Abstract
We describe a linear-time algorithm that inputs a planar graph G and outputs a planar graph of size O(k) and with domination number k, where k is the domination number of G, i.e., the size of a smallest dominating set in G. In the language of parameterized computation, the new algorithm is a linear-time kernelization for the NP-complete Planar Dominating Set problem that produces a kernel of linear size. Such an algorithm was previously known (van Bevern et al., these proceedings), but the new algorithm and its analysis are considerably simpler.
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Hagerup, T. (2012). Simpler Linear-Time Kernelization for Planar Dominating Set. In: Marx, D., Rossmanith, P. (eds) Parameterized and Exact Computation. IPEC 2011. Lecture Notes in Computer Science, vol 7112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28050-4_15
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DOI: https://doi.org/10.1007/978-3-642-28050-4_15
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