Computation of Centroidal Voronoi Tessellations in High Dimensional Spaces

Owing to the natural interpretation and various desirable mathematical properties, centroidal Voronoi tessellations (CVTs) have found a wide range of applications correspondingly vast development in their literature. However, computation CVTs higher dimensional spaces remains difficult. In this paper, we exploit non-uniqueness for computation. We construct such high by decomposing into one-dimensional spaces. then prove that tessellation is under condition independence among densities over 1-D Various numerical evaluations backup theoretical result through low energy grid-like tessellations, are obtained with minimal time. also compare proposed decomposition method popular MacQueen’s probabilistic method.