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Extension and Its Price for the Connected Vertex Cover Problem

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Combinatorial Algorithms (IWOCA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11638))

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Abstract

We consider extension variants of Vertex Cover and Independent Set, following a line of research initiated in [9]. In particular, we study the Ext-CVC and the Ext-NSIS problems: given a graph \(G=(V,E)\) and a vertex set \(U \subseteq V\), does there exist a minimal connected vertex cover (respectively, a maximal non-separating independent set) S, such that \(U\subseteq S\) (respectively, \(U \supseteq S\)). We present hardness results for both problems, for certain graph classes such as bipartite, chordal and weakly chordal. To this end we exploit the relation of Ext-CVC to Ext-VC, that is, to the extension variant of Vertex Cover. We also study the Price of Extension (PoE), a measure that reflects the distance of a vertex set U to its maximum efficiently computable subset that is extensible to a minimal connected vertex cover, and provide negative and positive results for PoE in general and special graphs.

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Notes

  1. 1.

    This class is introduced in [19], as the class of graphs \(G=(V,E)\) with no chordless cycle of five or more vertices in G or in its complement \(\overline{G}=(V,\overline{E})\).

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Authors and Affiliations

  1. Université Paris-Dauphine, PSL University, CNRS, LAMSADE, 75016, Paris, France

    Mehdi Khosravian Ghadikoalei & Jérôme Monnot

  2. School of Electrical and Computer Engineering, National Technical University of Athens, Polytechnioupoli, 15780, Zografou, Athens, Greece

    Nikolaos Melissinos & Aris Pagourtzis

Authors
  1. Mehdi Khosravian Ghadikoalei
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  2. Nikolaos Melissinos
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  3. Jérôme Monnot
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  4. Aris Pagourtzis
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Correspondence to Aris Pagourtzis .

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Editors and Affiliations

  1. Arizona State University, Tempe, AZ, USA

    Charles J. Colbourn

  2. University of Pisa, Pisa, Italy

    Roberto Grossi

  3. University of Pisa, Pisa, Italy

    Nadia Pisanti

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Khosravian Ghadikoalei, M., Melissinos, N., Monnot, J., Pagourtzis, A. (2019). Extension and Its Price for the Connected Vertex Cover Problem. In: Colbourn, C., Grossi, R., Pisanti, N. (eds) Combinatorial Algorithms. IWOCA 2019. Lecture Notes in Computer Science(), vol 11638. Springer, Cham. https://doi.org/10.1007/978-3-030-25005-8_26

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  • DOI: https://doi.org/10.1007/978-3-030-25005-8_26

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