 
Summary: 1 date: November 15, 1999 le: optriang
OPTIMAL TRIANGULATIONS
Introduction. A triangulation of a given set S
of n points in the Euclidean plane is a maximal
set of noncrossing line segments (called edges)
which have both endpoints in S. Any triangu
lation of S partitions the interior of the con
vex hull of S into triangles. Triangulations are
used in many areas of engineering and scien
tic applications such as nite element meth
ods, approximation theory, numerical computa
tion, computeraided geometric design, compu
tational geometry, etc. Many applications are
surveyed in [5], [8], [17], [56].
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
for planar graphs implies that the number e(S)
of edges, and the number t(S) of triangles, do
not depend on the way of triangulating S. In
