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Summary: Computing the Largest Empty
Convex Subset of a Set of Points
David Avis
David Rappaport
McGill University
805 Sherbrooke Street West
Montreal, Quebec. H3A 2K6
Abstract
A largest empty convex subset of a flnite set of
points, S, is a maximum cardlnality subset of S, that
(1) are the vertices of a convex polygon, and (2) con-
tam no other points of S lnterlor to their convex hull.
An O(n') time and 0( ne) space algorithm is intro-
duced to And such subsets, where n represents the
cardinality of S. Empirical results are obtalned and
presented. In particular, a configuration of 20 points
is obtained with no empty convex hexagon, giving a
partial answer to a question of Paul Erdijs.
1. Introduction
Esther Klein showed that from any flve points
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