Skip to main content

Population Protocols and Related Models

  • Chapter
  • First Online:
Theoretical Aspects of Distributed Computing in Sensor Networks

Abstract

This is a joint work with Ioannis Chatzigiannakis and Othon Michail. We discuss here the population protocol model and most of its well-known extensions. The population protocol model aims to represent sensor networks consisting of tiny computational devices with sensing capabilities that follow some unpredictable and uncontrollable mobility pattern. It adopts a minimalistic approach and, thus, naturally computes a quite restricted class of predicates and exhibits almost no fault tolerance. Most recent approaches make extra realistic and implementable assumptions, in order to gain more computational power and/or speedup the time to convergence and/or improve fault tolerance. In particular, the mediated population protocol model, the community protocol model, and the PALOMA model, which are all extensions of the population protocol model, are thoroughly discussed. Finally, the inherent difficulty of verifying the correctness of population protocols that run on complete communication graphs is revealed, but a promising algorithmic solution is presented.

This work has been partially supported by the ICT Programme of the European Union under contract number ICT-2008-215270 (FRONTS).

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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

Notes

  1. 1.

    We say possibly, because performance mainly depends on the scheduler. But if the scheduler is assumed to be probabilistic, then exploiting all agents should improve expected performance.

Referneces

  1. D. Angluin, J. Aspnes, M. Chan, M. J. Fischer, H. Jiang, and R. Peralta. Stably computable properties of network graphs. In Proceedings Distributed Computing in Sensor Systems: 1st IEEE International Conference, pages 63–74, Marina del Ray, California, USA, 2005.

    Google Scholar 

  2. D. Angluin, J. Aspnes, Z. Diamadi, M. J. Fischer, and R. Peralta. Computation in networks of passively mobile finite-state sensors. Distributed Computing, 18(4):235–253, 2006. Also in 23rd Annual ACM Symposium on Principles of Distributed Computing (PODC), pages 290–299, ACM, New York, NY, USA, 2004.

    Article  Google Scholar 

  3. D. Angluin, J. Aspnes, Z. Diamadi, M. J. Fischer, and R. Peralta. Urn automata. Technical Report YALEU/DCS/TR-1280, Yale University Department of Computer Science, Nov. 2003.

    Google Scholar 

  4. D. Angluin, J. Aspnes, and D. Eisenstat. Fast computation by population protocols with a leader. Distributed Computing, 21(3):183–199, September 2008.

    Article  Google Scholar 

  5. D. Angluin, J. Aspnes, and D. Eisenstat. Stably computable predicates are semilinear. In Proc. 25th Annual ACM Symposium on Principles of Distributed Computing, pages 292–299, Denver, Colorado, USA, 2006.

    Google Scholar 

  6. D. Angluin, J. Aspnes, D. Eisenstat, and E. Ruppert. The computational power of population protocols. Distributed Computing, 20(4): 279–304, November 2007.

    Article  Google Scholar 

  7. J. Aspnes and E. Ruppert. An introduction to population protocols. Bulletin of the European Association for Theoretical Computer Science, 93:98–117, October, 2007. Columns: Distributed Computing, Editor: M. Mavronicolas.

    MATH  MathSciNet  Google Scholar 

  8. R. Bakhshi, F. Bonnet, W. Fokkink, and B. Haverkort. Formal analysis techniques for gossiping protocols. In ACM SIGOPS Operating Systems Review, 41(5):28–36, Special Issue on Gossip-Based Networking, October 2007.

    Article  Google Scholar 

  9. J. Beauquier, J. Clement, S. Messika, L. Rosaz, and B. Rozoy. Self-stabilizing counting in mobile sensor networks. Technical Report 1470, LRI, Université Paris-Sud 11, 2007.

    Google Scholar 

  10. G. Behrmann, A. David, and K. G. Larsen. A tutorial on Uppaal. In Formal Methods for the Design of Real-Time Systems: Proceedings of the 4th International School on Formal Methods for the Design of Comput., Commun. and Software Syst. (SFM-RT 2004), number 3185 in LNCS, pages 200–236, Springer, 2004.

    Google Scholar 

  11. O. Bournez, P. Chassaing, J. Cohen, L. Gerin, and X. Koegler. On the convergence of population protocols when population goes to infinity. In Applied Mathematics and Computation, 215(4):1340–1350, 2009.

    Article  MATH  MathSciNet  Google Scholar 

  12. I. Chatzigiannakis, S. Dolev, S. P. Fekete, O. Michail, and P. G. Spirakis. Not all fair probabilistic schedulers are equivalent. In 13th International Conference On Principles Of DIstributed Systems (OPODIS), pages 33–47, Nimes, France, December 15–18, 2009.

    Google Scholar 

  13. I. Chatzigiannakis, O. Michail, S. Nikolaou, A. Pavlogiannis, and P. G. Spirakis. Algorithmic verification of population protocols. FRONTS Technical Report FRONTS-TR-2010-12, http://fronts.cti.gr/aigaion/?TR=148, Jan. 2010.

  14. I. Chatzigiannakis, O. Michail, S. Nikolaou, A. Pavlogiannis, and P. G. Spirakis. Passively mobile communicating logarithmic space machines. FRONTS Technical Report FRONTS-TR-2010-16, http://fronts.cti.gr/aigaion/?TR=154, Feb. 2010.

