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The k-Separator Problem

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Computing and Combinatorics (COCOON 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7936))

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Abstract

Given a vertex-weighted undirected graph G = (V,E,w) and a positive integer k, we consider the k-separator problem: it consists in finding a minimum-weight subset of vertices whose removal leads to a graph where the size of each connected component is less than or equal to k. We show that this problem can be solved in polynomial time for some graph classes: for cycles and trees by a dynamic programming approach and by using a peculiar graph transformation coupled with recent results from the literature for m K 2-free, (G 1, G 2, G 3, P 6)-free, interval-filament, asteroidal triple-free, weakly chordal, interval and circular-arc graphs. Approximation algorithms are also presented.

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Author information

Authors and Affiliations

  1. CNRS Samovar UMR 5157, Institut Mines-Télécom, Télécom SudParis, 9 Rue Charles Fourier, 91011, Evry Cedex, France

    Walid Ben-Ameur, Mohamed-Ahmed Mohamed-Sidi & José Neto

Authors
  1. Walid Ben-Ameur
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  2. Mohamed-Ahmed Mohamed-Sidi
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  3. José Neto
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Texas at Dallas, 75080, Richardson, TX, USA

    Ding-Zhu Du

  2. College of Computer Science and Technology, Zhejiang University, 310027, Hangzhou, China

    Guochuan Zhang

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Ben-Ameur, W., Mohamed-Sidi, MA., Neto, J. (2013). The k-Separator Problem. In: Du, DZ., Zhang, G. (eds) Computing and Combinatorics. COCOON 2013. Lecture Notes in Computer Science, vol 7936. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38768-5_31

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  • DOI: https://doi.org/10.1007/978-3-642-38768-5_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38767-8

  • Online ISBN: 978-3-642-38768-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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