Abstract
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 \(\textsf{NP}\)-hard; however, it becomes tractable when the number of popular faces is small: We present a probabilistic \(\textsf{FPT}\)-approach in the number of popular faces.
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Acknowledgements
This work was initiated at the 16th European Research Week on Geometric Graphs in Strobl in 2019. A.W. is supported by the Austrian Science Fund (FWF): W1230. S.T. has been funded by the Vienna Science and Technology Fund (WWTF) [10.47379/ICT19035]. A preliminary version of this work has been presented at the 38th European Workshop on Computational Geometry (EuroCG 2022) in Perugia [9]. A full version of this paper, which includes appendices but is otherwise identical, is available as a technical report [10].
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de Nooijer, P. et al. (2023). Removing Popular Faces in Curve Arrangements. In: Bekos, M.A., Chimani, M. (eds) Graph Drawing and Network Visualization. GD 2023. Lecture Notes in Computer Science, vol 14466. Springer, Cham. https://doi.org/10.1007/978-3-031-49275-4_2
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DOI: https://doi.org/10.1007/978-3-031-49275-4_2
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