Task scheduling using a block dependency DAG for block-oriented sparse Cholesky factorization

Heejo Lee, Jong Kim, Sung Je Hong, Sunggu Lee
2003 Parallel Computing  
Block-oriented sparse Cholesky factorization decomposes a sparse matrix into rectangular subblocks; each block can then be handled as a computational unit in order to increase data reuse in a hierarchical memory system. Also, the factorization method increases the degree of concurrency and reduces the overall communication volume so that it performs more efficiently on a distributed-memory multiprocessor system than the customary column-oriented factorization method. But until now, mapping of
more » ... ocks to processors has been designed for load balance with restricted communication patterns. In this paper, we represent tasks using a block dependency DAG that represents the execution behavior of block sparse Cholesky factorization in a distributed-memory system. Since the characteristics of tasks for block Cholesky factorization are different from those of the conventional parallel task model, we propose a new task scheduling algorithm using a block dependency DAG. The proposed algorithm consists of two stages: early-start clustering, and affined cluster mapping (ACM). The early-start clustering stage is used to cluster tasks while preserving the earliest start time of a task without limiting parallelism. After task clustering, the ACM stage allocates clusters to processors considering both communication cost and load balance. Experimental results on q (S. Lee). 0167-8191/02/$ -see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 -8 1 9 1 ( 0 2 ) 0 0 2 2 0 -X www.elsevier.com/locate/parco Parallel Computing 29 (2003) 135-159 a Myrinet cluster system show that the proposed task scheduling approach outperforms other processor mapping methods.
doi:10.1016/s0167-8191(02)00220-x fatcat:joqgju7aabasfpdcqh3qbvwraq