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

pplication 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× 10^8 . However, it is approximately 2.13× 10^8 for our proposed algorithm. This results in a reduction of 64.33