItaly

Personalised recommendations