Advertisement

Random Walks in Distributed Computing: A Survey

  • Marc Bui
  • Thibault Bernard
  • Devan Sohier
  • Alain Bui
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3473)

Abstract

In this survey, we give an overview of the use of random walks as a traversal scheme to derive distributed control algorithms over a network of computers. It is shown that this paradigm for information exchange can be an attractive technique by using electric network theory as a mathematical tool for performance evaluation.

Keywords

Distributed System Random Walks Electrical Network Distributed Algorithms 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. AKL+79.
    Aleliunas, R., Karp, R., Lipton, R., Lovasz, L., Rackoff, C.: Randomwalks, universal traversal sequences and the complexity of maze problems. In: 20th IEEE Annual Symposium on Foundations of Computer Science, October 1979, pp. 218–223 (1979)Google Scholar
  2. BBBS03.
    Bernard, T., Bui, A., Bui, M., Sohier, D.: A new method to automatically compute processing times for random walks based distributed algorithm. In: Paprzycki, M. (ed.) ISPDC 2003, Second IEEE International Symposium on Parallel and Distributed Computing Proceeding, vol. 2069, pp. 31–36. IEEE Computer Society Press, Los Alamitos (2003)CrossRefGoogle Scholar
  3. BBF04.
    Bernard, T., Bui, A., Flauzac, O.: Random distributed self-stabilizing structures maintenance. In: Ramos, F.F., Unger, H., Larios, V. (eds.) ISSADS 2004. LNCS, vol. 3061, pp. 231–240. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  4. BBS03.
    Bui, A., Bui, M., Sohier, D.: Randomly distributed tasks in bounded time. In: Böhme, T., Heyer, G., Unger, H. (eds.) IICS 2003. LNCS, vol. 2877, pp. 36–47. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  5. BDDN01.
    Bui, M., Das, S.K., Datta, A.K., Nguyen, D.T.: Randomized mobile agent based routing in wireless networks. International Journal of Foundations of Computer Science 12(3), 365–384 (2001)CrossRefGoogle Scholar
  6. BFG+03.
    Baala, H., Flauzac, O., Gaber, J., Bui, M., El-Ghazawi, T.: A self-stabilizing distributed algorithm for spanning tree construction in wireless ad-hoc network. Journal of Parallel and Distributed Computing 63(1), 97–104 (2003)zbMATHCrossRefGoogle Scholar
  7. BIZ89.
    Bar-Ilan, J., Zernik, D.: Random leaders and random spanning trees. In: Bermond, J.-C., Raynal, M. (eds.) WDAG 1989. LNCS, vol. 392, pp. 1–12. Springer, Heidelberg (1989)Google Scholar
  8. Bro89.
    Broder, A.Z.: Generating random spanning trees. In: FOCS 1989 Proceedings of the 29st annual IEEE Symposium on foundation of computer sciences, pp. 442–447 (1989)Google Scholar
  9. CRR+97.
    Chandra, A.K., Raghavan, P., Ruzzo, W.L., Smolensky, R., Tiwari, P.: The electrical resistance of a graph captures its commute and cover times. Computational Complexity 6(4) (1997)Google Scholar
  10. DS00.
    Doyle, P.G., Laurie Snell, J.: Random Walks and Electric Networks (2000)Google Scholar
  11. Fla01.
    Flauzac, O.: Random circulating word information management for tree construction and shortest path routing tables computation. In: On Principle Of DIstributed Systems, pp. 17–32. Studia Informatica Universalis (2001)Google Scholar
  12. IJ90.
    Israeli, A., Jalfon, M.: Token management schemes and random walks yield selfstabilizing mutual exclusion. In: PODC 1990, Proceeding of the ninth ACM Annual Symposium on Principles of distributed Computing, pp. 119–131 (1990)Google Scholar
  13. Lov93.
    Lovasz, L.: Random walks on graphs: A survey. In: Szonyi, T., Miklos, D., Sos, V.T. (eds.) Combinatorics: Paul Erdos is Eighty. Janos Bolyai Mathematical Society, vol. 2, pp. 353–398 (1993)Google Scholar
  14. Tet91.
    Tetali, P.: Random walks and effective resistance of networks. J. Theoretical Probability 1, 101–109 (1991)CrossRefMathSciNetGoogle Scholar
  15. TW91.
    Tetali, P., Winkler, P.: On a random walk arising in self-stabilizing token management. In: PODC 1991, Proceeding of the tenth ACM Annual Symposium on Principles of distributed Computing, pp. 273–280 (1991)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Marc Bui
    • 2
  • Thibault Bernard
    • 1
  • Devan Sohier
    • 1
    • 2
  • Alain Bui
    • 1
  1. 1.Département de Mathématiques et InformatiqueUniversité de Reims Champagne ArdennesReims cedexFrance
  2. 2.LRIA – EPHEParisFrance

Personalised recommendations