Skip to main content
SpringerLink
Log in

Efficient Exploration of Anonymous Undirected Graphs

  • Conference paper
Combinatorial Algorithms (IWOCA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8288))

Included in the following conference series:

  • 854 Accesses

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.

The research was partially funded by the ANR project “DISPLEXITY”.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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. Aldous, D., Fill, J.: Reversible Markov Chains and Random Walks on Graphs (2001), http://stat-www.berkeley.edu/users/aldous/RWG/book.html

  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)

    Article  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. 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. 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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  9. Cooper, J.N., Spencer, J.: Simulating a random walk with constant error. Combinatorics, Probability & Computing 15(6), 815–822 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  11. Doerr, B., Friedrich, T.: Deterministic random walks on the two-dimensional grid. Combinatorics, Probability & Computing 18(1-2), 123–144 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  13. Elsässer, R., Sauerwald, T.: Tight bounds for the cover time of multiple random walks. Theoretical Computer Science 412(24), 2623–2641 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  17. Kijima, S., Koga, K., Makino, K.: Deterministic random walks on finite graphs. In: ANALCO, pp. 18–27 (2012)

    Google Scholar 

  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. Kosowski, A.: A õ (n 2) time-space trade-off for undirected s-t connectivity. In: SODA, pp. 1873–1883 (2013)

    Google Scholar 

  20. Kosowski, A., Navarra, A.: Graph decomposition for memoryless periodic exploration. Algorithmica 63(1-2), 26–38 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  21. Lovász, L.: Random walks on graphs: A survey. Bolyai Society Mathematical Studies 2, 353–397 (1996)

    Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  25. Sauerwald, T.: Expansion and the cover time of parallel random walks. In: PODC, pp. 315–324. ACM (2010)

    Google Scholar 

  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)

    Article  Google Scholar 

  27. Yanovski, V., Wagner, I.A., Bruckstein, A.M.: A distributed ant algorithm for efficiently patrolling a network. Algorithmica 37(3), 165–186 (2003)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CNRS - LaBRI, Université de Bordeaux, 351 cours de la Libération, 33405, Talence, France

    Ralf Klasing

Authors
  1. Ralf Klasing
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. UFR des Sciences et Techniques, LITIS, Université de Rouen, 76821, EA 4180, Mont Saint Aignan Cedex, France

    Thierry Lecroq  & Laurent Mouchard  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Klasing, R. (2013). Efficient Exploration of Anonymous Undirected Graphs. In: Lecroq, T., Mouchard, L. (eds) Combinatorial Algorithms. IWOCA 2013. Lecture Notes in Computer Science, vol 8288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45278-9_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-45278-9_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45277-2

  • Online ISBN: 978-3-642-45278-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation