Refined Search Tree Technique for DOMINATING SET on Planar Graphs

Authors:
Jochen Alber;Hongbing Fan;Michael R. Fellows;Henning Fernau;Rolf Niedermeier;Frances A. Rosamond;Ulrike Stege
Affiliations:
-;-;-;-;-;-;-
Venue:
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Year:
2001

Citing 1
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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(8kn), 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.