A New Algorithm for Finding Trees with Many Leaves

  • Authors:

  • Joachim Kneis;Alexander Langer;Peter Rossmanith

  • Affiliations:

  • Dept. of Computer Science, RWTH Aachen University, Germany;Dept. of Computer Science, RWTH Aachen University, Germany;Dept. of Computer Science, RWTH Aachen University, Germany

  • Venue:
  • ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
  • Year:
  • 2008

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Abstract

We present an algorithm that finds trees with at least k leaves in undirected and directed graphs. These problems are known as Maximum Leaf Spanning Tree for undirected graphs, and, respectively, Directed Maximum Leaf Out-Tree and Directed Maximum Leaf Spanning Out-Tree in the case of directed graphs. The run time of our algorithm is $O({\it poly}(|V|) + 4^k k^2)$ on undirected graphs, and O(4 k |V| ·|E|) on directed graphs. This improves over the previously fastest algorithms for these problems with run times of $O({\it poly}(|V|) + 6.75^k {\it poly}(k))$ and $2^{O(k \log k)} {\it poly}(|V|)$, respectively.