Efficient Algorithms for Multi-dimensional Block-Cyclic Redistribution of Arrays

  • Authors:
  • Young Won Lim;Neungsoo Park;Viktor K. Prasanna

  • Affiliations:
  • -;-;-

  • Venue:
  • ICPP '97 Proceedings of the international Conference on Parallel Processing
  • Year:
  • 1997

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Abstract

We present a uniform framework for a classical problem, redistribution of a multi-dimensional array. Using a generalized circulant matrix formalism, we derive eficient direct, indirect a,nd hybrid contention-free communication schedules. Our indirect schedule reduces the number of communication steps significantly compared with the previous approaches. Our approach exploits the regularity of the block-cyclic redistribution to minimize the index computation overheads. For the case of 2-d redistribution, when the block size increases by factors Of K1 and K2 along each dimension and the process topology remains fixed, our indirect schedule performs the redistribution in O(lOg(K1K2)) communication steps. For the case of fixed block size and the processor topology is transposed, our indirect schedule results in O(log(L/G)) communication Step. Implementations of our algorithms on the IBM SP-2 show superior performance over previous approaches.