# Geometric separator theorems and applications

```@article{Smith1998GeometricST,
title={Geometric separator theorems and applications},
author={Warren D. Smith and Nicholas C. Wormald},
journal={Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)},
year={1998},
pages={232-243}
}```
• Published 8 November 1998
• Mathematics
• Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)
We find a large number of "geometric separator theorems" such as: I: Given N disjoint isooriented squares in the plane, there exists a rectangle with /spl les/2N/3 squares inside, /spl les/2N/3 squares outside, and /spl les/(4+0(1))/spl radic/N partly in & out. II: There exists a rectangle that is crossed by the minimal spanning tree of N sites in the plane at /spl les/(4/spl middot/3/sup 1/4/+0(1))/spl radic/N points, having /spl les/2N/3 sites inside and outside. These theorems yield a large…
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