[CLR90] Consider the simplified optimal polygon-triangulation problem. This problem can be defined as follows. Given a simple polygon, break the polygon into a set of triangles by connecting nodes of the polygon with chords. This process is illustrated in Figure 12.10. The cost of constructing a triangle with nodes vi, vj, and vk is defined by a function f (vi, vj, vk). For this problem, let the cost be the total length of the edges of the triangle (using Euclidean distance). The optimal polygon-triangulation problem breaks up a polygon into a set of triangles such that the total length of each triangle (the sum of the individual lengths) is minimized. Give a DP formulation for this problem. Classify it into one of the four categories and derive a parallel formulation for p processing elements. Determine its parallel run time, speedup, and isoefficiency function.
