English

Exact VC-dimension for $L_1$-visibility of points in simple polygons

Computational Geometry 2017-05-05 v1

Abstract

The VC-dimension plays an important role for the algorithmic problem of guarding art galleries efficiently. We prove that inside a simple polygon at most 55 points can be shattered by L1L_1-visibility polygons and give an example where 5 points are shattered. The VC-dimension is exactly 55. The proof idea for the upper bound is different from previous approaches. Keywords: Art gallery, VC-dimension, L1L_1-visibility, polygons

Keywords

Cite

@article{arxiv.1705.01723,
  title  = {Exact VC-dimension for $L_1$-visibility of points in simple polygons},
  author = {Elmar Langetepe and Simone Lehmann},
  journal= {arXiv preprint arXiv:1705.01723},
  year   = {2017}
}