On extreme points of the PPT Polytope

The polytope of pointed pseudo triangulations was described in [RSS01]. This polytope is a combinatorial tool to observe all possible pseudo triangulations of a certain point set. Each point of the polytope refers to one possible pseudo triangulation of the point set. To polytope vertices are connected by an edge if their pseudo triangulations just differ in one edge-flip. Once we have a PPT-polytope, a question is, if we could find pseudo triangulations with special properties by solving a linear program over the polytope. There are two possible ways we investigated this area. In the first part we take a canonical form of an objective function and look at the properties of the pseudo triangulations which are optimal for that function. In the second part we do it vice versa. Here our focus lies on a special triangulation and we want to have an objective function for the PPT polytope. The point set is given by n points P = p1, . . . , pn Each point pi has the coordinates (xi, yi). A pseudo triangulations consist also of edges. The edges are denoted by E = {(i, j)|0 < i < j ≤ n}. A convex point set is numbered in clockwise order. Sometimes the determinant