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The Weakest Oracle for Symmetric Consensus in Population Protocols

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Algorithms for Sensor Systems (ALGOSENSORS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 9536))

Abstract

We consider the symmetric consensus problem, a version of consensus adapted to population protocols, a model for large scale networks of resource-limited mobile sensors. After proving that consensus is impossible in the considered model, we look for oracles to circumvent this impossibility. An oracle is an external (to the system) module providing some information allowing to solve the problem. We define a class of oracles adapted to population protocols, and we prove that an oracle in this class, namely DejaVu, allows to obtain a solution. Finally, and this is the major contribution of the paper, we prove that DejaVu is the weakest oracle for solving the problem.

This work has been partially supported by the Israeli-French Maimonide and the INS2I PEPS JCJC research projects.

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Notes

  1. 1.

    The class of functions computable by a terminating protocol.

  2. 2.

    These values will later be provided by an oracle.

  3. 3.

    Immediate means that, if \(p'\) involves x and \(p_x \leadsto p' \leadsto p\), then \(p'=p_x\) or \(p' = p\).

  4. 4.

    Not necessarily symmetric, in this lemma.

References

  1. Aguilera, M.K., Chen, W., Toueg, S.: Using the heartbeat failure detector for quiescent reliable communication and consensus in partitionable networks. Theor. Comput. Sci. 220(1), 3–30 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  2. Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M.J., Peralta, R.: Computation in networks of passively mobile finite-state sensors. Distrib. Comput. 18(4), 235–253 (2006)

    Article  MATH  Google Scholar 

  3. Attiya, H., Welch, J.: Distributed Computing. McGraw-Hill, Hightstown (1998)

    Google Scholar 

  4. Beauquier, J., Blanchard, P., Burman, J.: Self-stabilizing leader election in population protocols over arbitrary communication graphs. In: Baldoni, R., Nisse, N., van Steen, M. (eds.) OPODIS 2013. LNCS, vol. 8304, pp. 38–52. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  5. Bonnet, F., Raynal, M.: The price of anonymity: optimal consensus despite asynchrony, crash and anonymity. In: Keidar, I. (ed.) DISC 2009. LNCS, vol. 5805, pp. 341–355. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  6. Bonnet, F., Raynal, M.: Anonymous asynchronous systems: the case of failure detectors. In: Lynch, N.A., Shvartsman, A.A. (eds.) DISC 2010. LNCS, vol. 6343, pp. 206–220. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  7. Bouzid, Z., Travers, C.: Anonymity, failures, detectors and consensus. Technical report (2012)

    Google Scholar 

  8. Bouzid, Z., Travers, C.: Brief announcement: anonymity, failures, detectors and consensus. In: Aguilera, M.K. (ed.) DISC 2012. LNCS, vol. 7611, pp. 427–428. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  9. Cartier, P., Foata, D.: Problèmes combinatoire de commutation et réarrangements. Lect. Notes Math. 85 (1969)

    Google Scholar 

  10. Chandra, T.D., Toueg, S.: Unreliable failure detectors for reliable distributed systems. J. ACM 43(2), 225–267 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  11. Cortés, J., Martínez, S., Karatas, T., Bullo, F.: Coverage control for mobile sensing networks. IEEE Trans. Robot. Autom. 20(2), 243–255 (2004)

    Article  Google Scholar 

  12. Delporte-Gallet, C., Fauconnier, H., Guerraoui, R., Tielmann, A.: The weakest failure detector for message passing set-agreement. In: Taubenfeld, G. (ed.) DISC 2008. LNCS, vol. 5218, pp. 109–120. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  13. Fischer, M., Jiang, H.: Self-stabilizing leader election in networks of finite-state anonymous agents. In: Shvartsman, M.M.A.A. (ed.) OPODIS 2006. LNCS, vol. 4305, pp. 395–409. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  14. Fischer, M.H., Lynch, N.A., Paterson, M.S.: Impossibility of consensus with one faulty process. J. ACM 32(2), 374–382 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  15. Lamport, L.: Time, clocks, and the ordering of events in a distributed system. Commun. ACM 21(7), 558–565 (1978)

