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On Cluster Editing Problem with Clusters of Small Sizes

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Optimization and Applications (OPTIMA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14395))

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Abstract

In the cluster editing problem, one has to partition the set of vertices of a graph into disjoint subsets (called clusters) minimizing the number of edges between clusters and the number of missing edges within clusters. We consider a version of the problem in which cluster sizes are bounded from above by a positive integer s. This problem is NP-hard for any fixed \(s \geqslant 3\). We propose polynomial-time approximation algorithms for this version of the problem. Their performance guarantees are equal to 5/3 and 5/2 for the cases \(s = 3\) and \(s = 4\), respectively.

We also show that the cluster editing problem is APX-complete for the case \(s = 3\) even if the maximum degree of the graphs is bounded by 4.

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Acknowledgements

The research of the first author was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project FWNF-2022-0019). The research of the second author was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project FWNF-2022-0020).

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Authors and Affiliations

  1. Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russia

    Alexander Kononov & Victor Il’ev

  2. Dostoevsky Omsk State University, Omsk, Russia

    Victor Il’ev

Authors
  1. Alexander Kononov
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  2. Victor Il’ev
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Corresponding author

Correspondence to Alexander Kononov .

Editor information

Editors and Affiliations

  1. FRC CSC RAS, Moscow, Russia

    Nicholas Olenev

  2. FRC CSC RAS, Moscow, Russia

    Yuri Evtushenko

  3. University of Montenegro, Podgorica, Montenegro

    Milojica Jaćimović

  4. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  5. FRC CSC RAS, Moscow, Russia

    Vlasta Malkova

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Kononov, A., Il’ev, V. (2023). On Cluster Editing Problem with Clusters of Small Sizes. In: Olenev, N., Evtushenko, Y., Jaćimović, M., Khachay, M., Malkova, V. (eds) Optimization and Applications. OPTIMA 2023. Lecture Notes in Computer Science, vol 14395. Springer, Cham. https://doi.org/10.1007/978-3-031-47859-8_23

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  • DOI: https://doi.org/10.1007/978-3-031-47859-8_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-47858-1

  • Online ISBN: 978-3-031-47859-8

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