  In graph modification problems, one is given a graph G and the goal is to
apply a minimum number of modification operations (such as edge deletions) to G
such that the resulting graph fulfills a certain property. For example, the
Cluster Deletion problem asks to delete as few edges as possible such that the
resulting graph is a disjoint union of cliques. Graph modification problems
appear in numerous applications, including the analysis of biological and
social networks. Typically, graph modification problems are NP-hard, making
them natural candidates for parameterized complexity studies. We discuss
several fruitful interactions between the development of fixed-parameter
algorithms and the design of heuristics for graph modification problems,
featuring quite different aspects of mutual benefits.
