Henning Fernau

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Abstract. We present an algorithm that constructively produces a solution to the k -DOMINATING SET problem for planar graphs in time O(c^ \sqrt k n) , where c=4^ 6\sqrt 34 . To obtain this result, we show that the treewidth of a planar graph with domination number γ (G) is O(\sqrt \rule 0pt 4pt \smash γ (G) ) , and that such a tree decomposition can be(More)
Determining whether a parameterized problem is kernelizable and has a small kernel size has recently become one of the most interesting topics of research in the area of parameterized complexity and algorithms. Theoretically, it has been proved that a parameterized problem is kernelizable if and only if it is fixed-parameter tractable. Practically, applying(More)
The <i>k</i>-Leaf Out-Branching problem is to find an out-branching, that is a rooted oriented spanning tree, with at least <i>k</i> leaves in a given digraph. The problem has recently received much attention from the viewpoint of parameterized algorithms. Here, we take a kernelization based approach to the <i>k</i>-Leaf-Out-Branching problem. We give the(More)
We show how appropriately chosen functions f which we call distinguishing can be used to make deterministic "nite automata backward deterministic. This idea can be exploited to design regular language classes called f-distinguishable which are identi"able in the limit from positive samples. Special cases of this approach are the k-reversible and terminal(More)
We consider the concepts of a t-total vertex cover and a t-total edge cover (t ≥ 1), which generalize the notions of a vertex cover and an edge cover, respectively. A ttotal vertex (respectively edge) cover of a connected graph G is a vertex (edge) cover S of G such that each connected component of the subgraph of G induced by S has least t vertices(More)