Abstract
We establish refined search tree techniques for the parameterized DOMINATING SET problem on planar graphs. We derive a fixed parameter algorithm with running time O(8 k n), where k is the size of the dominating set and n is the number of vertices in the graph. For our search tree, we firstly provide a set of reduction rules. Secondly, we prove an intricate branching theorem based on the Euler formula. In addition, we give an example graph showing that the bound of the branching theorem is optimal with respect to our reduction rules. Our final algorithm is very easy (to implement); its analysis, however, is involved.
Supported by the Deutsche Forschungsgemeinschaft (DFG), research project PEAL (Parameterized complexity and Exact ALgorithms), NI 369/1-1.
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References
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© 2001 Springer-Verlag Berlin Heidelberg
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Alber, J. et al. (2001). Refined Search Tree Technique for Dominating Set on Planar Graphs. In: Sgall, J., Pultr, A., Kolman, P. (eds) Mathematical Foundations of Computer Science 2001. MFCS 2001. Lecture Notes in Computer Science, vol 2136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44683-4_11
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DOI: https://doi.org/10.1007/3-540-44683-4_11
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