English

Efficient covering of convex domains by congruent discs

Computational Geometry 2021-08-03 v1 Combinatorics

Abstract

In this paper, we consider the problem of covering a plane region with unit discs. We present an improved upper bound and the first nontrivial lower bound on the number of discs needed for such a covering, depending on the area and perimeter of the region. We provide algorithms for efficient covering of convex polygonal regions using unit discs. We show that the computational complexity of the algorithms is pseudo-polynomial in the size of the input and the output. We also show that these algorithms provide a constant factor approximation of the optimal covering of the region.

Keywords

Cite

@article{arxiv.2108.00707,
  title  = {Efficient covering of convex domains by congruent discs},
  author = {Shai Gul and Reuven Cohen and Simi Haber},
  journal= {arXiv preprint arXiv:2108.00707},
  year   = {2021}
}