Finding All Global Minimum Cuts in Practice

Authors Monika Henzinger , Alexander Noe , Christian Schulz , Darren Strash

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Author Details

Monika Henzinger
  • University of Vienna, Faculty of Computer Science, Austria
Alexander Noe
  • University of Vienna, Faculty of Computer Science, Austria
Christian Schulz
  • University of Vienna, Faculty of Computer Science, Austria
Darren Strash
  • Hamilton College, Department of Computer Science, Clinton, NY, USA

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Monika Henzinger, Alexander Noe, Christian Schulz, and Darren Strash. Finding All Global Minimum Cuts in Practice. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 59:1-59:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


We present a practically efficient algorithm that finds all global minimum cuts in huge undirected graphs. Our algorithm uses a multitude of kernelization rules to reduce the graph to a small equivalent instance and then finds all minimum cuts using an optimized version of the algorithm of Nagamochi, Nakao and Ibaraki. In shared memory we are able to find all minimum cuts of graphs with up to billions of edges and millions of minimum cuts in a few minutes. We also give a new linear time algorithm to find the most balanced minimum cuts given as input the representation of all minimum cuts.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Paths and connectivity problems
  • Mathematics of computing → Graph algorithms
  • Mathematics of computing → Network flows
  • Minimum Cut
  • Graph Algorithm
  • Algorithm Engineering
  • Cut Enumeration
  • Balanced Cut
  • Global Minimum Cut
  • Large-scale Graph Analysis


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