Rethinking the implementation and application of the Benczur-Karger minimum cuts algorithm

Abstract

In graph theory and network analysis, finding the minimum cut in a graph is a fundamental algorithmic challenge. This paper explores the development and application of Benczur-Karger’s minimum cut algorithms, focusing on the relationship between theoretical advancements and practical implementation. Despite the algorithm's advantages, there are challenges related to its implementation complexities and the effects of compression factor settings. To address these issues, this paper first implements Benczur-Karger’s minimum cuts algorithm in Python and discusses the implementation details. Additionally, we propose a new compression factor setting for Benczur-Karger’s minimum cuts algorithm and conduct an experiment with this new setting. The experimental results show that our proposed compression factor performs better than the original one. Finally, we discuss the application of Benczur-Karger’s minimum cuts algorithm in social network analysis, a field where its use has been limited. The code is available at https://github.com/HarleyHanqin/Modified_BK.