FPT algorithms and kernels for the Directedk- Leaf problem

  • Authors:

  • Jean Daligault;Gregory Gutin;Eun Jung Kim;Anders Yeo

  • Affiliations:

  • Université Montpellier II, LIRMM, 161 rue Ada, 34392 Montpellier Cedex 5, France;Department of Computer Science, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK;Department of Computer Science, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK;Department of Computer Science, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 2010

Quantified Score

Hi-index 0.00

Visualization

Abstract

A subgraph T of a digraph D is an out-branching if T is an oriented spanning tree with only one vertex of in-degree zero (called the root). The vertices of T of out-degree zero are leaves. In the Directed Max Leaf problem, we wish to find the maximum number of leaves in an out-branching of a given digraph D (or, to report that D has no out-branching). In the Directedk-Leaf problem, we are given a digraph D and an integral parameter k, and we are to decide whether D has an out-branching with at least k leaves. Recently, Kneis et al. (2008) obtained an algorithm for Directedk-Leaf of running time 4^k@?n^O^(^1^). We describe a new algorithm for Directedk-Leaf of running time 3.72^k@?n^O^(^1^). This algorithms leads to an O(1.9973^n)-time algorithm for solving Directed Max Leaf on a digraph of order n. The latter algorithm is the first algorithm of running time O(@c^n) for Directed Max Leaf, where @c