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A Simple Algorithm for Minimum Cuts in Near-Linear Time

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

Published in: LIPIcs, Volume 162, 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)


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.

Cite as

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)


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@InProceedings{bhardwaj_et_al:LIPIcs.SWAT.2020.12,
  author =	{Bhardwaj, Nalin and Molina Lovett, Antonio J. and Sandlund, Bryce},
  title =	{{A Simple Algorithm for Minimum Cuts in Near-Linear Time}},
  booktitle =	{17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)},
  pages =	{12:1--12:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-150-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{162},
  editor =	{Albers, Susanne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2020.12},
  URN =		{urn:nbn:de:0030-drops-122594},
  doi =		{10.4230/LIPIcs.SWAT.2020.12},
  annote =	{Keywords: minimum cut, sparsification, near-linear time, packing}
}
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