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

Keywords

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

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Hardware and Architecture
  • Computer Networks and Communications
  • Computer Graphics and Computer-Aided Design
  • Artificial Intelligence

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