Advertisement

Does Path Cleaning Help in Dynamic All-Pairs Shortest Paths?

  • C. Demetrescu
  • P. Faruolo
  • G. F. Italiano
  • M. Thorup
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4168)

Abstract

In the dynamic all-pairs shortest path problem we wish to maintain information about distances in a weighted graph subject to dynamic operations such as edge insertions, edge deletions, and edge weight updates. The most efficient algorithms for this problem maintain a suitable superset of shortest paths in the graph. This superset retains information about the history of previous graph updates so as to avoid pathological situations where algorithms are continuously forced to rebuild large portions of their data structures. On the other hand, the set of maintained paths may grow too large, resulting in both prohibitive space consumption and inefficient updates. To circumvent this problem, the algorithms perform suitable path cleaning operations. In this paper, we implement and experiment with a recent efficient algorithm by Thorup, which differs from the previous algorithms mainly in the way path cleaning is done, and we carry out a thorough experimental investigation on known implementations of dynamic shortest path algorithms. Our experimental study puts the new results into perspective with respect to previous work and gives evidence that path cleaning, although crucial for the theoretical bounds, appears to be instead of very limited impact in practice.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Buriol, L., Resende, M., Thorup, M.: Speeding up dynamic shortest path algorithms. Technical report, AT&T Labs Research Report TD5RJ8B (2003)Google Scholar
  2. 2.
    Demetrescu, C., Emiliozzi, S., Finocchi, I., Ribichini, A.: The Leonardo Library, http://www.leonardo-vm.org
  3. 3.
    Demetrescu, C., Emiliozzi, S., Italiano, G.F.: Experimental analysis of dynamic all pairs shortest path algorithms. In: Proc. 15th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2004), pp. 362–371 (2004)Google Scholar
  4. 4.
    Demetrescu, C., Frigioni, D., Marchetti-Spaccamela, A., Nanni, U.: Maintaining shortest paths in digraphs with arbitrary arc weights: An experimental study. In: Näher, S., Wagner, D. (eds.) WAE 2000. LNCS, vol. 1982. Springer, Heidelberg (2001)Google Scholar
  5. 5.
    Demetrescu, C., Italiano, G.F.: A new approach to dynamic all pairs shortest paths. J. ACM 51(6), 968–992 (2004) (preliminary version in STOC 2003)Google Scholar
  6. 6.
    Dijkstra, E.W.: A note on two problems in connexion with graphs. Numerische Mathematik 1, 269–271 (1959)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Fortz, B., Thorup, M.: Internet traffic engineering by optimizing OSPF weights. In: Proc. 19th IEEE INFOCOM, pp. 519–528 (2000)Google Scholar
  8. 8.
    Frigioni, D., Ioffreda, M., Nanni, U., Pasqualone, G.: Analysis of dynamic algorithms for the single source shortest path problem. ACM Journal on Experimental Algorithmics 3 (1998)Google Scholar
  9. 9.
    Frigioni, D., Miller, T., Nanni, U., Pasqualone, G., Shaefer, G., Zaroliagis, C.D.: An experimental study of dynamic algorithms for directed graphs. In: Bilardi, G., Pietracaprina, A., Italiano, G.F., Pucci, G. (eds.) ESA 1998. LNCS, vol. 1461, pp. 320–331. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  10. 10.
    Goldberg, A.V.: Shortest path algorithms: Engineering aspects. In: Eades, P., Takaoka, T. (eds.) ISAAC 2001. LNCS, vol. 2223. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  11. 11.
    Henzinger, M.R., King, V.: Maintaining minimum spanning forests in dynamic graphs. SIAM J. Computing 31(2), 364–374 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    King, V.: Fully dynamic algorithms for maintaining all-pairs shortest paths and transitive closure in digraphs. In: Proc. 40th IEEE Symposium on Foundations of Computer Science (FOCS 1999), pp. 81–99 (1999)Google Scholar
  13. 13.
    Loubal, P.: A network evaluation procedure. Highway Research Record 205, 96–109 (1967)Google Scholar
  14. 14.
    Narvaez, P., Siu, K.Y., Tzeng, H.Y.: New dynamic SPT algorithm based on a ball-and-string model. IEEE/ACM Transactions on Networking 9, 706–718 (2001)CrossRefGoogle Scholar
  15. 15.
    Ramalingam, G.: Bounded Incremental Computation. LNCS, vol. 1089. Springer, Heidelberg (1996)zbMATHCrossRefGoogle Scholar
  16. 16.
    Thorup, M.: Fully-dynamic all-pairs shortest paths: Faster and allowing negative cycles. In: Hagerup, T., Katajainen, J. (eds.) SWAT 2004. LNCS, vol. 3111, pp. 384–396. Springer, Heidelberg (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • C. Demetrescu
    • 1
  • P. Faruolo
    • 2
  • G. F. Italiano
    • 3
  • M. Thorup
    • 4
  1. 1.Dip. di Informatica e SistemisticaUniv. Roma “La Sapienza”Italy
  2. 2.Dip. di Informatica ed ApplicazioniUniv. SalernoItaly
  3. 3.Dip. di Informatica, Sistemi e ProduzioneUniv. Roma “Tor Vergata”Italy
  4. 4.AT&T Labs-ResearchFlorham ParkUSA

Personalised recommendations