Abstract
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 levels allows us to bound the total edge length of GT(S). In particular, we show |GT(S)| ≤ 3 · 2k + 1|MWT(S)|, where k is the number of levels and MWT(S) is the minimum-weight triangulation of S.
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Aichholzer, O., Aurenhammer, F., Rote, G. et al. Constant-Level Greedy Triangulations Approximate the MWT Well. Journal of Combinatorial Optimization 2, 361–369 (1998). https://doi.org/10.1023/A:1009776619164
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DOI: https://doi.org/10.1023/A:1009776619164