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

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 t...

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Bibliographic Details
Published in:Parallel computing Vol. 29; no. 1; pp. 135 - 159
Main Authors: Lee, Heejo, Kim, Jong, Hong, Sung Je, Lee, Sunggu
Format: Journal Article
Language:English
Published: Elsevier B.V 2003
Subjects:
Block-oriented Cholesky factorization
Directed acyclic graph
Parallel sparse matrix factorization
Task scheduling
Task scheduling
Directed acyclic graph
Block-oriented Cholesky factorization
Parallel sparse matrix factorization
ISSN:0167-8191, 1872-7336
Online Access:Get full text
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Summary: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 blocks 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 a Myrinet cluster system show that the proposed task scheduling approach outperforms other processor mapping methods.
ISSN:0167-8191
1872-7336
DOI:10.1016/S0167-8191(02)00220-X