Affiliation:
1. Department of Computer Science, ETH Zurich, Switzerland
Abstract
We introduce the abstract notion of a chain, which is a sequence of
n
points in the plane, ordered by
x
-coordinates, so that the edge between any two consecutive points is unavoidable as far as triangulations are concerned. A general theory of the structural properties of chains is developed, alongside a general understanding of their number of triangulations.
We also describe an intriguing new and concrete configuration, which we call the Koch chain due to its similarities to the Koch curve. A specific construction based on Koch chains is then shown to have Ω (9.08
n
) triangulations. This is a significant improvement over the previous and long-standing lower bound of Ω (8.65
n
) for the maximum number of triangulations of planar point sets.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
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