  15. I. Chatzigiannakis, O. Michail, and P. G. Spirakis. Decidable graph languages by mediated population protocols. In 23rd International Symposium on Distributed Computing (DISC), Elche, Spain, Sept. 2009. (Also FRONTS Technical Report FRONTS-TR-2009-16, http://fronts.cti.gr/aigaion/?TR=80)

  16. I. Chatzigiannakis, O. Michail, and P. G. Spirakis. Experimental verification and performance study of extremely large sized population protocols. FRONTS Technical Report FRONTS-TR-2009-3, http://fronts.cti.gr/aigaion/?TR=61, Jan. 2009.

  17. I. Chatzigiannakis, O. Michail, and P. G. Spirakis. Mediated population protocols. In 36th International Colloquium on Automata, Languages and Programming (ICALP), pages 363–374, Rhodes, Greece, 2009.

    Google Scholar 

  18. I. Chatzigiannakis, O. Michail, and P. G. Spirakis. Recent advances in population protocols. In 34th International Symposium on Mathematical Foundations of Computer Science (MFCS), August 24–28, 2009, Novy Smokovec, High Tatras, Slovakia.

    Google Scholar 

  19. I. Chatzigiannakis and P. G. Spirakis. The dynamics of probabilistic population protocols. In Distributed Computing, 22nd International Symposium, DISC, vol. 5218, Lecture Notes in Computer Science, pages 498–499, 2008.

    Google Scholar 

  20. J. Cheriyan and K. Mehlhorn. Algorithms for dense graphs and networks on the random access computer. Algorithmica, 15: 521–549, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  21. E. M. Clarke, O. Grumberg, and D. A. Peled. Model checking. MIT Press, New York, NY, 2000.

    Google Scholar 

  22. C. Delporte-Gallet, H. Fauconnier, R. Guerraoui, and E. Ruppert. When birds die: Making population protocols fault-tolerant. In Proc. 2nd IEEE International Conference on Distributed Computing in Sensor Systems, pages 51–66, 2006.

    Google Scholar 

  23. Z. Diamadi and M. J. Fischer. A simple game for the study of trust in distributed systems. Wuhan University Journal of Natural Sciences, 6(1-2):72–82, Mar. 2001. Also appears as Yale Technical Report TR-1207, Jan. 2001.

    Article  Google Scholar 

  24. R. Fenichel. Distribution of Indistinguishable Objects into Distinguishable Slots. Communications of the ACM, 11(6): 430, June 1968.

    Article  Google Scholar 

  25. H. N. Gabow. Path-based depth-first search for strong and biconnected components. Information Processing Letters, 74:107–114, 2000.

    Article  MathSciNet  Google Scholar 

  26. D. T. Gillespie. A rigorous derivation of the chemical master equation. Physica A, 188:404–425, 1992.

    Article  Google Scholar 

  27. D. T. Gillespie. Exact stochastic simulation of coupled chemical reactions. Journal of Physical Chemistry, 81(25):2340–2361, 1977.

    Article  Google Scholar 

  28. S. Ginsburg and E. H. Spanier. Semigroups, Presburger formulas, and languages. Pacific Journal of Mathematics, 16:285–296, 1966.

    MATH  MathSciNet  Google Scholar 

  29. R. Guerraoui and E. Ruppert. Names trump malice: Tiny mobile agents can tolerate byzantine failures. In 36th International Colloquium on Automata, Languages and Programming (ICALP), pages 484–495, Rhodes, Greece, 2009.

    Google Scholar 

  30. A. Hinton, M. Z. Kwiatkowska, G. Norman, and D. Parker. Prism: A tool for automatic verification of probabilistic systems. In Proceedings of 2nd International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS ’06), vol. 3920, LNCS, pages 441–444. Springer, 2006.

    Google Scholar 

  31. G. Holzmann. The Spin Model Checker, Primer and Reference Manual. Addison-Wesley, New York, NY, 2003.

    Google Scholar 

  32. M. Huth and M. Ryan. Logic in Computer Science: Modelling and Reasoning About Systems. Cambridge University Press, Cambridge, UK, 2004.

    MATH  Google Scholar 

  33. T. G. Kurtz. Approximation of population processes. Number 36 in CBMS-NSF Regional Conference Series in Applied Mathematics, Society for Industrial and Applied Mathematics, Philadelphia, 1981.

    Google Scholar 

  34. P. C. Olveczky and S. Thorvaldsen. Formal modeling and analysis of wireless sensor network algorithms in Real-Time Maude. Parallel and Distributed Processing Symposium, International, p. 157, Proceedings 20th IEEE International Parallel % Distributed Processing Symposium, Rhodes, Greece, 2006.

    Google Scholar 

  35. C. H. Papadimitriou. Computational Complexity. Addison-Wesley, New York, NY, 1994.

    MATH  Google Scholar 

  36. R. Tarjan. Depth-first search and linear graph algorithms. SIAM Journal on Computing, 1(2):146–160, 1972.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Paul G. Spirakis .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Spirakis, P.G. (2011). Population Protocols and Related Models. In: Nikoletseas, S., Rolim, J. (eds) Theoretical Aspects of Distributed Computing in Sensor Networks. Monographs in Theoretical Computer Science. An EATCS Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14849-1_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-14849-1_5

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14848-4

  • Online ISBN: 978-3-642-14849-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics