Multi-level direct K-way hypergraph partitioning with multiple constraints and fixed vertices
Journal of Parallel and Distributed Computing
A Parallel Matrix Scaling Algorithm
High Performance Computing for Computational Science - VECPAR 2008
Efficient successor retrieval operations for aggregate query processing on clustered road networks
Information Sciences: an International Journal
A Matrix Partitioning Interface to PaToH in MATLAB
Parallel Computing
On Two-Dimensional Sparse Matrix Partitioning: Models, Methods, and a Recipe
SIAM Journal on Scientific Computing
Hypergraph Partitioning-Based Fill-Reducing Ordering for Symmetric Matrices
SIAM Journal on Scientific Computing
Replicated partitioning for undirected hypergraphs
Journal of Parallel and Distributed Computing
Partitioning Hypergraphs in Scientific Computing Applications through Vertex Separators on Graphs
SIAM Journal on Scientific Computing
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We provide an exposition of hypergraph models for parallelizing sparse matrix-vector multiplies. 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 replacements 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 hypergraph 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 matrix partitioning.