Tight Bounds and Faster Algorithms for Directed Max-Leaf Problems

  title={Tight Bounds and Faster Algorithms for Directed Max-Leaf Problems},
  author={Paul S. Bonsma and Frederic Dorn},
An out-tree T of a directed graph D is a rooted tree subgraph with all arcs directed outwards from the root. An out-branching is a spanning out-tree. By l(D) and ls(D) we denote the maximum number of leaves over all out-trees and out-branchings of D, respectively. We give fixed parameter tractable algorithms for deciding whether ls(D) ≥ k and whether l(D) ≥ k for a digraph D on n vertices, both with time complexity 2 log k) · n. This improves on previous algorithms with complexity 2 3 log k… CONTINUE READING

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