Fixed-parameter tractability results for full-degree spanning tree and its dual

We provide first-time fixed-parameter tractability results for the NP-complete problems Maximum Full-Degree Spanning Tree and Minimum-Vertex Feedback Edge Set. These problems are dual to each other: In Maximum Full-Degree Spanning Tree, the task is to find a spanning tree for a given graph that maximizes the number of vertices that preserve their degree. For Minimum-Vertex Feedback Edge Set the task is to minimize the number of vertices that end up with a reduced degree. Parameterized by the solution size, we exhibit that Minimum-Vertex Feedback Edge Set is fixed-parameter tractable and has a problem kernel with the number of vertices linearly depending on the parameter k. Our main contribution for Maximum Full-Degree Spanning Tree, which is W[1]-hard, is a linear-size problem kernel when restricted to planar graphs. Moreover, we present subexponential-time algorithms in the case of planar graphs.

• Type: Journal
• Year: 2010
• Where: NETWORKS
• Authors: Jiong Guo, Rolf Niedermeier, Sebastian Wernicke
• Keywords: Computer Networks, Full-Degree Spanning Tree, Maximum Full-Degree Spanning, Minimum-Vertex Feedback Edge, NETWORKS 2010