  A face in a curve arrangement is called popular if it is bounded by the same
curve multiple times. Motivated by the automatic generation of curved nonogram
puzzles, we investigate possibilities to eliminate the popular faces in an
arrangement by inserting a single additional curve. This turns out to be
NP-hard; however, it becomes tractable when the number of popular faces is
small: We present a probabilistic FPT-approach in the number of popular faces.