    Article  MATH  Google Scholar 

  16. Lawton, J.R., Beard, R.W.: Synchronized multiple spacecraft rotations. Automatica 38(8), 1359–1364 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  17. Lynch, N.: Distributed Algorithms. Morgan Kaufmann, San Francisco (1996)

    MATH  Google Scholar 

  18. Michail, O., Spirakis, P.G.: Terminating population protocols via some minimal global knowledge assumptions. J. Parallel Distrib. Comput. 81–82, 1–10 (2015)

    Article  Google Scholar 

  19. Mostéfaoui, A., Rajsbaum, S., Raynal, M., Travers, C.: The combined power of conditions and information on failures to solve asynchronous set agreement. SIAM J. Comput. 38(4), 1574–1601 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  20. Mostéfaoui, A., Rajsbaum, S., Raynal, M., Travers, C.: On the computability power and the robustness of set agreement-oriented failure detector classes. Distrib. Comput. 21(3), 201–222 (2008)

    Article  MATH  Google Scholar 

  21. Olfati-Saber, R., Fax, J.A., Murray, R.M.: Reply to “comments on “consensus and cooperation in networked multi-agent systems””. Proc. IEEE 98(7), 1354–1355 (2010)

    Article  Google Scholar 

  22. Olfati-Saber, R., Shamma, J.S.: Consensus filters for sensor networks and distributed sensor fusion. In: 44th IEEE Conference Decision and Control and 2005 European Control Conference (CDC-ECC 2005), pp. 6698–6703, December 2005

    Google Scholar 

  23. Oshman, R.:. Distributed computation in wireless and dynamic networks. Ph.D. thesis, MIT, Department of Electrical Engineering and Computer Science (2012)

    Google Scholar 

  24. Ren, W., Beard, R.W., Atkins, E.M.: A survey of consensus problems in multi-agent coordination. In: American Control Conference, pp. 1859–1864 (2005)

    Google Scholar 

  25. Tel, G.: Introduction to Distributed Algorithms, 2nd edn. Cambridge University Press, Cambridge (2000)

    Book  MATH  Google Scholar 

  26. Xi, W., Tan, X., Baras, J.S.: A stochastic algorithm for self-organization of autonomous swarms. In: Proceedings of 44th IEEE Conference Decision and Control and 2005 European Control Conference (CDC-ECC 2005), pp. 765–770 (2005)

    Google Scholar 

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Authors and Affiliations

  1. LRI, Paris-South 11 University, Orsay, France

    Joffroy Beauquier & Janna Burman

  2. LPD, EPFL, Lausanne, Switzerland

    Peva Blanchard

  3. Technion, Haifa, Israel

    Shay Kutten

Authors
  1. Joffroy Beauquier
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  2. Peva Blanchard
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  3. Janna Burman
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  4. Shay Kutten
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Corresponding author

Correspondence to Peva Blanchard .

Editor information

Editors and Affiliations

  1. Carleton University, Ottawa, Ontario, Canada

    Prosenjit Bose

  2. University of Liverpool, Liverpool, United Kingdom

    Leszek Antoni Gąsieniec

  3. Graz University of Technology, Graz, Austria

    Kay Römer

  4. ETH Zurich, Zürich, Switzerland

    Roger Wattenhofer

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Beauquier, J., Blanchard, P., Burman, J., Kutten, S. (2015). The Weakest Oracle for Symmetric Consensus in Population Protocols. In: Bose, P., Gąsieniec, L., Römer, K., Wattenhofer, R. (eds) Algorithms for Sensor Systems. ALGOSENSORS 2015. Lecture Notes in Computer Science(), vol 9536. Springer, Cham. https://doi.org/10.1007/978-3-319-28472-9_4

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  • DOI: https://doi.org/10.1007/978-3-319-28472-9_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-28471-2

  • Online ISBN: 978-3-319-28472-9

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