Constant-level greedy triangulations approximate the MWT well
The well-known greedy triangulation GT(S) of a finite point set S 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 GT(S) that does not rely on the length ordering of the edges. Rather, it provides a decomposition of GT(S) into levels, and the number of revels allows us to bound the total edge length of GT(S). In particular, we show less than or equal to 3.2(k+1) , where k is the number of levels and MWT(S) is the minimum-weight triangulation of S.
greedy triangulation minimum-weight triangulation