Practical Minimum Cut Algorithms

TL;DR

This paper presents a fast, near-minimum cut algorithm for undirected graphs that combines cluster contraction with label propagation, outperforming existing methods in speed and accuracy.

Contribution

It introduces a linear-time, near-minimum cut algorithm using cluster contraction and provides both sequential and parallel implementations with extensive experimental validation.

Findings

Finds optimal cuts on nearly all tested instances

Runs significantly faster than state-of-the-art algorithms

Parallel implementation demonstrates good scalability

Abstract

The minimum cut problem for an undirected edge-weighted graph asks us to divide its set of nodes into two blocks while minimizing the weight sum of the cut edges. Here, we introduce a linear-time algorithm to compute near-minimum cuts. Our algorithm is based on cluster contraction using label propagation and Padberg and Rinaldi's contraction heuristics [SIAM Review, 1991]. We give both sequential and shared-memory parallel implementations of our algorithm. Extensive experiments on both real-world and generated instances show that our algorithm finds the optimal cut on nearly all instances significantly faster than other state-of-the-art algorithms while our error rate is lower than that of other heuristic algorithms. In addition, our parallel algorithm shows good scalability.