Skip to main content
SpringerLink
Log in

Global Versus Local Computations: Fast Computing with Identifiers

  • Conference paper
  • First Online:
Structural Information and Communication Complexity (SIROCCO 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10641))

Abstract

This paper studies what can be computed by using probabilistic local interactions with agents with a very restricted power in polylogarithmic parallel time.

It is known that if agents are only finite state (corresponding to the Population Protocol model by Angluin et al.), then only semilinear predicates over the global input can be computed. In fact, if the population starts with a unique leader, these predicates can even be computed in a polylogarithmic parallel time.

If identifiers are added (corresponding to the Community Protocol model by Guerraoui and Ruppert), then more global predicates over the input multiset can be computed. Local predicates over the input sorted according to the identifiers can also be computed, as long as the identifiers are ordered. The time of some of those predicates might require exponential parallel time.

In this paper, we consider what can be computed with Community Protocol in a polylogarithmic number of parallel interactions. We introduce the class CPPL corresponding to protocols that use \(O(n\log ^kn)\), for some k, expected interactions to compute their predicates, or equivalently a polylogarithmic number of parallel expected interactions.

We provide some computable protocols, some boundaries of the class, using the fact that the population can compute its size. We also prove two impossibility results providing some arguments showing that local computations are no longer easy: the population does not have the time to compare a linear number of consecutive identifiers. The Linearly Local languages, such that the rational language \((ab)^*\), are not computable.

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 EPUB and 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

References

  1. Angluin, D., Aspnes, J., Eisenstat, D., Ruppert, E.: The computational power of population protocols. Distrib. Comput. DISC 20, 279–304 (2007)

    Article  MATH  Google Scholar 

  2. Angluin, D., Aspnes, J., Chan, M., Fischer, M.J., Jiang, H., Peralta, R.: Stably computable properties of network graphs. In: Prasanna, V.K., Iyengar, S.S., Spirakis, P.G., Welsh, M. (eds.) DCOSS 2005. LNCS, vol. 3560, pp. 63–74. Springer, Heidelberg (2005). https://doi.org/10.1007/11502593_8

    Chapter  Google Scholar 

  3. Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M.J., Peralta, R.: Computation in networks of passively mobile finite-state sensors. In: Principles of Distributed Computing, PODC, July 2004

    Google Scholar 

  4. Angluin, D., Aspnes, J., Eisenstat, D.: Fast computation by population protocols with a leader. Distrib. Comput. DISC 21, 183–199 (2008)

    Article  MATH  Google Scholar 

  5. Angluin, D., Aspnes, J., Fischer, M.J., Jiang, H.: Self-stabilizing population protocols. In: Anderson, J.H., Prencipe, G., Wattenhofer, R. (eds.) OPODIS 2005. LNCS, vol. 3974, pp. 103–117. Springer, Heidelberg (2006). https://doi.org/10.1007/11795490_10

    Chapter  Google Scholar 

  6. Beauquier, J., Blanchard, P., Burman, J., Delaët, S.: Computing time complexity of population protocols with cover times - the zebranet example. In: Défago, X., Petit, F., Villain, V. (eds.) SSS 2011. LNCS, vol. 6976, pp. 47–61. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-24550-3_6

    Chapter  Google Scholar 

  7. Beauquier, J., Burman, J., Kutten, S.: Making population protocols self-stabilizing. In: Guerraoui, R., Petit, F. (eds.) SSS 2009. LNCS, vol. 5873, pp. 90–104. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-05118-0_7

    Chapter  Google Scholar 

  8. Beauquier, J., Burman, J., Rosaz, L., Rozoy, B.: Non-deterministic population protocols. In: Baldoni, R., Flocchini, P., Binoy, R. (eds.) OPODIS 2012. LNCS, vol. 7702, pp. 61–75. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-35476-2_5

    Chapter  Google Scholar 

  9. Bournez, O., Cohen, J., Rabie, M.: Homonym population protocols. In: Bouajjani, A., Fauconnier, H. (eds.) NETYS 2015. LNCS, vol. 9466, pp. 125–139. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-26850-7_9

    Chapter  Google Scholar 

  10. Chatzigiannakis, I., Michail, O., Nikolaou, S., Pavlogiannis, A., Spirakis, P.G.: Passively mobile communicating machines that use restricted space. In: International Workshop on Foundations of Mobile Computing, FOMC 2011 (2011)

    Google Scholar 

  11. Daley, D.J., Kendall, D.G.: Stochastic rumours. IMA J. Appl. Math. 1, 42–55 (1965)

    Article  MathSciNet  Google Scholar 

  12. Delporte-Gallet, C., Fauconnier, H., Guerraoui, R., Ruppert, E.: When birds die: making population protocols fault-tolerant. In: Gibbons, P.B., Abdelzaher, T., Aspnes, J., Rao, R. (eds.) DCOSS 2006. LNCS, vol. 4026, pp. 51–66. Springer, Heidelberg (2006). https://doi.org/10.1007/11776178_4

    Chapter  Google Scholar 

  13. Doty, D., Soloveichik, D.: Stable leader election in population protocols requires linear time. In: Moses, Y. (ed.) DISC 2015. LNCS, vol. 9363, pp. 602–616. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48653-5_40

    Chapter  Google Scholar 

  14. Fraigniaud, P., Korman, A., Lebhar, E.: Local MST computation with short advice. In: Symposium on Parallelism in Algorithms and Architectures, SPAA (2007)

    Google Scholar 

  15. Gillespie, D.T.: A rigorous derivation of the chemical master equation. Phys. A 188, 404–425 (1992)

    Article  Google Scholar 

  16. Guerraoui, R., Ruppert, E.: Names trump malice: tiny mobile agents can tolerate byzantine failures. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5556, pp. 484–495. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02930-1_40

    Chapter  Google Scholar 

  17. Hethcote, H.W.: The mathematics of infectious diseases. SIAM Rev. 42, 599–653 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  18. Mertzios, G.B., Nikoletseas, O.E., Raptopoulos, C.L., Spirakis, P.G.: Stably computing order statistics with arithmetic population protocols. In: Mathematical Foundations of Computer Science, MFCS (2016)

    Google Scholar 

  19. Michail, O., Chatzigiannakis, I., Spirakis, P.G.: Mediated population protocols. Theor. Comput. Sci. 412, 2434–2450 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  20. Murray, J.D.: Mathematical Biology. I: An Introduction, 3rd edn. Springer, Heidelberg (2002). https://doi.org/10.1007/b98868

    MATH  Google Scholar 

  21. Schönhage, A.: Storage modification machines. SIAM J. Comput. 9, 490–508 (1980)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LIP, ENS de Lyon, 69007, Lyon, France

    Mikaël Rabie

Authors
  1. Mikaël Rabie
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mikaël Rabie .

Editor information

Editors and Affiliations

  1. LIF, Aix-Marseille University, Marseille Cedex 9, France

    Shantanu Das

  2. LIP6, Université Pierre et Marie Curie - Paris 6, Paris, France

    Sebastien Tixeuil

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Rabie, M. (2017). Global Versus Local Computations: Fast Computing with Identifiers. In: Das, S., Tixeuil, S. (eds) Structural Information and Communication Complexity. SIROCCO 2017. Lecture Notes in Computer Science(), vol 10641. Springer, Cham. https://doi.org/10.1007/978-3-319-72050-0_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-72050-0_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-72049-4

  • Online ISBN: 978-3-319-72050-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation