Analysis of Random Walks Using Tabu Lists

  • Karine Altisen
  • Stéphane Devismes
  • Antoine Gerbaud
  • Pascal Lafourcade
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7355)


A tabu random walk on a graph is a partially self-avoiding random walk which uses a bounded memory to avoid cycles. This memory is called a tabu list and contains vertices already visited by the walker. The size of the tabu list being bounded, the way vertices are inserted and removed from the list, called here an update rule, has an important impact on the performance of the walk, namely the mean hitting time between two given vertices.

We define a large class of tabu random walks, characterized by their update rules. We enunciate a necessary and sufficient condition on these update rules that ensures the finiteness of the mean hitting time of their associated walk on every finite and connected graph. According to the memory allocated to the tabu list, we characterize the update rules which yield smallest mean hitting times on a large class of graphs. Finally, we compare the performances of three collections of classical update rules according to the size of their associated tabu list.


Random Walk Wireless Sensor Network Connected Graph Positive Probability Tabu List 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ochirkhand, E.O., Minier, M., Valois, F., Kountouris, A.: Resilient networking in wireless sensor networks. Research report, Inria (2010)Google Scholar
  2. 2.
    Ponsonnet, C.: Secure probabilistic routing in wireless sensor networks. Master thesis, Laboratoire Verimag (2011)Google Scholar
  3. 3.
    Lovász, L.: Random walks on graphs: A survey. In: Miklós, D., Sós, V.T., Szönyi, T. (eds.) Combinatorics, Paul Erdös is Eighty. Bolyai Society Mathematical Studies, vol. 2, pp. 1–46. János Bolyai Mathematical Society (1993)Google Scholar
  4. 4.
    Aldous, D., Fill, J.: Reversible Markov Chains and Random Walks on Graphs. Book in preparation (20XX),
  5. 5.
    Slade, G.: The self-avoiding walk: A brief survey. In: Blath, J., Imkeller, P., Roelly, S. (eds.) To appear in Surveys in Stochastic Processes, Proceedings of the Thirty-third SPA Conference in Berlin, 2009. The EMS Series of Congress Reports (2010)Google Scholar
  6. 6.
    Li, K.: Performance analysis and evaluation of random walk algorithms on wireless networks. In: IPDPS Workshops, pp. 1–8 (2010)Google Scholar
  7. 7.
    Altisen, K., Devismes, S., Lafourcade, P., Ponsonnet, C.: Routage par marche aléatoire à listes tabous. In: Algotel 2011, Cap Estérel, Mai 23-26 (2011)Google Scholar
  8. 8.
    Ortner, R., Woess, W.: Non-backtracking random walks and cogrowth of graphs. Canad. J. Math. 59(4), 828–844 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Altisen, K., Devismes, S., Gerbaud, A., Lafourcade, P.: Comparisons of mean hitting times for tabu random walks on finite graphs. Technical report, Laboratoire Verimag (2011),
  10. 10.
    Hughes, B.: Random walks and random environments, vol. 1. Oxford University Press (1995)Google Scholar
  11. 11.
    Levin, D., Peres, Y., Wilmer, E.: Markov chains and mixing times. American Mathematical Society (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Karine Altisen
    • 1
  • Stéphane Devismes
    • 1
  • Antoine Gerbaud
    • 1
  • Pascal Lafourcade
    • 1
  1. 1.VERIMAGGrenoble UniversitéFrance

Personalised recommendations