Linear problem kernels for planar graph problems with small distance property
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Planar graph vertex partition for linear problem kernels
Journal of Computer and System Sciences
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We provide first-time fixed-parameter tractability results for the NP-hard problems MAXIMUM FULL-DEGREE SPANNING TREE (FDST) and MINIMUM-VERTEX FEEDBACK EDGE SET. These problems are dual to each other. In MAXIMUM FDST, 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 a dynamic programing algorithm for graphs of bounded treewidth. © 2009 Wiley Periodicals, Inc. NETWORKS, 2010 A preliminary version of this article appears in the Proceedings of the 2nd International Workshop on Parameterized and Exact Computation (IWPEC'06), Zürich, Switzerland, September 2006, volume 4169 of Lecture Notes in Computer Science, pages 203–214, Springer.