Ranking Unit Squares with Few Visibilities

Details Ranking Unit Squares with Few Visibilities Ranking Unit Squares with Few Visibilities

2008-07-14

arxiv.org/abs/0807.2178v1

Computer Science

Computational Geometry

4 pages, 2 EPS-figures

Scientific paper

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.

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