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i Acknowledgements First of all, I would like to thank my supervisor Pinar Heggernes for her help and guidance, both with my reasearch and with all other aspects of being a graduate student. This thesis would not have existed without her. Thomassen and Yngve Villanger. A special thanks goes to Saket Saurabh, with whom I have shared many sleepless nights and(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 kernel-izable if and only if it is fixed-parameter tractable. Practically,(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)
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)
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)