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 k d of the non-blocking set, we obtain an algorithm that runs in time \({\mathcal O}^{*}(1.4123^{k_{d}})\) when allowing exponential space.
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Dehne, F., Fellows, M., Fernau, H., Prieto, E., Rosamond, F. (2006). nonblocker: Parameterized Algorithmics for minimum dominating set . In: Wiedermann, J., Tel, G., Pokorný, J., Bieliková, M., Štuller, J. (eds) SOFSEM 2006: Theory and Practice of Computer Science. SOFSEM 2006. Lecture Notes in Computer Science, vol 3831. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11611257_21
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DOI: https://doi.org/10.1007/11611257_21
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