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Recursively divisible problems

  • Rolf Niedermeier
Session 5b: Invited Presentation
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1178)

Abstract

We introduce the concept of a (p, d)-divisible problem, where p reflects the number of processors and d the number of communication phases of a parallel algorithm solving the problem. We call problems that are recursively (n, O(1))-divisible in a work-optimal way with 0 <ε < 1ideally divisible and give motivation drawn from parallel computing for the relevance of that concept. We show that several important problems are ideally divisible. For example, sorting is recursively (n1/3, 4)-divisible in a work-optimal way. On the other hand, we also provide some results of lower bound type. For example, ideally divisible problems appear to be a proper subclass of the functional complexity class FP of sequentially feasible problems. Finally, we also give some extensions and variations of the concept of (p, d)-divisibility.

Keywords

Parallel Algorithm Communication Phase Sorting Problem Proper Subclass Parallel Random Access Machine 
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 1996

Authors and Affiliations

  • Rolf Niedermeier
    • 1
  1. 1.Wilhelm-Schickard-Institut für InformatikUniversität TübingenTübingenFed. Rep. of Germany

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