  We describe how to approximate, in quasi-polynomial time, the largest
independent set of polygons, in a given set of polygons. Our algorithm works by
extending the result of Adamaszek and Wiese \cite{aw-asmwi-13, aw-qmwis-14} to
polygons of arbitrary complexity. Surprisingly, the algorithm also works or
computing the largest subset of the given set of polygons that has some
sparsity condition. For example, we show that one can approximate the largest
subset of polygons, such that the intersection graph of the subset does not
contain a cycle of length $4$ (i.e., $K_{2,2}$).
