Skip to main content
SpringerLink
Log in

Computing Without Communicating: Ring Exploration by Asynchronous Oblivious Robots

  • Conference paper
Principles of Distributed Systems (OPODIS 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4878))

Included in the following conference series:

Abstract

We consider the problem of exploring an anonymous unoriented ring by a team of k identical, oblivious, asynchronous mobile robots that can view the environment but cannot communicate. This weak scenario is standard when the spatial universe in which the robots operate is the two-dimentional plane, but (with one exception) has not been investigated before. We indeed show that, although the lack of these capabilities renders the problems considerably more difficult, ring exploration is still possible.

We show that the minimum number ρ(n) of robots that can explore a ring of size n is O(logn) and that ρ(n) = Ω(logn) for arbitrarily large n. On one hand we give an algorithm that explores the ring starting from any initial configuration, provided that n and k are co-prime, and we show that there always exist such k in O(logn). On the other hand we show that Ω(logn) agents are necessary for arbitrarily large n. Notice that, when k and n are not co-prime, the problem is sometimes unsolvable (i.e., there are initial configurations for which the exploration cannot be done). This is the case, e.g., when k divides n.

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. Agmon, N., Peleg, D.: Fault-Tolerant Gathering Algorithms for Autonomous Mobile Robots. SIAM J. Comput. 36(1), 56–82 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  2. Albers, S., Henzinger, M.R.: Exploring unknown environments. SIAM J. Comput. 29, 1164–1188 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  3. Averbakh, I., Berman, O.: A heuristic with worst-case analysis for minimax routing of two traveling salesmen on a tree. Discr. Appl. Math. 68, 17–32 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  4. Averbakh, I., Berman, O.: (p − 1)/(p + 1)-approximate algorithms for p-traveling salesmen problems on a tree with minmax objective. Discr. Appl. Mathematics 75, 201–216 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  5. Awerbuch, B., Betke, M., Rivest, R., Singh, M.: Piecemeal graph learning by a mobile robot. In: Proc. 8th Conf. on Comput. Learning Theory, pp. 321–328 (1995)

    Google Scholar 

  6. Bender, M.A., Fernandez, A., Ron, D., Sahai, A., Vadhan, S.: The power of a pebble: Exploring and mapping directed graphs. In: STOC 1998. Proc. 30th Ann. Symp. on Theory of Computing, pp. 269–278 (1998)

    Google Scholar 

  7. Bender, M.A., Slonim, D.: The power of team exploration: Two robots can learn unlabeled directed graphs, Proc. 35th Ann. In: FOCS 1994. Symp. on Foundations of Computer Science, pp. 75–85 (1994)

    Google Scholar 

  8. Betke, M., Rivest, R., Singh, M.: Piecemeal learning of an unknown environment. Machine Learning 18, 231–254 (1995)

    Google Scholar 

  9. Cieliebak, M., Flocchini, P., Prencipe, G., Santoro, N.: Solving the Robots Gathering Problem. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  10. Cohen, R., Peleg, D.: Robot convergence via center-of-gravity algorithms. In: Kralovic, R., Sýkora, O. (eds.) SIROCCO 2004. LNCS, vol. 3104, pp. 79–88. Springer, Heidelberg (2004)

    Google Scholar 

  11. Czyzowicz, J., Gasieniec, L., Pelc, A.: Gathering few fat mobile robots in the plane. In: Asano, T. (ed.) ISAAC 2006. LNCS, vol. 4288, pp. 744–753. Springer, Heidelberg (2006)

    Google Scholar 

  12. Das, S., Flocchini, P., Kutten, S., Nayak, A., Santoro, N.: Map construction of unknown graphs by multiple agents. Theoretical Computer Science (to appear 2007)

    Google Scholar 

  13. Défago, X., Konagaya, A.: Circle formation for oblivious anonymous mobile robots with no common sense of orientation. In: Workshop on Principles of Mobile Computing, pp. 97–104 (2002)

    Google Scholar 

  14. Deng, X., Papadimitriou, C.H.: Exploring an unknown graph. Journal of Graph Theory 32, 265–297 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  15. Dessmark, A., Pelc, A.: Optimal graph exploration without good maps. In: Möhring, R.H., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 374–386. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  16. Diks, K., Fraigniaud, P., Kranakis, E., Pelc, A.: Tree exploration with little memory. In: SODA 2002. Proc. 13th Ann. ACM-SIAM Symp. on Discrete Algorithms, pp. 588–597. ACM Press, New York (2002)

