Triangulations (tilings) and certain block triangular matrices

For a convex polygonP withn sides, a ‘partitioning’ ofP inton−2 nonoverlapping triangles each of whose vertices is a vertex ofP is called a triangulation or tiling, and each triangle is a tile. Each tile has a given cost associated with it which may differ one from another. This paper considers the problem of finding a tiling ofP such that the sum of the costs of the tiles used is a minimum, and explores the curiosity that (an abstract formulation of) it can be cast as a linear program. Further the special structure of the linear program permits a recursive O(n3) algorithm.