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A Simple Algorithm for Minimum Cuts in Near-Linear Time

Authors Nalin Bhardwaj, Antonio J. Molina Lovett, Bryce Sandlund

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Author Details

Nalin Bhardwaj
  • University of California San Diego, CA, USA
Antonio J. Molina Lovett
  • Department of Computer Science, Princeton University, NJ, USA
Bryce Sandlund
  • Cheriton School of Computer Science, University of Waterloo, Canada

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Nalin Bhardwaj, Antonio J. Molina Lovett, and Bryce Sandlund. A Simple Algorithm for Minimum Cuts in Near-Linear Time. In 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 162, pp. 12:1-12:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.SWAT.2020.12

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
Keywords
  • minimum cut
  • sparsification
  • near-linear time
  • packing

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