On the Directed Degree-Preserving Spanning Tree Problem

In this paper we initiate a systematic study of the Reduced Degree Spanning Tree problem, where given a digraph D and a nonnegative integer k, the goal is to construct a spanning out-tree with at most k vertices of reduced out-degree. This problem is a directed analog of the wellstudied Minimum-Vertex Feedback Edge Set problem. We show that this problem is fixed-parameter tractable and 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 runtime O∗ (5.942k ). This adds the Reduced Degree Spanning Tree problem to the small list of directed graph problems for which fixed-parameter tractable algorithms are known. Finally, we consider the dual of Reduced Degree Spanning Tree, that is, given a digraph D and a nonnegative integer k, the goal is to construct a spanning out-tree of D with at least k vertices of full out-degree. We show that this problem is...

• Type: Conference
• Year: 2009
• Where: IWPEC
• Authors: Daniel Lokshtanov, Venkatesh Raman, Saket Saurabh, Somnath Sikdar
• Keywords: Applied Computing, Degree Spanning Tree, IWPEC 2009, Reduced Degree, Tree Problem