A New Subgraph of Minimum Weight Triangulations

In this paper, two sufficient conditions for identifying a subgraph of minimum weight triangulation of a planar point set are presented. These conditions are based on local geometric properties of an edge to be identified. Unlike the previous known sufficient conditions for identifying subgraphs, such as Keil’s β-skeleton and Yang and Xu’s double circles, The local geometric requirement in our conditions is not necessary symmetric with respect to the edge to be identified. The identified subgraph is different from all the known subgraphs including the newly discovered subgraph: so-called the intersection of local-optimal triangulations by Dickerson et al. An O(n3) time algorithm for finding this subgraph from a set of n points is presented.