On the directed Full Degree Spanning Tree problem

We study the parameterized complexity of a directed analog of the Full Degree Spanning Tree problem where, given a digraph D and a nonnegative integer k, the goal is to construct a spanning out-tree T of D such that at least k vertices in T have the same out-degree as in D. We show that this problem is W[1]-hard even on the class of directed acyclic graphs. In the dual version, called Reduced Degree Spanning Tree, one is required to construct a spanning out-tree T such that at most k vertices in T have out-degrees that are different from that in D. We show that this problem is fixed-parameter tractable and that it admits a problem kernel with at most 8k vertices on strongly connected digraphs and O(k2 ) vertices on general digraphs. We also give an algorithm for this problem on general digraphs with running time O(5.942k · nO(1) ), where n is the number of vertices in the input digraph.

• Type: Journal
• Year: 2011
• Where: DISOPT
• Authors: Daniel Lokshtanov, Venkatesh Raman, Saket Saurabh, Somnath Sikdar
• Keywords: Degree Spanning Tree, DISOPT 2011, Education, General Digraphs, Tree Problem