  We study the following combinatorial problem. Given a planar graph $G=(V,E)$
and a set of simple cycles $\mathcal C$ in $G$, find a planar embedding
$\mathcal E$ of $G$ such that the number of cycles in $\mathcal C$ that bound a
face in $\mathcal E$ is maximized. We establish a tight border of tractability
for this problem in biconnected planar graphs by giving conditions under which
the problem is NP-hard and showing that relaxing any of these conditions makes
the problem polynomial-time solvable. Moreover, we give a $2$-approximation
algorithm for series-parallel graphs and a $(4+\varepsilon)$-approximation for
biconnected planar graphs.
