Advertisement

Distributed algorithms for updating shortest paths

  • Giuseppe F. Italiano
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 579)

Abstract

We present a distributed algorithm for updating all pairs shortest paths when an edge is either inserted or has its cost decreased. For unit edge costs (i.e., for maintaining all pairs minimum hops) our algorithm transmits a total of O(V3 log V) messages during the insertion of O(V2) edges. This gives basically O(V log V) messages per change in the amortized sense. For integer edge costs in [1, W], our algorithm transmits at most O(WV3 log(VW)) messages during O(WV2) edge insertions or edge cost decreases. Again, this gives O(V log(VW)) messages per change in the amortized sense. The algorithm runs asynchronously, requires O(V) time per change and O(V) space per node.

This result favorably compares to using the best known distributed algorithm for computing all pairs shortest paths from scratch, and to other dynamic distributed algorithms previously proposed in the literature.

Keywords

Short Path Sequential Algorithm Message Complexity Edge Cost Good Pair 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Y. Afek, B. Awerbuch, and E. Gafni. Applying static network protocols to dynamic networks. In Proc. 28th Annual IEEE Symp. on Foundations of Computer Science, pages 358–370, 1987.Google Scholar
  2. [2]
    A. V. Aho, J. E. Hopcroft, and J. D. Ullman. The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading, MA, 1974.Google Scholar
  3. [3]
    G. Ausiello, G. F. Italiano, A. Marchetti Spaccamela, and U. Nanni. Incremental algorithms for minimal length paths. In Proc. 1st Annual ACM-SIAM Symp. on Discrete Algorithms, pages 12–21, 1990. A journal version to appear in J. Algorithms.Google Scholar
  4. [4]
    B. Awerbuch. On the effects of feedback in dynamic network protocols. In Proc. 29th Annual IEEE Symp. on Foundations of Computer Science, pages 231–245, 1988.Google Scholar
  5. [5]
    B. Awerbuch. Distributed shortest paths algorithms. In Proc. 21st Annual ACM Symp. on Theory of Computing, pages 490–500, 1989.Google Scholar
  6. [6]
    B. Awerbuch, I. Cidon, and S. Kutten. Communication-optimal maintainance of replicated information. In Proc. 31st Annual IEEE Symp. on Foundations of Computer Science, pages 492–502, 1990.Google Scholar
  7. [7]
    B. Awerbuch and M. Sipser. Dynamic networks are as fast as static networks. In Proc. 29th Annual IEEE Symp. on Foundations of Computer Science, pages 206–219, 1988.Google Scholar
  8. [8]
    E. Gafni. Topology resynchronization: a new paradigm for fault tolerance in distributed algorithms. In Proc. of the Amsterdam Workshop on Distributed Algorithms, 1987.Google Scholar
  9. [9]
    R. G. Gallager. A shortest path routing algorithm with automatic resynch. Technical report, MIT, Lab. for Information and Decision Systems, 1976.Google Scholar
  10. [10]
    R. G. Gallager. An optimal routing algorithm using distributed computation. IEEE Trans, on Commun., COM-25:73–85, 1977.Google Scholar
  11. [11]
    J. Jaffe and F. Moss. A responsive distributed routing protocol. IEEE Trans, on Commun., COM-30:1758–1762, 1982.Google Scholar
  12. [12]
    K. V. S. Ramarao and S. Venkatesan. On finding and updating shortest paths. In Proc. 24th Annual Allerton Conf. on Communication, Control and Computing, pages 1079–1988, 1986.Google Scholar
  13. [13]
    A. S. Tanenbaum. Computer networks. Prentice-Hall, Englewood Cliffs, NJ, 1981.Google Scholar
  14. [14]
    R. E. Tarjan. Data structures and network algorithms, volume 44. CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM, 1983.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Giuseppe F. Italiano
    • 1
  1. 1.IBM Research DivisionT. J. Watson Research CenterYorktown Heights

Personalised recommendations