An exact exponential-time algorithm for the Directed Maximum Leaf Spanning Tree problem

  • Authors:
  • Daniel Binkele-Raible;Henning Fernau

  • Affiliations:
  • Univ. Trier, FB 4-Abteilung Informatik, 54286 Trier, Germany;Univ. Trier, FB 4-Abteilung Informatik, 54286 Trier, Germany

  • Venue:
  • Journal of Discrete Algorithms
  • Year:
  • 2012

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Abstract

Given a directed graph G=(V,A), the Directed Maximum Leaf Spanning Tree problem asks to compute a directed spanning tree with as many leaves as possible. By designing a branching algorithm analyzed with Measure&Conquer, we show that the problem can be solved in time O^@?(1.9044^n) using polynomial space. Allowing exponential space, this run time upper bound can be lowered to O^@?(1.8139^n). We also provide an example showing a lower-bound for the running time of our algorithm.