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Interacting Urns Processes for Clustering of Large-Scale Networks of Tiny Artifacts

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  • Pierre Leone
  • Elad M. Schiller

Abstract

We analyze a distributed variation on the Pólya urn process in which a network of tiny artifacts manages the individual urns. Neighboring urns interact by repeatedly adding the same colored ball based on previous random choices. We discover that the process rapidly converges to a definitive random ratio between the colors in every urn. Moreover, the rate of convergence of the process at a given node depends on the global topology of the network. In particular, the same ratio appears for the case of complete communication graphs. Surprisingly, this effortless random process supports useful applications, such as clustering and computation of pseudo-geometric coordinate. We present numerical studies that validate our theoretical predictions.

Suggested Citation

  • Pierre Leone & Elad M. Schiller, 2010. "Interacting Urns Processes for Clustering of Large-Scale Networks of Tiny Artifacts," International Journal of Distributed Sensor Networks, , vol. 6(1), pages 936195-9361, July.
    • Handle: RePEc:sae:intdis:v:6:y:2010:i:1:p:936195
    DOI: 10.1155/2010/936195
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