Summary: Decomposing Irregularly Sparse Matrices
for Parallel Matrix-Vector Multiplication?
Umit V. Catalyurek and Cevdet Aykanat
Computer Engineering Department, Bilkent University
06533 Bilkent, Ankara, Turkey
Abstract. In this work, we show the de ciencies of the graph model
for decomposing sparse matrices for parallel matrix-vector multiplica-
tion. Then, we propose two hypergraph models which avoid all de cien-
cies of the graph model. The proposed models reduce the decomposition
problem to the well-known hypergraph partitioning problem widely en-
countered in circuit partitioning in VLSI. We have implemented fast
Kernighan-Lin based graph and hypergraph partitioning heuristics and
used the successful multilevel graph partitioning tool (Metis) for the ex-
perimental evaluation of the validity of the proposed hypergraph models.
We have also developed a multilevel hypergraph partitioning heuristic
for experimenting the performance of the multilevel approach on hy-
pergraph partitioning. Experimental results on sparse matrices, selected
from Harwell-Boeing collection and NETLIB suite, con rm both the va-
lidity of our proposed hypergraph models and appropriateness of the
multilevel approach to hypergraph partitioning.