Improved Parallel Algorithm for Finding Minimum Cuts in Stochastic Flow Networks

Abstract

This article solves the convergence problem in the Parallel BK algorithm for large-scale flow networks. We introduce a merging method and a pseudo-Boolean representation-based invariance analysis that optimize the algorithm's performance compared to classical approaches such as Ford-Fulkerson, Edmonds-Karp, Push-Relabel, and Kargers Algorithm. Our approach improves energy efficiency, reduces memory usage, and lowers time complexity by leveraging parallelization techniques. We evaluate the performance of these algorithms using Python simulations on various benchmark graphs, ranging from small to large-scale networks. The results show that our method reduces memory consumption by up to 40% and speeds up execution time by 30%, while maintaining high accuracy in finding minimum cuts. This paper demonstrates the algorithm's potential for applications in image segmentation, wireless sensor networks, and network reliability analysis