High-precision ultra-fast minimum cut approximation through aggregated hash of cut collection

Abstract

Due to the wide application of s-t minimum cut (min-cut) in various scenarios, many acceleration algorithms have been proposed to solve it. However, the query times of the acceleration algorithms currently available are still high in large-scale graphs, rendering them useless in frequently solving scenarios. We re-examine the min-cut problem from a novel perspective of cut collection hash. By extracting aggregated hashes of mapped cut collections in one-dimensional space, a Monte Carlo-like method is used to quickly compare them and estimate the minimum cut between any two nodes with low computational effort and high accuracy. After the graph is preprocessed using a few hundred depth-first traversals, the time complexity of the min-cut solution can be logarithmic in terms of the average degree and capacity of the graph. Experiments on large-scale graphs show that compared to the fastest exact algorithm, the proposed algorithm can increase the speed of the min-cut solution by up to seven orders of magnitude, when only a few mathematical comparisons per pair are needed to obtain exact min-cut values of no less than 99.9% node pairs.