Removing Popular Faces in Curve Arrangements
Phoebe de Nooijer, Soeren Terziadis, Alexandra Weinberger, Zuzana, Mas\'arov\'a, Tamara Mchedlidze, Maarten L\"offler, G\"unter Rote
TL;DR
This paper explores the problem of removing popular faces in curve arrangements, motivated by puzzle generation, and proposes a probabilistic fixed-parameter tractable approach for small numbers of such faces.
Contribution
It introduces the first fixed-parameter tractable method for eliminating popular faces in arrangements, addressing an NP-hard problem with a probabilistic algorithm.
Findings
NP-hardness of removing popular faces
Probabilistic FPT-approach for small numbers of popular faces
Effective in generating curved nonogram puzzles
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 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.
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Taxonomy
TopicsDigital Image Processing Techniques · Computational Geometry and Mesh Generation · Image Processing and 3D Reconstruction