  Dealing with the NP-complete Dominating Set problem on undirected graphs, we
demonstrate the power of data reduction by preprocessing from a theoretical as
well as a practical side. In particular, we prove that Dominating Set
restricted to planar graphs has a so-called problem kernel of linear size,
achieved by two simple and easy to implement reduction rules. Moreover, having
implemented our reduction rules, first experiments indicate the impressive
practical potential of these rules. Thus, this work seems to open up a new and
prospective way how to cope with one of the most important problems in graph
theory and combinatorial optimization.
