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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| Vydáno v: | Parallel computing Ročník 29; číslo 1; s. 135 - 159 |
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| Jazyk: | angličtina |
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Elsevier B.V
2003
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| ISSN: | 0167-8191, 1872-7336 |
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| 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. |
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| AbstractList | 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. |
| Author | Hong, Sung Je Lee, Sunggu Lee, Heejo Kim, Jong |
| Author_xml | – sequence: 1 givenname: Heejo surname: Lee fullname: Lee, Heejo email: heejo@ahnlab.com organization: Ahnlab, Inc., 8F V-Valley Bldg., 724 Suseo-dong, Gangnam-gu Seoul 135-744, South Korea – sequence: 2 givenname: Jong surname: Kim fullname: Kim, Jong email: jkim@postech.ac.kr organization: Department of Computer Science and Engineering, Pohang University of Science and Technology, Pohang 790-784, South Korea – sequence: 3 givenname: Sung Je surname: Hong fullname: Hong, Sung Je email: sjhong@postech.ac.kr organization: Department of Computer Science and Engineering, Pohang University of Science and Technology, Pohang 790-784, South Korea – sequence: 4 givenname: Sunggu surname: Lee fullname: Lee, Sunggu email: slee@postech.ac.kr organization: Department of Electrical Engineering, Pohang University of Science and Technology, Pohang 790-784, South Korea |
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| Cites_doi | 10.1109/SUPERC.1994.344344 10.1109/71.242154 10.1007/3-540-45591-4_70 10.1137/S106482759426715X 10.1137/1033099 10.1109/71.503776 10.1137/0716027 10.1145/77626.79170 10.21236/ADA228143 10.1016/0743-7315(92)90012-C 10.1109/71.481597 10.1145/338407.338535 10.1109/71.598277 10.1145/62038.62043 10.1145/143369.143446 10.1137/0914048 10.1145/277651.277658 10.1006/jpdc.1997.1319 10.1016/0024-3795(86)90167-9 10.1145/295656.295660 10.1109/71.308533 10.1145/76909.76910 10.1137/0915085 10.1137/0912063 10.1016/0167-8191(90)90056-F 10.1137/0914063 10.1007/3-540-48311-X_148 10.1023/A:1019122726788 10.1137/0909021 |
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| Keywords | Task scheduling Directed acyclic graph Block-oriented Cholesky factorization Parallel sparse matrix factorization |
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| SubjectTerms | Block-oriented Cholesky factorization Directed acyclic graph Parallel sparse matrix factorization Task scheduling |
| Title | Task scheduling using a block dependency DAG for block-oriented sparse Cholesky factorization |
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