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Algorithms for tree-shaped task partition and allocation on heterogeneous multiprocessors

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Abstract

Application with a set of dependent distributed tasks is generally regarded as a direct acyclic graph or an out-tree. Tree-shaped task graphs are widely applied in a variety of computational domains, including electronic structure computations and sparse matrix factorization. Efficient algorithms for tree-shaped task partition and allocation can dominate the performance of heterogeneous computing systems, as most relevant publications have pointed out. This paper presents efficient algorithms for partitioning and allocating tree-shaped tasks on heterogeneous multiprocessor systems with limited memory to improve task-parallel computing. The proposed main algorithm consists of two stages: partition and allocation. During partition, an algorithm is provided for partitioning a task tree into multiple subtrees. It iteratively partitions the subtrees on the critical path of the quotient tree. During allocation, two algorithms are proposed for task allocation to minimize the task tree’s execution time. One is to preferentially allocate the largest subtree of the whole tree, and the other is to preferentially allocate the subtree located on the quotient tree’s critical path. Experimental results show that the proposed algorithms significantly improve the latest works in terms of average makespan, both on randomly generated trees and on a real-world dataset. On a real-world dataset, the average makespan of existing work is approximately \(6.28\times 10^8\). However, it is approximately \(2.13\times 10^8\) for our proposed algorithm. This results in a reduction of 64.33%. On randomly generated trees, the average makespan of existing work is approximately 8973. However, it is approximately 4040 for our proposed algorithm. This results in a reduction of 54.96%.

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Data availability

The assembly trees dataset are generated by a set of sparse matrices, which can be obtained from the University of Florida Sparse Matrix Collection http://www.cise.ufl.edu/research/sparse/matrices/.

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Acknowledgements

Part of the work has been presented in 2021 IEEE International Conference on Parallel & Distributed Processing with Applications, Sept. 30 – Oct. 3, 2021, New York, USA.

Funding

This work was supported in part by the National Natural Science Foundation of China under Grant 62072118 and 62202108. It was also supported in part by Huangpu International Sci & Tech Cooperation Foundation of Guangzhou, China under Grant No. 2021GH12, Guangdong Natural Science Foundation under Grant Nos. 2023A1515011230, 2023A1515030183 and 2021B1515120010.

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    Authors and Affiliations

    1. School of Computer Science and Technology, Guangdong University of Technology, Guangzhou, 510006, China

      Suna He, Jigang Wu, Bing Wei & Jiaxin Wu

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    1. Suna He
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    2. Jigang Wu
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    Contributions

    S.H., J.W. and B.W. conceived of the presented idea. J.W. encouraged S.H. to investigate the critical path and supervised the findings of this work. S.H. carried out the experiment and wrote the main manuscript text. All authors discussed the results and revised the manuscript.

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    Correspondence to Jigang Wu.

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    He, S., Wu, J., Wei, B. et al. Algorithms for tree-shaped task partition and allocation on heterogeneous multiprocessors. J Supercomput 79, 13210–13240 (2023). https://doi.org/10.1007/s11227-023-05186-3

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