A Simple and Fast Min-cut Algorithm

Abstract

We present an algorithm which calculates a minimum cut and its weight in an undirected graph with nonnegative real edge weights, n vertices and m edges, in time $O(max(log n, min(m/n, \delta_{G}/\varepsilon))n^2)$, where ε is the minimal edge weight, and δ _G the minimal weighted degree. For integer edge weights this time is further improved to O(δ _G n ²) and O(λ _G n ²).

In both cases these bounds are improvements of the previously known best bounds of deterministic algorithms. These were O(nm + log nn ²) for real edge weights and O(nM+n ²) and O(M+λ _G n ²) for integer weights, where M is the sum of all edge weights.