Task Scheduling using Block Dependency DAG of Block-Oriented Sparse Cholesky Factorizationy

The block-oriented sparse Cholesky factorization decomposes a sparse matrix into rectangular sub-blocks, and handles each block as a computational unit in order to increase data reuse in a hierarchical memory system. As well, the factorization method increases the degree of concurrency with the reduction of communication volumes so that it performs more eeciently on a distributed-memory multiprocessor system than the customary column-oriented factorization. But until now, mapping of blocks to processors has been designed in the direction of load balance within restricted communication patterns. In this paper, we represent tasks using a block dependency DAG, which shows the execution behavior of the block sparse Cholesky factorization. Since the characteristics of tasks for the block Cholesky fac-torization are diierent from those of the conventional parallel task model, we also propose a new task scheduling algorithm using block dependency DAG. The proposed algorithm consists of two stages: early-start clustering, and aaned cluster mapping. The early-start clustering stage is used to cluster tasks with preserving the earliest start time of a task without limiting parallelism. After task clustering, the aaned cluster mapping algorithm allocates clusters to processors considering both communication cost and load balance. Experimental results on the Fujitsu parallel system show that the proposed task scheduling approach outperforms other processor mapping methods.