Nonblocker: parameterized algorithmics for minimum dominating set

Authors:
Frank Dehne;Michael Fellows;Henning Fernau;Elena Prieto;Frances Rosamond
Affiliations:
School of Computer Science, Carleton University, Canada;School of Electrical Engineering and Computer Science, The University of Newcastle, Australia;School of Electrical Engineering and Computer Science, The University of Newcastle, Australia;School of Electrical Engineering and Computer Science, The University of Newcastle, Australia;School of Electrical Engineering and Computer Science, The University of Newcastle, Australia
Venue:
SOFSEM'06 Proceedings of the 32nd conference on Current Trends in Theory and Practice of Computer Science
Year:
2006

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Abstract

We provide parameterized algorithms for nonblocker, the parametric dual of the well known dominating set problem. We exemplify three methodologies for deriving parameterized algorithms that can be used in other circumstances as well, including the (i) use of extremal combinatorics (known results from graph theory) in order to obtain very small kernels, (ii) use of known exact algorithms for the (nonparameterized) minimum dominating set problem, and (iii) use of exponential space. Parameterized by the size kd of the non-blocking set, we obtain an algorithm that runs in time ${\mathcal O}^{*}(1.4123^{k_{d}})$ when allowing exponential space.