BIT Numerical Mathematics

, Volume 20, Issue 3, pp 279–288 | Cite as

The fifty percent rule revisited

  • D. Julian
  • M. Davies
Part I Computer Science


Combinatorial reasoning is applied to the analysis of two kinds of dynamic storage allocation system to derive results about the degree and characteristics of memory fragmentation. The simple first-fit scheme with immediate replacement, discussed by Knuth, is analyzed further, providinginter alia a new derivation of the “fifty percent rule”. Next a system with garbage collections is considered, and the mean and variance of the number of holes following a garbage collection are determined, along with other results. The cell distributions resulting from these two idealized policies are contrasted.


Dynamic storage allocation garbage collection memory fragmentation fifty percent rule 


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Copyright information

© BIT Foundations 1980

Authors and Affiliations

  • D. Julian
    • 1
  • M. Davies
    • 1
  1. 1.Department of Computer ScienceThe University of Western OntarioLondonCanada

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