A simple min-cut algorithm

TLDR

The algorithm is simple, compact, easy to implement, and has a surprisingly simple proof of correctness, and unlike most approaches it does not use flow techniques. We present an algorithm for finding the minimum cut of an undirected edge‑weighted graph. The algorithm proceeds in about |V| identical phases, each performing a maximum adjacency search, with a straightforward runtime analysis. Its runtime matches that of the fastest known algorithm.

Abstract

We present an algorithm for finding the minimum cut of an undirected edge-weighted graph. It is simple in every respect. It has a short and compact description, is easy to implement, and has a surprisingly simple proof of correctness. Its runtime matches that of the fastest algorithm known. The runtime analysis is straightforward. In contrast to nearly all approaches so far, the algorithm uses no flow techniques. Roughly speaking, the algorithm consists of about | V | nearly identical phases each of which is a maximum adjacency search .