Simpler linear-time kernelization for planar dominating set

Authors:
Torben Hagerup
Affiliations:
Institut für Informatik, Universität Augsburg, Augsburg, Germany
Venue:
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Year:
2011

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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.