Usage of task and data parallelism for finding the lower boundary vectors in a stochastic-flow network

In a stochastic-flow network, a minimal system state vector under which the maximum flow of the network from a source node to a destination node is equal to d is called a lower boundary vector (LBV). As the number of LBVs increases exponentially with the size of the network, the available algorithms in the literature could be improved to be more practical for real-world large-sized systems. We employ task and data parallelism to propose an efficient algorithm for determining all the LBVs to tackle this problem. We present an efficient approach for removing duplicate solutions to improve an available algorithm to find all the LBVs. We show the correctness and compute the complexity results of the proposed approach and demonstrate its efficiency. Then, we propose vectorized, parallelized, and vectorized–parallelized versions of the main algorithm. We illustrate the standard version through a benchmark example and discuss the other proposed versions’ correctness. We conduct several experimental results on two known benchmark networks and more than one thousand random problems to demonstrate the practical efficiency of the vectorized–parallelized version. Moreover, Dolan and Moré’s performance profile is used to provide a more intuitive comparison between all four versions.