Removing Popular Faces in Curve Arrangements

02/24/2022

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by   Phoebe de Nooijer, et al.

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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 popular faces in an arrangement by inserting a single additional curve. This turns out to be already NP-hard; however, we present a probabilistic FPT-approach in the number of such faces.