An O(√n)-worst-case-time solution to the granularity problem

  • A. Pietracaprina
  • F. P. Preparata
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 665)


In this paper we deal with the granularity problem, that is, the problem of implementing a shared memory in a distributed system where n processors are connected to n memory modules through a complete network (Module Parallel Computer). We present a memory organization scheme where m(n2) variables, each replicated into a 2c — 1 copies (for constant c), are evenly distributed among the n modules, so that a suitable access protocol allows any set of at most n distinct read/write operations to be performed by the processors in O(√n) parallel steps in the worst case. The well known strategy based on multiple copies is needed to avoid the worst-case O(n)-time, since only a majority of the copies of each variable need be accessed for any operation. The memory organization scheme can be extended to deal with m(n3) variables attaining an O(n2/3)-time complexity in the worst case.

Key Words

Algorithms and Data Structures Theory of Parallel and Distributed Computing P-RAM Simulation 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • A. Pietracaprina
    • 1
    • 2
  • F. P. Preparata
    • 2
  1. 1.Department of Computer ScienceUniversity of Illinois at Urbana-ChampaignUrbana
  2. 2.Department of Computer ScienceBrown UniversityProvidence

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