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Two trees with the same number of leaves have to be embedded in two layers in the plane such that the leaves are aligned in two adjacent layers. Additional matching edges between the leaves give a one-to-one correspondence between pairs of leaves of the different trees. Do there exist two planar embeddings of the two trees that minimize the crossings of the(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 present an algorithm that constructively produces a solution to the k-dominating set problem for planar graphs in time O(c √ k n), where c = 3 6 √ 34. To obtain this result, we show that the treewidth of a pla-nar graph with domination number γ(G) is O(γ(G)), and that such a tree decomposition can be found in O(γ(G)n) time. The same technique can be used(More)
In this paper, we show how to systematically improve on parame-terized algorithms and their analysis, focusing on search-tree based algorithms for d-Hitting Set, especially for d = 3. We concentrate on algorithms which are easy to implement, in contrast with the highly sophisticated algorithms which have been elsewhere designed to improve on the exponential(More)
We present solutions of benchmark instances to the solitaire computer game Atomix found with different heuristic search methods. The problem is PSPACE-complete. An implementation of the heuristic algorithm A* is presented that needs no priority queue, thereby having very low memory overhead. The limited memory algorithm IDA* is handicapped by the fact that,(More)
We study (vertex-disjoint) packings of paths of length two (i.e., of P2's) in graphs under a parameterized perspective. Starting from a maximal P2-packing P of size j we use extremal combinatorial arguments for determining how many vertices of P appear in some P2-packing of size (j + 1) (if it exists). We prove that one can 'reuse' 2.5j vertices. Based on a(More)
In MaxSat, we ask for an assignment which satisfies the maximum number of clauses for a boolean formula in CNF. We present an algorithm yielding a run time upper bound of O * (2 K 6.2158) for Max-2-Sat (each clause contains at most 2 literals), where K is the number of clauses. The run time has been achieved by using heuristic priorities on the choice of(More)