    Google Scholar 

  17. Duncan, C.A., Kobourov, S.G., Kumar, V.S.A.: Optimal constrained graph exploration. In: SODA 2001. Proc. 12th Ann. ACM-SIAM Symp. on Discrete Algorithms, pp. 807–814. ACM Press, New York (2001)

    Google Scholar 

  18. Fleischer, R., Trippen, G.: Exploring an unknown graph efficiently. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 11–22. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  19. Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Hard tasks for weak robot. In: Aggarwal, A.K., Pandu Rangan, C. (eds.) ISAAC 1999. LNCS, vol. 1741, pp. 93–102. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  20. Fraigniaud, P., Gasieniec, L., Kowalski, D., Pelc, A.: Collective tree exploration. In: Farach-Colton, M. (ed.) LATIN 2004. LNCS, vol. 2976, pp. 141–151. Springer, Heidelberg (2004)

    Google Scholar 

  21. Frederickson, G.N., Hecht, M.S., Kim, C.E.: Approximation algorithms for some routing problems. SIAM J. Comput. 7, 178–193 (1978)

    Article  MathSciNet  Google Scholar 

  22. Gasieniec, L., Pelc, A., Radzik, T., Zhang, X.: Tree exploration with logarithmic memory. In: SODA 2007. Proc. 18th Annual ACM-SIAM Symp. on Discrete Algorithms, New Orleans, Louisiana, USA (January 2007)

    Google Scholar 

  23. Klasing, R., Markou, E., Pelc, A.: Gathering asynchronous oblivious mobile robots in a ring. In: Asano, T. (ed.) ISAAC 2006. LNCS, vol. 4288, Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  24. Li, X., Santoro, N.: An Integrated self-deployment and coverage maintenance scheme for mobile sensor networks. In: Cao, J., Stojmenovic, I., Jia, X., Das, S.K. (eds.) MSN 2006. LNCS, vol. 4325, Springer, Heidelberg (2006)

    Google Scholar 

  25. Panaite, P., Pelc, A.: Exploring unknown undirected graphs. Journal of Algorithms 33, 281–295 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  26. Prencipe, G.: On the feasibility of gathering by autonomous mobile robots. In: Pelc, A., Raynal, M. (eds.) SIROCCO 2005. LNCS, vol. 3499, pp. 246–261. Springer, Heidelberg (2005)

    Google Scholar 

  27. Prencipe, G., Santoro, N.: Distributed algorithms for mobile robots. In: TCS 2006. Proc. 5th IFIP Int. Conf. on Theoretical Computer Science, pp. 47–62 (2006)

    Google Scholar 

  28. Ruiz, S.M.: A Result on Prime Numbers. Math. Gaz. 81, 269 (1997)

    Article  Google Scholar 

  29. Souissi, S., Défago, X., Yamashita, M.: Gathering asynchronous mobile robots with inaccurate compasses. In: Shvartsman, A.A. (ed.) OPODIS 2006. LNCS, vol. 4305, pp. 333–349. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  30. Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: formation of geometric patterns. SIAM J. Comput. 28(4), 1347–1363 (1999)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. SITE, University of Ottawa, Canada

    Paola Flocchini

  2. CNRS, LaBRI, Université Bordeaux I, France

    David Ilcinkas

  3. Département d’informatique, Université du Québec en Outaouais, Canada

    Andrzej Pelc

  4. School of Computer Science, Carleton University, Canada

    Nicola Santoro

Authors
  1. Paola Flocchini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David Ilcinkas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Andrzej Pelc
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Nicola Santoro
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Eduardo Tovar Philippas Tsigas Hacène Fouchal

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Flocchini, P., Ilcinkas, D., Pelc, A., Santoro, N. (2007). Computing Without Communicating: Ring Exploration by Asynchronous Oblivious Robots. In: Tovar, E., Tsigas, P., Fouchal, H. (eds) Principles of Distributed Systems. OPODIS 2007. Lecture Notes in Computer Science, vol 4878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77096-1_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-77096-1_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77095-4

  • Online ISBN: 978-3-540-77096-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation