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MaxCut Above Guarantee

Authors Ivan Bliznets , Vladislav Epifanov

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Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Fixed parameter tractability
Keywords
  • Tripartite
  • 3-colorable
  • chordal
  • maximum cut
  • FPT-algorithm
  • linear kernel

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Abstract

In this paper, we study the computational complexity of the Maximum Cut problem parameterized above guarantee. Our main result provides a linear kernel for the Maximum Cut problem in connected graphs parameterized above the spanning tree. This kernel significantly improves the previous O(k⁵) kernel given by Madathil, Saurabh, and Zehavi [ToCS 2020]. We also provide subexponential running time algorithms for this problem in special classes of graphs: chordal, split, and co-bipartite. We complete the picture by lower bounds under the assumption of the ETH. Moreover, we initiate a study of the Maximum Cut problem above 2/3|E| lower bound in tripartite graphs.

Cite As Get BibTex

Ivan Bliznets and Vladislav Epifanov. MaxCut Above Guarantee. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 22:1-22:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.MFCS.2023.22

Author Details

Ivan Bliznets
  • Utrecht University, The Netherlands
Vladislav Epifanov
  • HSE University, St. Petersburg, Russia

Funding

Supported by the project CRACKNP that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 853234).

Acknowledgements

We want to thank anonymous reviewers for their suggestions that helped to improve the presentation of the paper.

References

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