Memoization method for storing of minimum-weight triangulation of a convex polygon

Abstract

This study presents a practical view of dynamic programming, specifically in the context of the application of finding optimal solutions for the polygon triangulation problem. The problem of the optimal triangulation of a polygon is considered to be a recursive substructure. The basic idea of the constructed method lies in finding an adequate method for the rapid generation of optimal triangulations and storing them in as small a memory space as possible. Our method is based on a memoization technique, and its emphasis is in storing the results of the calculated values and returning the cached result when the same values occur again. The significance of the method is in the generation of the optimal triangulation for a large number of n. All of the calculated weights in the triangulation process are stored and performed in the same table. The processing of the results and implementation of the method were carried out in the Java environment, and the experimental results were compared with the square matrix and Hurtado-Noy method.