Randomized permutations in a coarse grained parallel environment

ABSTRACT

We show how to uniformly distribute data at random (not to be confounded with permutation routing) in a coarse grained parallel environment with p processors. In contrast to previously known work, our method is able to fulfill the three goals of uniformity, work-optimality and balance among the processors simultaneously. To guarantee the uniformity we investigate the matrix of communication requests between the processors. We show that its distribution is a generalization of the multivariate hypergeometric distribution and we give algorithms to compute it efficiently.

REFERENCES

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INDEX TERMS

Primary Classification:
  D. Software
  D.1 PROGRAMMING TECHNIQUES
      D.1.3 Concurrent Programming
          Subjects: Distributed programming

Additional Classification:
  D. Software
  D.1 PROGRAMMING TECHNIQUES
      D.1.3 Concurrent Programming
          Subjects: Parallel programming

  G. Mathematics of Computing
  G.2 DISCRETE MATHEMATICS
      G.2.1 Combinatorics
          Subjects: Permutations and combinations

General Terms:
Algorithms, Performance, Theory

Keywords:
coarse grained parallelism, randomized permutations, uniformly generated communication matrix