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Contention Resolution with Heterogeneous Job Sizes

  • Michael A. Bender
  • Jeremy T. Fineman
  • Seth Gilbert
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4168)

Abstract

We study the problem of contention resolution for different-sized jobs on a simple channel. When a job makes a run attempt, it learns only whether the attempt succeeded or failed. We first analyze binary exponential backoff, and show that it achieves a makespan of \(V2^{\Theta(\sqrt{\log{n}})}\) with high probability, where V is the total work of all n contending jobs. This bound is significantly larger than when jobs are constant sized. A variant of exponential backoff, however, achieves makespan O(V logV) with high probability. Finally, we introduce a new protocol, size-hashed backoff, specifically designed for jobs of multiple sizes that achieves makespan O(V log3logV). The error probability of the first two bounds is polynomially small in n and the latter is polynomially small in logV.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Michael A. Bender
    • 1
  • Jeremy T. Fineman
    • 2
  • Seth Gilbert
    • 2
  1. 1.Dept. of Computer ScienceStony Brook UniversityUSA
  2. 2.CSAIL, Massachusetts Institute of TechnologyCambridgeUSA

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