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Approaches Based on Permutations for Partitioning Sparse Matrices on Multiprocessors

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Abstract

This paper introduces new approaches to the data distribution-partition problem for sparse matrices in a multiprocessor environment. In this work, the data partition problem of a sparse matrix is modeled as a Min-Max Problem subject to the uniformity constrain when the goal is to balance the load for both sparse and dense operations. This problem is NP-Complete and two heuristic solutions (ABO and GPB) are proposed. The key of ABO and GPB is to determine the permutation of rows/columns of the input sparse matrix to obtain a sorted matrix with a homogeneous density of nonzero elements. Due to the heuristic nature of the proposed methods their validation is carried out by a comparative study of the parallel efficiency of two types of problems (sparse and mixed) when ABO, GPB, Block, Cyclic and MRD data distributions are applied.

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Authors and Affiliations

  1. Department Computer Architecture and Electronics, University of Almeria, 04120, Almeria, Spain

    E. M. Garz & I. GarcÍa

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  1. E. M. Garz
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  2. I. GarcÍa
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Correspondence to E. M. Garz.

Additional information

This work has been partially supported by the Spanish CICYT through grant TIC2002-00228.

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Garz, E.M., GarcÍa, I. Approaches Based on Permutations for Partitioning Sparse Matrices on Multiprocessors. J Supercomput 34, 41–61 (2005). https://doi.org/10.1007/s11227-005-0311-2

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  • DOI: https://doi.org/10.1007/s11227-005-0311-2

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