Minimum Cut Acceleration by Exploiting Tree-Cut Injection for Upper Bound Estimation

Abstract

As a basic problem in graph theory, the minimum cut (min-cut) problem has important applications in communication related researches. There are injections from the set of all traversal trees to the set of all cuts. However, this kind of injection is completely ignored in existing methods, which may lead to the lose of acceleration opportunity. Accordingly, we propose Traversal Tree-Cut Injection based Min-Cut Acceleration algorithm (TCMA). By collecting enough cuts from different traversal trees in an undirected graph, the upper bound of min-cut value between any node pair can be calculated as the minimal value of all related cuts, which can match the accurate min-cut value with high probability. We compare TCMA with other methods using random and real-world graphs. The results show that different from other methods, TCMA is general enough to not rely on any special topology, and can achieve both high acceleration ratio and precision in various graphs, thus can be used as an effective supplement to existing methods.