Computing with large populations using interactions

  • Authors:
  • Olivier Bournez;Pierre Fraigniaud;Xavier Koegler

  • Affiliations:
  • LIX, Ecole Polytechnique and CNRS, France;LIAFA, CNRS and University Paris Diderot, France;LIAFA, CNRS and University Paris Diderot, France

  • Venue:
  • MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
  • Year:
  • 2012

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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 computesν. 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.