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Separator Based Data Reduction for the Maximum Cut Problem

Authors Jonas Charfreitag , Christine Dahn , Michael Kaibel , Philip Mayer , Petra Mutzel , Lukas Schürmann

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Author Details

Jonas Charfreitag
  • Institute of Computer Science, University of Bonn, Germany
Christine Dahn
  • Institute of Computer Science, University of Bonn, Germany
Michael Kaibel
  • Institute of Computer Science, University of Bonn, Germany
Philip Mayer
  • Institute of Computer Science, University of Bonn, Germany
Petra Mutzel
  • Institute of Computer Science, University of Bonn, Germany
Lukas Schürmann
  • Institute of Computer Science, University of Bonn, Germany

Funding

This work was partially funded by the German Research Foundation (DFG) EXC-2047/1 - 390685813 and FOR-5361 - 459420781, and by the BMBF (Germany) and state of NRW as part of the Lamarr-Institute, LAMARR22B.

Acknowledgements

We thank Konstantinos Papadopoulos for his contribution to this work.

Cite AsGet BibTex

Jonas Charfreitag, Christine Dahn, Michael Kaibel, Philip Mayer, Petra Mutzel, and Lukas Schürmann. Separator Based Data Reduction for the Maximum Cut Problem. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 4:1-4:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.SEA.2024.4

Abstract

Preprocessing is an important ingredient for solving the maximum cut problem to optimality on real-world graphs. In our work, we derive a new framework for data reduction rules based on vertex separators. Vertex separators are sets of vertices, whose removal increases the number of connected components of a graph. Certain small separators can be found in linear time, allowing for an efficient combination of our framework with existing data reduction rules. Additionally, we complement known data reduction rules for triangles with a new one. In our computational experiments on established benchmark instances, we clearly show the effectiveness and efficiency of our proposed data reduction techniques. The resulting graphs are significantly smaller than in earlier studies and sometimes no vertex is left, so preprocessing has fully solved the instance to optimality. The introduced techniques are also shown to offer significant speedup potential for an exact state-of-the-art solver and to help a state-of-the-art heuristic to produce solutions of higher quality.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial optimization
  • Mathematics of computing → Solvers
  • Theory of computation → Network optimization
Keywords
  • Data Reduction
  • Maximum Cut
  • Vertex Separators

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Supplementary Materials

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