A 2k-vertex kernel for maximum internal spanning tree

Abstract

14th International Symposium, WADS 2015, Victoria, BC, Canada, August 5-7, 2015We consider the parameterized version of the maximum internal spanning tree problem: given an n-vertex graph and a parameter k, does the graph have a spanning tree with at least k internal vertices? Fomin et al. [J. Comput. System Sci., 79:1-6] crafted a very ingenious reduction rule, and showed that a simple application of this rule is sufficient to yield a 3k-vertex kernel for this problem. Here we propose a novel way to use the same reduction rule, resulting in an improved 2k-vertex kernel. Our algorithm applies first a greedy procedure consisting of a sequence of local exchange operations, which ends with a local-optimal spanning tree, and then uses this special tree to find a reducible structure. As a corollary of our kernel, we obtain a 4k·nO(1)-time deterministic algorithm, improving all previous algorithms for the problem.Department of Computin