Removing Popular Faces in Curve Arrangements - de Nooijer, Phoebe; Terziadis, Soeren; Weinberger, Alexandra; Masárová, Zuzana; Mchedlidze, Tamara; Löffler, Maarten; Rote, Günter (Journal of Graph Algorithms and Applications, 2024)
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 randomized FPT-time algorithm where the parameter is the number of popular faces.