A Simple Algorithm for Minimum Cuts in Near-Linear Time

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Nalin Bhardwaj, Antonio Molina Lovett, Bryce Sandlund

Published: 2020, Last Modified: 11 May 2026SWAT 2020EveryoneRevisionsBibTeXCC BY-SA 4.0
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 [Karger, 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 log³ n) time with high probability, matching the complexity of Karger’s approach.