Practical Fully Dynamic Minimum Cut Algorithms

TL;DR

This paper introduces a practical, fully dynamic algorithm for maintaining the global minimum cut in large graphs, demonstrating significant speed improvements over static methods through efficient implementation.

Contribution

It is the first implementation of a fully dynamic minimum cut algorithm that combines theoretical foundations with practical optimizations for large graphs.

Findings

Up to multiple orders of magnitude speedup compared to static approaches

Effective handling of both edge insertions and deletions

Demonstrated efficiency on large dynamic graphs

Abstract

We present a practically efficient algorithm for maintaining a global minimum cut in large dynamic graphs under both edge insertions and deletions. While there has been theoretical work on this problem, our algorithm is the first implementation of a fully-dynamic algorithm. The algorithm uses the theoretical foundation and combines it with efficient and finely-tuned implementations to give an algorithm that can maintain the global minimum cut of a graph with rapid update times. We show that our algorithm gives up to multiple orders of magnitude speedup compared to static approaches both on edge insertions and deletions.