  The theoretical notions of graph classes with bounded expansion and that are
nowhere dense are meant to capture structural sparsity of real world networks
that can be used to design efficient algorithms. In the area of sparse graphs,
the flagship problems are Dominating Set and its generalization r-Dominating
Set. They have been precursors for model checking of first order logic on
sparse graph classes. On class of graphs of bounded expansions the r-Dominating
Set problem admits a constant factor approximation, a fixed-parameter
algorithm, and an efficient preprocessing routine: the so-called linear kernel.
This should be put in constrast with general graphs where Dominating Set is
APX-hard and W[2]-complete. In this paper we provide an experimental evaluation
of kernelization algorithm for Dominating Set in sparse graph classes and
compare it with previous approaches designed to the preprocessing for
Dominating Set.
