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Minimizing Communication Cost in Fine-Grain Partitioning of Sparse Matrices

Summary: Minimizing Communication Cost in Fine-Grain
Partitioning of Sparse Matrices
Bora U¸car and Cevdet Aykanat
Department of Computer Engineering, Bilkent University, 06800, Ankara, Turkey
Abstract. We show a two-phase approach for minimizing various com-
munication-cost metrics in fine-grain partitioning of sparse matrices for
parallel processing. In the first phase, we obtain a partitioning with the
existing tools on the matrix to determine computational loads of the
processor. In the second phase, we try to minimize the communication-
cost metrics. For this purpose, we develop communication-hypergraph
and partitioning models. We experimentally evaluate the contributions
on a PC cluster.
1 Introduction
Repeated matrix-vector multiplications (SpMxV) y = Ax that involve the same
large, sparse, structurally symmetric or nonsymmetric square or rectangular ma-
trix are kernel operations in various iterative solvers. Efficient parallelization of
these solvers requires matrix A to be partitioned among the processors in such
a way that communication overhead is kept low while maintaining computa-
tional load balance. Because of possible dense vector operations, some of these


Source: Aykanat, Cevdet - Department of Computer Engineering, Bilkent University
Uçar, Bora - Laboratoire de l'Informatique du Parallélisme, Ecole Normale Supérieure de Lyon


Collections: Computer Technologies and Information Sciences