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International Workshop on Combinatorial Algorithms

IWOCA 2018: Combinatorial Algorithms pp 90–101Cite as

Fully Leafed Induced Subtrees

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10979))

Abstract

We consider the problem \(\mathrm {LIS}\) of deciding whether there exists an induced subtree with exactly \(i \le n\) vertices and \(\ell \) leaves in a given graph G with n vertices. We study the associated optimization problem, that consists in computing the maximal number of leaves, denoted by \(L_G(i)\), realized by an induced subtree with i vertices, for \(0 \le i \le n\). We begin by proving that the \(\mathrm {LIS}\) problem is NP-complete in general. Then, we describe a nontrivial branch and bound algorithm that computes the function \(L_G\) for any simple graph G. In the special case where G is a tree of maximum degree \(\varDelta \), we provide a \(\mathcal {O}(n^3\varDelta )\) time and \(\mathcal {O}(n^2)\) space algorithm to compute the function \(L_G\).

A. Blondin Massé is supported by a grant from the National Sciences and Engineering Research Council of Canada (NSERC) through Individual Discovery Grant RGPIN-417269-2013. M. Lapointe and É. Nadeau are both supported by a scholarship from the NSERC.

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Author information

Authors and Affiliations

  1. Laboratoire de Combinatoire et d’Informatique Mathématique, Université du Québec à Montréal, Montreal, Canada

    Alexandre Blondin Massé, Mélodie Lapointe, Émile Nadeau & Élise Vandomme

  2. Laboratoire Interdisciplinaire de Recherche en Imagerie et en Combinatoire, Université du Québec à Trois-Rivières, Trois-Rivières, Canada

    Julien de Carufel & Alain Goupil

Authors
  1. Alexandre Blondin Massé
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  2. Julien de Carufel
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  3. Alain Goupil
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  4. Mélodie Lapointe
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  5. Émile Nadeau
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  6. Élise Vandomme
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Corresponding author

Correspondence to Élise Vandomme .

Editor information

Editors and Affiliations

  1. Department of Informatics, King’s College London, London, United Kingdom

    Costas Iliopoulos

  2. Department of Computer Science, School of Computing, National University of Singapore, Singapore, Singapore

    Hon Wai Leong

  3. Department of Computer Science, School of Computing, National University of Singapore, Singapore, Singapore

    Wing-Kin Sung

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Blondin Massé, A., de Carufel, J., Goupil, A., Lapointe, M., Nadeau, É., Vandomme, É. (2018). Fully Leafed Induced Subtrees. In: Iliopoulos, C., Leong, H., Sung, WK. (eds) Combinatorial Algorithms. IWOCA 2018. Lecture Notes in Computer Science(), vol 10979. Springer, Cham. https://doi.org/10.1007/978-3-319-94667-2_8

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  • DOI: https://doi.org/10.1007/978-3-319-94667-2_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-94666-5

  • Online ISBN: 978-3-319-94667-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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