 
Summary: ENCAPSULATING MULTIPLE COMMUNICATIONCOST METRICS
IN PARTITIONING SPARSE RECTANGULAR MATRICES FOR
PARALLEL MATRIXVECTOR MULTIPLIES
BORA UC¸AR AND CEVDET AYKANAT
SIAM J. SCI. COMPUT. c 2004 Society for Industrial and Applied Mathematics
Vol. 25, No. 6, pp. 18371859
Abstract. This paper addresses the problem of onedimensional partitioning of structurally
unsymmetric square and rectangular sparse matrices for parallel matrixvector and matrixtranspose
vector multiplies. The objective is to minimize the communication cost while maintaining the balance
on computational loads of processors. Most of the existing partitioning models consider only the
total message volume hoping that minimizing this communicationcost metric is likely to reduce
other metrics. However, the total message latency (startup time) may be more important than
the total message volume. Furthermore, the maximum message volume and latency handled by a
single processor are also important metrics. We propose a twophase approach that encapsulates
all these four communicationcost metrics. The objective in the first phase is to minimize the total
message volume while maintaining the computationalload balance. The objective in the second phase
is to encapsulate the remaining three communicationcost metrics. We propose communication
hypergraph and partitioning models for the second phase. We then present several methods for
partitioning communication hypergraphs. Experiments on a wide range of test matrices show that
the proposed approach yields very effective partitioning results. A parallel implementation on a PC
