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Simpler linear-time kernelization for planar dominating set. (English) Zbl 1352.68109
Marx, Dániel (ed.) et al., Parameterized and exact computation. 6th international symposium, IPEC 2011, Saarbrücken, Germany, September 6–8, 2011. Revised selected papers. Berlin: Springer (ISBN 978-3-642-28049-8/pbk). Lecture Notes in Computer Science 7112, 181-193 (2012).
Summary: 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 [R. van Bevern et al., Lect. Notes Comput. Sci. 7112, 194–206 (2012; Zbl 1352.68119)], but the new algorithm and its analysis are considerably simpler.
For the entire collection see [Zbl 1238.68016].

MSC:
68Q25 Analysis of algorithms and problem complexity
05C10 Planar graphs; geometric and topological aspects of graph theory
05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
05C85 Graph algorithms (graph-theoretic aspects)
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