تقرير
Dispersive Vertex Guarding for Simple and Non-Simple Polygons
| العنوان: | Dispersive Vertex Guarding for Simple and Non-Simple Polygons |
|---|---|
| المؤلفون: | Fekete, Sándor P., Mitchell, Joseph S. B., Rieck, Christian, Scheffer, Christian, Schmidt, Christiane |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science |
| مصطلحات موضوعية: | Computer Science - Computational Geometry, F.2.2 |
| الوصف: | We study the Dispersive Art Gallery Problem with vertex guards: Given a polygon $\mathcal{P}$, with pairwise geodesic Euclidean vertex distance of at least $1$, and a rational number $\ell$; decide whether there is a set of vertex guards such that $\mathcal{P}$ is guarded, and the minimum geodesic Euclidean distance between any two guards (the so-called dispersion distance) is at least $\ell$. We show that it is NP-complete to decide whether a polygon with holes has a set of vertex guards with dispersion distance $2$. On the other hand, we provide an algorithm that places vertex guards in simple polygons at dispersion distance at least $2$. This result is tight, as there are simple polygons in which any vertex guard set has a dispersion distance of at most $2$. Comment: 13 pages, 14 figures; accepted at the 36th Canadian Conference on Computational Geometry (CCCG 2024) |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2406.05861 |
| رقم الأكسشن: | edsarx.2406.05861 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |