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Data Allocation Strategies for Dense Linear Algebra on two-dimensional Grids with Heterogeneous Communication Links

Olivier D.E. Beaumont, Arnaud Legrand, Yves Robert, 69 - Lyon (France). Lab. de l'Informatique du Parallelisme Centre National de la Recherche Scientifique (CNRS), 69 (France). Lab. de l'Informatique du Parallelisme Ecole Normale Superieure de Lyon, 69 (France). Lab. de l'Informatique du Parallelisme Lyon-1 Univ.

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Abstract

In this paper, we study the implementation of dense linear algebra kernels, such as matrix multiplication on 2D grids with homogeneous processors when the communication links between the processors are heterogeneous (i.e. the time to transfer a block of the matrix between two processors depends on these processors). We prove that finding the best allocation of the processors into a grid, with respect to the minimization of the communication overhead, is a NP-complete problem.

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In this paper, we study the implementation of dense linear algebra kernels, such as matrix multiplication on 2D grids with homogeneous processors when the communication links between the processors are heterogeneous (i.e. the time to transfer a block of the matrix between two processors depends on these processors). We prove that finding the best allocation of the processors into a grid, with respect to the minimization of the communication overhead, is a NP-complete problem.

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Available abstract

In this paper, we study the implementation of dense linear algebra kernels, such as matrix multiplication on 2D grids with homogeneous processors when the communication links between the processors are heterogeneous (i.e. the time to transfer a block of the matrix between two processors depends on these processors). We prove that finding the best allocation of the processors into a grid, with respect to the minimization of the communication overhead, is a NP-complete problem.

Key concepts: Linear algebra, Computer science, Matrix multiplication, Overhead (engineering), Parallel computing, Block (permutation group theory), Grid, Homogeneous

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