We present a novel parallel algorithm that solves the optimal directed acyclic graph search problem using less memory as compared to existing algorithms. Using a dynamic programming approach, the time and space complexity of the problem is found to be O(n⋅2n), where n represents the number of vertices. The previous algorithm uses adjacent communication to efficiently exchange data between computation nodes. However, it consumes too much memory, and thus is capable of solving up to n=36. Our novel algorithm, ParaOS-DC, employs direct communication to reduce the memory consumption; this is the main cause of the inefficiency of the previous algorithm. Through computational experiments, we confirmed that our proposed algorithm is much faster than the previous algorithm when memory is insufficient. We also succeeded in solving a problem for n=37 without any constraints, which is the largest problem size solved in literature till date.
Tamada, Y. (2018). Memory efficient parallel algorithm for optimal DAG structure search using direct communication. Journal of Parallel and Distributed Computing, 119, 27–35. https://doi.org/10.1016/j.jpdc.2018.03.011