A faster exact algorithm for the directed maximum leaf spanning tree problem

Authors:
Daniel Binkele-Raible;Henning Fernau
Affiliations:
Univ.Trier, FB 4—Abteilung Informatik, Trier, Germany;Univ.Trier, FB 4—Abteilung Informatik, Trier, Germany
Venue:
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
Year:
2010

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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 ${\mathcal{O}}^*({1.9044}^n)$ using polynomial space. Allowing exponential space, this run time upper bound can be lowered to ${\mathcal{O}}^*(1.8139^n)$.