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Summary: Small Weak Epsilon Nets
Boris Aronov
Franz Aurenhammer
Ferran Hurtado
Stefan Langerman§
David Rappaport¶
Shakhar Smorodinsky Carlos Seara
1 Introduction
Let P be a set of n points in R2
. A point q (not
necessarily in P) is called a centerpoint of P if each
closed halfplane containing q contains at least n
3
points of P. Note that, equivalently, any convex
set that contains more than 2
3 n points of P also
has to contain q. It is a well known fact that a
centerpoint always exists and the constant 2
3 is the
best possible (see, e.g., [6] for more details). Can
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