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arXiv · 1908.11829

A Simple Algorithm for Minimum Cuts in Near-Linear Time

Nalin Bhardwaj·Antonio Molina Lovett·Bryce Sandlund
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Abstract

We consider the minimum cut problem in undirected, weighted graphs. We give a simple algorithm to find a minimum cut that $2$-respects (cuts two edges of) a spanning tree $T$ of a graph $G$. This procedure can be used in place of the complicated subroutine given in Karger's near-linear time minimum cut algorithm (J. ACM, 2000). We give a self-contained version of Karger's algorithm with the new procedure, which is easy to state and relatively simple to implement. It produces a minimum cut on an $m$-edge, $n$-vertex graph in $O(m \log^3 n)$ time with high probability, matching the complexity of Karger's approach.

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Nalin Bhardwaj, Antonio Molina Lovett, Bryce Sandlund. 2019-08-30. A Simple Algorithm for Minimum Cuts in Near-Linear Time. https://arxiv.org/abs/1908.11829

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