A Simple Algorithm for Minimum Cuts in Near-Linear Time

08/30/2019

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by   Antonio Molina Lovett, et al.

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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. This performance matches that achieved by Karger, thereby matching the current state of the art.