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
Published inarXiv.org
Main Authors de Nooijer, Phoebe, Terziadis, Soeren, Weinberger, Alexandra, Masárová, Zuzana, Mchedlidze, Tamara, Löffler, Maarten, Rote, Günter
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 30.08.2023
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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.
ISSN:2331-8422