The dominating set problem is fixed parameter tractable for graphs of bounded genus

Authors:
J. Ellis;H. Fan;M. Fellows
Affiliations:
Department of Computer Science, University of Victoria, PO Box 3055, Victoria, British Columbia, V8W 3P6, Canada;Department of Physics and Computer Science, Wilfrid Laurier University, Waterloo, Ontario, N2L 305, Canada;Department of Computer Science, University of Newcastle, Newcastle, New South Wales, Australia
Venue:
Journal of Algorithms
Year:
2004

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Abstract

We describe an algorithm for the dominating set problem with time complexity O((4g+40)kn2) for graphs of bounded genus g ≥ 1, where k is the size of the set. It has previously been shown that this problem is fixed parameter tractable for planar graphs. We give a simpler proof for the previous O(8kn2) result for planar graphs. Our method is a refinement of the earlier techniques.