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, Trier, Germany D-54286;Department of Computer Science, RWTH Aachen University, Germany;Laboratoire d'Informatique Théorique et Appliquée, Université Paul Verlaine - Metz, Metz Cedex 01, France 57045;Department of Computer Science, RWTH Aachen University, Germany;Laboratoire d'Informatique Fondamentale d'Orléans, Université d'Orléans, Orléans Cedex 2, France 45067;Universität Trier, Trier, Germany D-54286;Department of Computer Science, RWTH Aachen University, Germany

  • Venue:
  • Parameterized and Exact Computation
  • Year:
  • 2009

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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(4 k poly(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(3.72 k poly(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 驴(2 n ) barrier and proposed an O(1.9407 n ) time algorithm [10]. Based on some properties of [6] and [13], we establish 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 驴(1.4422 n ) for the worst case running time of our algorithm.