 
Summary: 1 date: July 23, 2007 file: aurexu2
OPTIMAL TRIANGULATIONS
Introduction. A triangulation of a given set S
of n points in the Euclidean plane is a maxi
mal set of noncrossing straight line segments
(called edges) which have both endpoints in S.
As an equivalent definition, a triangulation of S
is a partition of the convex hull of S into tri
angular faces whose vertex set is exactly S. Tri
angulations are a versatile means for partition
ing and/or connecting geometric objects. They
are used in many areas of engineering and sci
entific applications such as finite element meth
ods, approximation theory, numerical computa
tion, computeraided geometric design, compu
tational geometry, etc. Many of their applica
tions are surveyed in [8], [11], [20], [61].
A triangulation of S can be viewed as a pla
nar graph whose vertex set is S and whose edge
set is a subset of S × S. The Eulerian relation
