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2011

On the directed Full Degree Spanning Tree problem

8 years 6 months ago
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.
Daniel Lokshtanov, Venkatesh Raman, Saket Saurabh,
Added 14 May 2011
Updated 14 May 2011
Type Journal
Year 2011
Where DISOPT
Authors Daniel Lokshtanov, Venkatesh Raman, Saket Saurabh, Somnath Sikdar
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