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ENCAPSULATING MULTIPLE COMMUNICATION-COST METRICS IN PARTITIONING SPARSE RECTANGULAR MATRICES FOR
 

Summary: ENCAPSULATING MULTIPLE COMMUNICATION-COST METRICS
IN PARTITIONING SPARSE RECTANGULAR MATRICES FOR
PARALLEL MATRIX-VECTOR 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 one-dimensional partitioning of structurally
unsymmetric square and rectangular sparse matrices for parallel matrix-vector and matrix-transpose-
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 communication-cost metric is likely to reduce
other metrics. However, the total message latency (start-up 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 two-phase approach that encapsulates
all these four communication-cost metrics. The objective in the first phase is to minimize the total
message volume while maintaining the computational-load balance. The objective in the second phase
is to encapsulate the remaining three communication-cost 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

  

Source: Aykanat, Cevdet - Department of Computer Engineering, Bilkent University
Uçar, Bora - Laboratoire de l'Informatique du Parallélisme, Ecole Normale Supérieure de Lyon

 

Collections: Computer Technologies and Information Sciences