Art gallery theorems and algorithms
Art gallery theorems and algorithms
Lectures on Discrete Geometry
VC-Dimension of Exterior Visibility
IEEE Transactions on Pattern Analysis and Machine Intelligence
A new upper bound for the VC-dimension of visibility regions
Proceedings of the twenty-seventh annual symposium on Computational geometry
A new upper bound for the VC-dimension of visibility regions
Computational Geometry: Theory and Applications
| Hi-index | 0.00 |
We show that (A), 14 points on the boundary of a Jordan curve, and (B), 16 points in convex position encircled by a Jordan curve, cannot be shattered by interior visibility domains. This means that there always exists a subset of the given points, for which no point of the curve's interior domain sees all points of the subset and no point of its complement. As a consequence, we obtain a new result on guarding art galleries. If each point of the art gallery sees at least an r -th part of the gallery's boundary, then the art gallery can be covered by 13 ·C ·r logr guards placed on the boundary. Here, C is the constant from the *** -net theorem.