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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 matrixvector mul
tiplies. Our aim is to emphasize the expressive power of hypergraph models. First, we set
forth an elementary hypergraph model for the parallel matrixvector multiply based on
onedimensional (1D) matrix partitioning. In the elementary model, the vertices represent
the data of a matrixvector 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 twodimensional
