The main purpose of this paper is to exposit two very different, but very general, motivational schemes in the art of parameterization and a concrete example connecting them. We introduce a dynamic version of the Dominating Set problem and prove that it is fixed-parameter tractable (FPT). The problem is motivated by settings where problem instances evolve. It also arises in the quest to improve a natural greedy heuristic for the Dominating Set problem.

This short paper highlights some open problems related to the work of Jianer Chen in the area of parameterized/multivariate algorithmics.