an:06046507
Zbl 1352.68119
van Bevern, Ren??; Hartung, Sepp; Kammer, Frank; Niedermeier, Rolf; Weller, Mathias
Linear-time computation of a linear problem kernel for dominating set on planar graphs
EN
Marx, D??niel (ed.) et al., Parameterized and exact computation. 6th international symposium, IPEC 2011, Saarbr??cken, Germany, September 6--8, 2011. Revised selected papers. Berlin: Springer (ISBN 978-3-642-28049-8/pbk). Lecture Notes in Computer Science 7112, 194-206 (2012).
2012
a
68Q25 05C10 05C69 05C85
Summary: We present a linear-time kernelization algorithm that transforms a given planar graph \(G\) with domination number \(\gamma (G)\) into a planar graph \(G^{\prime}\) of size \(O(\gamma (G))\) with \(\gamma (G) = \gamma (G^{\prime})\). In addition, a minimum dominating set for \(G\) can be inferred from a minimum dominating set for \(G^{\prime}\). In terms of parameterized algorithmics, this implies a linear-size problem kernel for the NP-hard Dominating Set problem on planar graphs, where the kernelization takes linear time. This improves on previous kernelization algorithms that provide linear-size kernels in cubic time.
For the entire collection see [Zbl 1238.68016].