On Balls and Bins with Deletions

  • Richard Cole
  • Alan Frieze
  • Bruce M. Maggs
  • Michael Mitzenmacher
  • Andréa W. Richa
  • Ramesh Sitaraman
  • Eli Upfal
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1518)

Abstract

We consider the problem of extending the analysis of balls and bins processes where a ball is placed in the least loaded of d randomly chosen bins to cover deletions. In particular, we are interested in the case where the system maintains a fixed load, and deletions are determined by an adversary before the process begins. We show that with high probability the load in any bin is O(log log n). In fact, this result follows from recent work by Cole et al. concerning a more difficult problem of routing in a butterfly network.

The main contribution of this paper is to give a different proof of this bound, which follows the lines of the analysis of Azar, Broder, Karlin, and Upfal for the corresponding static load balancing problem. We also give a specialized (and hence simpler) version of the argument from the paper by Cole et al. for the balls and bins scenario. Finally, we provide an alternative analysis also based on the approach of Azar, Broder, Karlin, and Upfal for the special case where items are deleted according to their age. Although this analysis does not yield better bounds than our argument for the general case, it is interesting because it utilizes a two-dimensional family of random variables in order to account for the age of the items. This technique may be of more general use.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Richard Cole
    • 1
  • Alan Frieze
    • 2
  • Bruce M. Maggs
    • 3
  • Michael Mitzenmacher
    • 4
  • Andréa W. Richa
    • 5
  • Ramesh Sitaraman
    • 6
  • Eli Upfal
    • 7
  1. 1.Courant InstituteNew York UniversityNew York
  2. 2.Department of Mathematical SciencesCarnegie Mellon UniversityPittsburghUSA
  3. 3.School of Computer ScienceCarnegie Mellon UniversityPittsburgh
  4. 4.Compaq Systems Research CenterPalo AltoUSA
  5. 5.School of Computer ScienceCarnegie Mellon UniversityPittsburgh
  6. 6.Department of Computer ScienceUniversity of MassachusettsAmherstUSA
  7. 7.Department of Computer ScienceBrown UniversityUSA

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