# Efficient Parallel Algorithm for Optimal DAG Structure Search on Parallel Computer with Torus Network

## 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.

### Keywords

Optimal DAG structure Optimal bayesian network structure Parallel algorithm Distributed algorithm Torus network### References

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