  Representing a polygon using a set of simple shapes has numerous applications
in different use-case scenarios. We consider the problem of covering the
interior of a rectilinear polygon with holes by a set of area-weighted,
axis-aligned rectangles such that the total weight of the rectangles in the
cover is minimized. Already the unit-weight case is known to be NP-hard and the
general problem has, to the best of our knowledge, not been studied
experimentally before.
  We show a new basic property of optimal solutions of the weighted problem.
This allows us to speed up existing algorithms for the unit-weight case, obtain
an improved ILP formulation for both the weighted and unweighted problem, and
develop several approximation algorithms and heuristics for the weighted case.
  All our algorithms are evaluated in a large experimental study on 186 837
polygons combined with six cost functions, which provides evidence that our
algorithms are both fast and yield close-to-optimal solutions in practice.
