A Simple and Fast Min-cut Algorithm

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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$O(max(log n, min(m/n, \delta_{G}/\varepsilon))n^2)$\end{document}, where ε is the minimal edge weight, and δG the minimal weighted degree. For integer edge weights this time is further improved to O(δGn2) and O(λGn2). In both cases these bounds are improvements of the previously known best bounds of deterministic algorithms. These were O(nm + log nn2) for real edge weights and O(nM+n2) and O(M+λGn2) for integer weights, where M is the sum of all edge weights.