## Fixed Parameter Algorithms for Dominating Set and Related Problems on Planar Graphs (2002)

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Citations: | 101 - 23 self |

### BibTeX

@MISC{Alber02fixedparameter,

author = {Jochen Alber and Hans L. Bodlaender and Henning Fernau and Ton Kloks and Rolf Niedermeier},

title = {Fixed Parameter Algorithms for Dominating Set and Related Problems on Planar Graphs},

year = {2002}

}

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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 . To obtain this result, we show that the treewidth of a planar graph with domination number (G) is O( (G)), and that such a tree decomposition can be found in O( (G)n) time. The same technique can be used to show that the k-face cover problem ( find a size k set of faces that cover all vertices of a given plane graph) can be solved in O(c n) time, where c 1 = 3 and k is the size of the face cover set. Similar results can be obtained in the planar case for some variants of k-dominating set, e.g., k-independent dominating set and k-weighted dominating set.