Random allocations and probabilistic languages

  • Philippe Flajolet
  • Danièle Gardy
  • Loÿs Thimonier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 317)


This paper introduces a unified framework for the analysis of a class of random allocation processes that include: (i) the birthday paradox; (ii) the coupon collector problem; (iii) least-recently-used (LRU) caching in memory management systems under the independent reference model; (iv) the move-to-front heuristic of self-organizing search. All analyses are relative to general (non uniform) probability distributions.

Our approach to these problems comprises two stages. First, the probabilistic phenomena of interest are described by means of regular languages extended by addition of the shuffle product. Next, systematic translation mechanisms from languages to generating functions are used to derive integral representations of expectations and probability distributions for allocation processes.


Regular Language Access Probability Page Fault Cache Algorithm Exponential Generate Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Philippe Flajolet
    • 1
  • Danièle Gardy
    • 2
  • Loÿs Thimonier
    • 3
    • 4
  1. 1.INRIA, RocquencourtLe ChesnayFrance
  2. 2.LRI, Université Paris-SudOrsayFrance
  3. 3.Université de PicardieAmiensFrance
  4. 4.LRI, Université Paris-SudFrance

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