**O. Aichholzer, F. Aurenhammer, G. Rote, and Y.-F. Xu**

The well-known greedy triangulation of a finite point set is
obtained by inserting compatible edges in increasing length order, where an
edge is compatible if it does not cross previously inserted ones. Exploiting
the concept of so-called light edges, we introduce a definition of
that does not rely on the length ordering of the edges. Rather, it provides a
decomposition of into levels, and the number of levels allows us to
bound the total edge length of . In particular, we show
, where is the number of levels and is
the minimum-weight triangulation of .