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Computing with Large Populations Using Interactions

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Mathematical Foundations of Computer Science 2012 (MFCS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7464))

Abstract

We define a general model capturing the behavior of a population of anonymous agents that interact in pairs. This model captures some of the main features of opportunistic networks, in which nodes (such as the ones of a mobile ad hoc networks) meet sporadically. For its reminiscence to Population Protocol, we call our model Large-Population Protocol, or LPP. We are interested in the design of LPPs enforcing, for every ν ∈ [0,1], a proportion ν of the agents to be in a specific subset of marked states, when the size of the population grows to infinity; In which case, we say that the protocol computes ν. We prove that, for every ν ∈ [0,1], ν is computable by a LPP if and only if ν is algebraic. Our positive result is constructive. That is, we show how to construct, for every algebraic number ν ∈ [0,1], a protocol which computes ν.

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Author information

Authors and Affiliations

  1. LIX, Ecole Polytechnique and CNRS, France

    Olivier Bournez

  2. LIAFA, CNRS and University Paris Diderot, France

    Pierre Fraigniaud & Xavier Koegler

Authors
  1. Olivier Bournez
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  2. Pierre Fraigniaud
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  3. Xavier Koegler
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Comenius University, Mlynska Dolina, 84248, Bratislava, Slovakia

    Branislav Rovan

  2. Department of Electronics and Computer Science, University of Southampton, SO17 1BJ, Southampton, UK

    Vladimiro Sassone

  3. Institute of Theoretical Computer Science, ETH Zürich, CAB H 39.2, Universitätstrasse 6, 8092, Zürich, Switzerland

    Peter Widmayer

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Bournez, O., Fraigniaud, P., Koegler, X. (2012). Computing with Large Populations Using Interactions. In: Rovan, B., Sassone, V., Widmayer, P. (eds) Mathematical Foundations of Computer Science 2012. MFCS 2012. Lecture Notes in Computer Science, vol 7464. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32589-2_23

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  • DOI: https://doi.org/10.1007/978-3-642-32589-2_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32588-5

  • Online ISBN: 978-3-642-32589-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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