An exact algorithm for the Maximum Leaf Spanning Tree problem

  • Authors:

  • Henning Fernau;Joachim Kneis;Dieter Kratsch;Alexander Langer;Mathieu Liedloff;Daniel Raible;Peter Rossmanith

  • Affiliations:

  • Universität Trier, FB 4Abteilung Informatik, D-54286 Trier, Germany;Department of Computer Science, RWTH Aachen University, Germany;Laboratoire dInformatique Théorique et Appliquée, Université Paul Verlaine - Metz, 57045 Metz Cedex 01, France;Department of Computer Science, RWTH Aachen University, Germany;Laboratoire dInformatique Fondamentale dOrléans, Université dOrléans, 45067 Orléans Cedex 2, France;Universität Trier, FB 4Abteilung Informatik, D-54286 Trier, Germany;Department of Computer Science, RWTH Aachen University, Germany

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2011

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Abstract

Given an undirected graph with n vertices, the Maximum Leaf Spanning Tree problem is to find a spanning tree with as many leaves as possible. When parameterized in the number of leaves k, this problem can be solved in time O(4^kpoly(n)) using a simple branching algorithm introduced by a subset of the authors (Kneis et al. 2008 [16]). Daligault et al. (2010) [6] improved the branching and obtained a running time of O(3.72^kpoly(n)). In this paper, we study the problem from an exponential time viewpoint, where it is equivalent to the Connected Dominating Set problem. Here, Fomin, Grandoni, and Kratsch showed how to break the @W(2^n) barrier and proposed an O(1.9407^n)-time algorithm (Fomin et al. 2008 [11]). Based on some useful properties of Kneis et al. (2008) [16] and Daligault et al. (2010) [6], we present a branching algorithm whose running time of O(1.8966^n) has been analyzed using the Measure-and-Conquer technique. Finally, we provide a lower bound of @W(1.4422^n) for the worst case running time of our algorithm.