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An Exact Algorithm for the Maximum Leaf Spanning Tree Problem

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Parameterized and Exact Computation (IWPEC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5917))

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Abstract

Given an undirected graph G with n nodes, the Maximum Leaf Spanning Tree problem asks to find a spanning tree of G with as many leaves as possible. When parameterized in the number of leaves k, this problem can be solved in time O(4kpoly(n)) using a simple branching algorithm introduced by a subset of the authors [13]. Daligault, Gutin, Kim, and Yeo [6] improved this branching algorithm and obtained a running time of O(3.72kpoly(n)). In this paper, we study the problem from an exact exponential time point of view, where it is equivalent to the Connected Dominating Set problem. For this problem Fomin, Grandoni, and Kratsch showed how to break the Ω(2n) barrier and proposed an O(1.9407n) time algorithm [10]. Based on some properties of [6] and [13], we establish a branching algorithm whose running time of O(1.8966n) has been analyzed using the Measure-and-Conquer technique. Finally we provide a lower bound of Ω(1.4422n) for the worst case running time of our algorithm.

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Authors and Affiliations

  1. Universität Trier, FB 4—Abteilung Informatik, D-54286, Trier, Germany

    Henning Fernau & Daniel Raible

  2. Department of Computer Science, RWTH Aachen University, Germany

    Joachim Kneis, Alexander Langer & Peter Rossmanith

  3. Laboratoire d’Informatique Théorique et Appliquée, Université Paul Verlaine - Metz, 57045, Metz Cedex 01, France

    Dieter Kratsch

  4. Laboratoire d’Informatique Fondamentale d’Orléans, Université d’Orléans, 45067, Orléans Cedex 2, France

    Mathieu Liedloff

Authors
  1. Henning Fernau
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  2. Joachim Kneis
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  3. Dieter Kratsch
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  4. Alexander Langer
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  5. Mathieu Liedloff
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  6. Daniel Raible
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  7. Peter Rossmanith
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Texas A&M University, College Station, 77843, Texas, USA

    Jianer Chen

  2. Institutt for informatikk, Universitetet i Bergen, Postboks 7803, 5020, Bergen, Norway

    Fedor V. Fomin

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© 2009 Springer-Verlag Berlin Heidelberg

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Fernau, H. et al. (2009). An Exact Algorithm for the Maximum Leaf Spanning Tree Problem. In: Chen, J., Fomin, F.V. (eds) Parameterized and Exact Computation. IWPEC 2009. Lecture Notes in Computer Science, vol 5917. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11269-0_13

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  • DOI: https://doi.org/10.1007/978-3-642-11269-0_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11268-3

  • Online ISBN: 978-3-642-11269-0

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