Refined Search Tree Technique for Dominating Set on Planar Graphs
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.
Keywordsdominating set planar graph fixed parameter algorithm search tree
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