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Copyright by SIAM. Unauthorized reproduction of this article is prohibited. SIAM REVIEW c 2007 Society for Industrial and Applied Mathematics
 

Summary: Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.
SIAM REVIEW c 2007 Society for Industrial and Applied Mathematics
Vol. 49, No. 4, pp. 595­603
Revisiting Hypergraph Models
for Sparse Matrix Partitioning
Bora Uc¸ar
Cevdet Aykanat
Abstract. We provide an exposition of hypergraph models for parallelizing sparse matrix-vector mul-
tiplies. Our aim is to emphasize the expressive power of hypergraph models. First, we set
forth an elementary hypergraph model for the parallel matrix-vector multiply based on
one-dimensional (1D) matrix partitioning. In the elementary model, the vertices represent
the data of a matrix-vector multiply, and the nets encode dependencies among the data.
We then apply a recently proposed hypergraph transformation operation to devise models
for 1D sparse matrix partitioning. The resulting 1D partitioning models are equivalent to
the previously proposed computational hypergraph models and are not meant to be re-
placements for them. Nevertheless, the new models give us insights into the previous ones
and help us explain a subtle requirement, known as the consistency condition, of hyper-
graph partitioning models. Later, we demonstrate the flexibility of the elementary model
on a few 1D partitioning problems that are hard to solve using the previously proposed
models. We also discuss extensions of the proposed elementary model to two-dimensional

  

Source: Aykanat, Cevdet - Department of Computer Engineering, Bilkent University

 

Collections: Computer Technologies and Information Sciences