Ranking Unit Squares with Few Visibilities
Computational Geometry
2008-07-15 v1 Data Structures and Algorithms
Abstract
Given a set of n unit squares in the plane, the goal is to rank them in space in such a way that only few squares see each other vertically. We prove that ranking the squares according to the lexicographic order of their centers results in at most 3n-7 pairwise visibilities for n at least 4. We also show that this bound is best possible, by exhibiting a set of n squares with at least 3n-7 pairwise visibilities under any ranking.
Keywords
Cite
@article{arxiv.0807.2178,
title = {Ranking Unit Squares with Few Visibilities},
author = {Bernd Gärtner},
journal= {arXiv preprint arXiv:0807.2178},
year = {2008}
}
Comments
4 pages, 2 EPS-figures