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Statistical mechanical load balancer for the web.

Jesse S A Bridgewater1, P Oscar Boykin, Vwani P Roychowdhury

  • 1Department of Electrical Engineering, University of California , Los Angeles, California 90095, USA. jsab@pobox.com

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 21, 2005
PubMed
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Statistical mechanics principles reveal that graphs can reach maximum entropy states, resembling Erdös-Rényi random graphs. This finding enables efficient local algorithms for generating random graphs and distributed load balancing.

Area of Science:

  • Statistical mechanics
  • Graph theory
  • Network science

Background:

  • The maximum entropy principle dictates that systems reach equilibrium distributions maximizing entropy.
  • Graphs with fixed edges can be thermalized via stochastic edge dynamics.

Purpose of the Study:

  • To demonstrate that graphs under stochastic edge dynamics achieve maximum entropy states.
  • To develop a local algorithm for generating Erdös-Rényi random graphs.
  • To adapt this framework for distributed load balancing.

Main Methods:

  • Defining a stochastic edge dynamic for graphs.
  • Analyzing node degree distribution using rate equations.
  • Implementing edge dynamics via short random walks on graphs.

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Main Results:

  • Graphs with fixed edges attain Erdös-Rényi random graph distributions.
  • Rate-equation analysis confirms the maximum entropy principle.
  • A local algorithm for generating Erdös-Rényi graphs is developed using random walks.

Conclusions:

  • The statistical mechanical framework provides a method for generating Erdös-Rényi graphs.
  • This approach can be adapted for efficient, distributed load balancing in computing and internet infrastructure.