Balls and bins models with feedback

  • Authors:
  • Eleni Drinea;Alan Frieze;Michael Mitzenmacher

  • Affiliations:
  • Harvard University;Carnegie Mellon University;Harvard University

  • Venue:
  • SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
  • Year:
  • 2002

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Abstract

We examine generalizations of the classical balls and bins models, where the probability a ball lands in a bin is proportional to the number of balls already in the bin raised to some exponent p. Such systems exhibit positive or negative feedback, depending on the exponent p, with a phase transition occurring at p = 1. Similar models have proven useful in economics and chemistry; for example, systems with positive feedback (p 1) tend naturally toward monopoly. We provide several results and useful heuristics for these models, including showing a bound on the time to achieve monopoly with high probability.