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.

翻译：曲线排列中的面若被同一条曲线多次包围，则称为流行面。受曲线式非洛谜题自动生成的启发，我们研究了通过插入单条额外曲线来消除排列中流行面的可能性。这一问题被证明是NP难的；然而，当流行面数量较小时，问题变得可解：我们提出了一种基于流行面数量的概率FPT方法。