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Efficient Exploration of Anonymous Undirected Graphs

  • Ralf Klasing
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8288)

Abstract

We consider the problem of exploring an anonymous undirected graph using an oblivious robot. The studied exploration strategies are designed so that the next edge in the robot’s walk is chosen using only local information. In this paper, we present some current developments in the area. In particular, we focus on recent work on equitable strategies and on the multi-agent rotor-router.

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References

  1. 1.
    Akbari, H., Berenbrink, P.: Parallel rotor walks on finite graphs and applications in discrete load balancing. In: SPAA, pp. 186–195 (2013)Google Scholar
  2. 2.
    Aldous, D., Fill, J.: Reversible Markov Chains and Random Walks on Graphs (2001), http://stat-www.berkeley.edu/users/aldous/RWG/book.html
  3. 3.
    Alon, N., Avin, C., Koucký, M., Kozma, G., Lotker, Z., Tuttle, M.R.: Many random walks are faster than one. Combinatorics, Probability & Computing 20(4), 481–502 (2011)CrossRefzbMATHGoogle Scholar
  4. 4.
    Bampas, E., Gąsieniec, L., Hanusse, N., Ilcinkas, D., Klasing, R., Kosowski, A.: Euler tour lock-in problem in the rotor-router model. In: Keidar, I. (ed.) DISC 2009. LNCS, vol. 5805, pp. 423–435. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  5. 5.
    Bampas, E., Gasieniec, L., Klasing, R., Kosowski, A., Radzik, T.: Robustness of the rotor-router mechanism. In: Abdelzaher, T., Raynal, M., Santoro, N. (eds.) OPODIS 2009. LNCS, vol. 5923, pp. 345–358. Springer, Heidelberg (2009)Google Scholar
  6. 6.
    Berenbrink, P., Cooper, C., Elsässer, R., Radzik, T., Sauerwald, T.: Speeding up random walks with neighborhood exploration. In: SODA, pp. 1422–1435 (2010)Google Scholar
  7. 7.
    Bhatt, S.N., Even, S., Greenberg, D.S., Tayar, R.: Traversing directed eulerian mazes. Journal of Graph Algorithms and Applications 6(2), 157–173 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Cooper, C., Ilcinkas, D., Klasing, R., Kosowski, A.: Derandomizing random walks in undirected graphs using locally fair exploration strategies. Distributed Computing 24(2), 91–99 (2011)CrossRefzbMATHGoogle Scholar
  9. 9.
    Cooper, J.N., Spencer, J.: Simulating a random walk with constant error. Combinatorics, Probability & Computing 15(6), 815–822 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Czyzowicz, J., Dobrev, S., Gasieniec, L., Ilcinkas, D., Jansson, J., Klasing, R., Lignos, I., Martin, R., Sadakane, K., Sung, W.-K.: More efficient periodic traversal in anonymous undirected graphs. Theoretical Computer Science 444, 60–76 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Doerr, B., Friedrich, T.: Deterministic random walks on the two-dimensional grid. Combinatorics, Probability & Computing 18(1-2), 123–144 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Efremenko, K., Reingold, O.: How well do random walks parallelize? In: Dinur, I., Jansen, K., Naor, J., Rolim, J. (eds.) APPROX 2009. LNCS, vol. 5687, pp. 476–489. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  13. 13.
    Elsässer, R., Sauerwald, T.: Tight bounds for the cover time of multiple random walks. Theoretical Computer Science 412(24), 2623–2641 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Gasieniec, L., Klasing, R., Martin, R.A., Navarra, A., Zhang, X.: Fast periodic graph exploration with constant memory. Journal of Computer and System Sciences 74(5), 808–822 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Gąsieniec, L., Radzik, T.: Memory efficient anonymous graph exploration. In: Broersma, H., Erlebach, T., Friedetzky, T., Paulusma, D. (eds.) WG 2008. LNCS, vol. 5344, pp. 14–29. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  16. 16.
    Ikeda, S., Kubo, I., Yamashita, M.: The hitting and cover times of random walks on finite graphs using local degree information. Theoretical Computer Science 410(1), 94–100 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Kijima, S., Koga, K., Makino, K.: Deterministic random walks on finite graphs. In: ANALCO, pp. 18–27 (2012)Google Scholar
  18. 18.
    Klasing, R., Kosowski, A., Pajak, D., Sauerwald, T.: The multi-agent rotor-router on the ring: a deterministic alternative to parallel random walks. In: PODC, pp. 365–374 (2013)Google Scholar
  19. 19.
    Kosowski, A.: A õ (n 2) time-space trade-off for undirected s-t connectivity. In: SODA, pp. 1873–1883 (2013)Google Scholar
  20. 20.
    Kosowski, A., Navarra, A.: Graph decomposition for memoryless periodic exploration. Algorithmica 63(1-2), 26–38 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Lovász, L.: Random walks on graphs: A survey. Bolyai Society Mathematical Studies 2, 353–397 (1996)Google Scholar
  22. 22.
    Malpani, N., Chen, Y., Vaidya, N.H., Welch, J.L.: Distributed token circulation in mobile ad hoc networks. IEEE Transactions on Mobile Computing 4(2), 154–165 (2005)CrossRefGoogle Scholar
  23. 23.
    Nonaka, Y., Ono, H., Sadakane, K., Yamashita, M.: The hitting and cover times of metropolis walks. Theoretical Computer Science 411(16-18), 1889–1894 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Priezzhev, V., Dhar, D., Dhar, A., Krishnamurthy, S.: Eulerian walkers as a model of self-organized criticality. Physical Review Letters 77(25), 5079–5082 (1996)CrossRefGoogle Scholar
  25. 25.
    Sauerwald, T.: Expansion and the cover time of parallel random walks. In: PODC, pp. 315–324. ACM (2010)Google Scholar
  26. 26.
    Wagner, I.A., Lindenbaum, M., Bruckstein, A.M.: Distributed covering by ant-robots using evaporating traces. IEEE Transactions on Robotics and Automation 15(5), 918–933 (1999)CrossRefGoogle Scholar
  27. 27.
    Yanovski, V., Wagner, I.A., Bruckstein, A.M.: A distributed ant algorithm for efficiently patrolling a network. Algorithmica 37(3), 165–186 (2003)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Ralf Klasing
    • 1
  1. 1.CNRS - LaBRIUniversité de BordeauxTalenceFrance

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