Abstract
The optimal directed acyclic graph search problem constitutes searching for a DAG with a minimum score, where the score of a DAG is defined on its structure. This problem is known to be NP-hard, and the state-of-the-art algorithm requires exponential time and space. It is thus not feasible to solve large instances using a single processor. Some parallel algorithms have therefore been developed to solve larger instances. A recently proposed parallel algorithm can solve an instance of 33 vertices, and this is the largest solved size reported thus far. In the study presented in this paper, we developed a novel parallel algorithm designed specifically to operate on a parallel computer with a torus network. Our algorithm crucially exploits the torus network structure, thereby obtaining good scalability. Through computational experiments, we confirmed that a run of our proposed method using up to 20,736 cores showed a parallelization efficiency of 0.94 as compared to a 1296-core run. Finally, we successfully computed an optimal DAG structure for an instance of 36 vertices, which is the largest solved size reported in the literature.
R. Suda—This work was supported by JSPS KAKENHI Grant Number 15K20965. The computational resource of Fujitsu FX10 was awarded by the “Large-scale HPC Challenge” Project, Information Technology Center, the University of Tokyo. This research was conducted using the Fujitsu PRIMEHPC FX10 System (Oakleaf-FX) at the Information Technology Center, the University of Tokyo.
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Honda, H., Tamada, Y., Suda, R. (2016). Efficient Parallel Algorithm for Optimal DAG Structure Search on Parallel Computer with Torus Network. In: Carretero, J., Garcia-Blas, J., Ko, R., Mueller, P., Nakano, K. (eds) Algorithms and Architectures for Parallel Processing. ICA3PP 2016. Lecture Notes in Computer Science(), vol 10048. Springer, Cham. https://doi.org/10.1007/978-3-319-49583-5_37
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