FPT algorithms and kernels for the Directed k-Leaf problem

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 k-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 the problem of running time 4k · nO(1) . We describe a new algorithm for the problem of running time 3.72k · nO(1) . In Rooted Directed k-Leaf Problem, apart from D and k, we are given a vertex r of D and we are to decide whether D has an out-branching rooted at r with at least k leaves. Very recently, Fernau et al. (2008) found an O(k3 )-size kernel for Rooted Directed k-Leaf. In this paper, we obtain an O(k) kernel for Rooted Directed k-Leaf restricted to acyclic digraphs.

• Type: Journal
• Year: 2010
• Where: JCSS
• Authors: Jean Daligault, Gregory Gutin, Eun Jung Kim, Anders Yeo
• Keywords: Directed K-Leaf, Directed K-leaf Problem, Et Al, JCSS 2010