We describe a linear-time algorithm that inputs a planar graph
and outputs a planar graph of size
) and with domination number
is the domination number of
, i.e., the size of a smallest dominating set in
. 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.