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How to Cut a Graph into Many Pieces

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Theory and Applications of Models of Computation (TAMC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6648))

Abstract

In this paper we consider the problem of finding a graph separator of a given size that decomposes the graph into the maximum number of connected components. We present the picture of the computational complexity and the approximability of this problem for several natural classes of graphs.

We first provide an overview of the hardness of approximation of this problem, which stems mainly from its close relation to the Independent Set and to the Maximum Clique problem. Next, we show that the problem is solvable in polynomial time for interval graphs and graphs of bounded treewidth. We also show that MaxiNum Components is fixed-parameter tractable on planar graphs with the size of the separator as the parameter. Our main contribution is the derivation of an efficient polynomial-time approximation scheme for the problem on planar graphs.

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Author information

Authors and Affiliations

  1. Department of Quantitative Economics, Maastricht University, P.O. Box 616, 6200, MD, Maastricht, The Netherlands

    Ruben van der Zwaan, André Berger & Alexander Grigoriev

Authors
  1. Ruben van der Zwaan
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  2. André Berger
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  3. Alexander Grigoriev
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Miami, 1365 Memorial Drive, 33146, Coral Gables, FL, USA

    Mitsunori Ogihara

  2. Department of Information and Communication Engineering, University of Electro-Comm, Chofugaoga 1-5-1, Chofu, 182-8585, Tokyo, Japan

    Jun Tarui

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van der Zwaan, R., Berger, A., Grigoriev, A. (2011). How to Cut a Graph into Many Pieces. In: Ogihara, M., Tarui, J. (eds) Theory and Applications of Models of Computation. TAMC 2011. Lecture Notes in Computer Science, vol 6648. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20877-5_20

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  • DOI: https://doi.org/10.1007/978-3-642-20877-5_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20876-8

  • Online ISBN: 978-3-642-20877-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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