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

Heejo Lee, Jong Kim, Sung Je Hong, Sunggu Lee

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)135-159
Number of pages25
JournalParallel Computing
Volume29
Issue number1
DOIs
Publication statusPublished - 2003 Jan 1
Externally publishedYes

Fingerprint

Cholesky factorisation
Task Scheduling
Factorization
Scheduling
Load Balance
Factorization Method
Clustering
Data storage equipment
Communication
Distributed Memory multiprocessors
Data Reuse
Task Model
Communication Cost
Multiprocessor Systems
Distributed Memory
Sparse matrix
Concurrency
Scheduling algorithms
Scheduling Algorithm
Parallelism

Keywords

  • Block-oriented Cholesky factorization
  • Directed acyclic graph
  • Parallel sparse matrix factorization
  • Task scheduling

ASJC Scopus subject areas

  • Computer Science Applications
  • Hardware and Architecture
  • Control and Systems Engineering

Cite this

Task scheduling using a block dependency DAG for block-oriented sparse Cholesky factorization. / Lee, Heejo; Kim, Jong; Hong, Sung Je; Lee, Sunggu.

In: Parallel Computing, Vol. 29, No. 1, 01.01.2003, p. 135-159.

Research output: Contribution to journalArticle

Lee, Heejo ; Kim, Jong ; Hong, Sung Je ; Lee, Sunggu. / Task scheduling using a block dependency DAG for block-oriented sparse Cholesky factorization. In: Parallel Computing. 2003 ; Vol. 29, No. 1. pp. 135-159.
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