Two-Fold Circle-Covering of the Plane under Congruent Voronoi Polygon Conditions
Metric Geometry
2016-04-21 v2
Abstract
The -coverage problem is to find the minimum number of disks such that each point in a given plane is covered by at least disks. Under unit disk condition, when =1, this problem has been solved by Kershner in 1939. However, when , it becomes extremely difficult. One tried to tackle this problem with different restrictions. In this paper, we restrict ourself to congruent Voronoi polygon, and prove the minimum density of the two-coverage with such a restriction. Our proof is simpler and more rigorous than that given recently by Yun et al.
Keywords
Cite
@article{arxiv.1410.1372,
title = {Two-Fold Circle-Covering of the Plane under Congruent Voronoi Polygon Conditions},
author = {Jingchao Chen},
journal= {arXiv preprint arXiv:1410.1372},
year = {2016}
}
Comments
8 pages, 6 figures