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

8 years 2 months ago
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.
Jiong Guo, Rolf Niedermeier, Sebastian Wernicke
Added 29 Jan 2011
Updated 29 Jan 2011
Type Journal
Year 2010
Where NETWORKS
Authors Jiong Guo, Rolf Niedermeier, Sebastian Wernicke
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