Additively weighted Voronoi diagram and weighted Delaunay decomposition are a generalization of Voronoi diagram and Delaunay triangulation, respectively. They have received much attention due to their relevance in many domains see [1], [2], [3]. In particular, their interest in control theory has been recently shown in [4], [5] to solve inverse parametric linear/quadratic programming problem. This paper elaborates on the identification of suitable sites and weights of such particular partitions via two algorithms. It will be shown that these algorithms require solving a bi-linear programming problem