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Erschienen in:
2012 | OriginalPaper | Buchkapitel
Linear-Time Computation of a Linear Problem Kernel for Dominating Set on Planar Graphs
verfasst von : René van Bevern, Sepp Hartung, Frank Kammer, Rolf Niedermeier, Mathias Weller
Erschienen in: Parameterized and Exact Computation
Verlag: Springer Berlin Heidelberg
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We present a linear-time kernelization algorithm that transforms a given planar graph
G
with domination number
γ
(
G
) into a planar graph
G
′ of size
O
(
γ
(
G
)) with
γ
(
G
) =
γ
(
G
′). In addition, a minimum dominating set for
G
can be inferred from a minimum dominating set for
G
′. 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.