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A PTAS for the Cluster Editing Problem on Planar Graphs

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Approximation and Online Algorithms (WAOA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10138))

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Abstract

The goal of the cluster editing problem is to add or delete a minimum number of edges from a given graph, so that the resulting graph becomes a union of disjoint cliques. The cluster editing problem is closely related to correlation clustering and has applications, e.g. in image segmentation. For general graphs this problem is \({\mathbb {APX}}\)-hard. In this paper we present an efficient polynomial time approximation scheme for the cluster editing problem on graphs embeddable in the plane with a few edge crossings. The running time of the algorithm is \({2^{O\left( \epsilon ^{-1} \log (\epsilon ^{-1})\right) }n}\) for planar graphs and \(2^{O\left( k^2\epsilon ^{-1}\log \left( k^2\epsilon ^{-1}\right) \right) }n\) for planar graphs with at most k crossings.

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Authors and Affiliations

  1. Maastricht University School of Business and Economics, P.O. Box 616, 6200 MD, Maastricht, The Netherlands

    André Berger, Alexander Grigoriev & Andrej Winokurow

Authors
  1. André Berger
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  2. Alexander Grigoriev
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  3. Andrej Winokurow
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Corresponding author

Correspondence to Alexander Grigoriev .

Editor information

Editors and Affiliations

  1. Institut für Informatik, Christian-Albrechts-Universität, Kiel, Germany

    Klaus Jansen

  2. Istituto Dalle Molle di Studi sull’ Intelligenza Artificiale, Manno (Lugano), Switzerland

    Monaldo Mastrolilli

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Berger, A., Grigoriev, A., Winokurow, A. (2017). A PTAS for the Cluster Editing Problem on Planar Graphs. In: Jansen, K., Mastrolilli, M. (eds) Approximation and Online Algorithms. WAOA 2016. Lecture Notes in Computer Science(), vol 10138. Springer, Cham. https://doi.org/10.1007/978-3-319-51741-4_3

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  • DOI: https://doi.org/10.1007/978-3-319-51741-4_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-51740-7

  • Online ISBN: 978-3-319-51741-4

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