Triangulations intersect nicely

O. Aichholzer, F. Aurenhammer, G. Rote, and M. Taschwer


We prove that two different triangulations of the same planar point set always intersect in a systematic manner, concerning both their edges and their triangles. As a consequence, improved lower bounds on the weight of a triangulation are obtained by solving an assignment problem. The new bounds cover the previously known bounds and can be computed in polynomial time. As a by-product, an easy-to-recognize class of point sets is exhibited where the minimum-weight triangulation coincides with the greedy triangulation.

Reference: O. Aichholzer, F. Aurenhammer, G. Rote, and M. Taschwer. Triangulations intersect nicely. In Proc. $11^{th}$ Ann. ACM Symp. Computational Geometry, pages 220-229, Vancouver, Canada, 1995.