Removing Popular Faces in Curve Arrangements

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...

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Bibliographic Details
Main Authors de Nooijer, Phoebe, Terziadis, Soeren, Weinberger, Alexandra, Masárová, Zuzana, Mchedlidze, Tamara, Löffler, Maarten, Rote, Günter
Format Journal Article
LanguageEnglish
Published 24.02.2022
Subjects
Computer Science - Computational Geometry
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Summary: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.
DOI:10.48550/arxiv.2202.12175