An algorithm to compute CVTs for finitely generated Cantor distributions

Centroidal Voronoi tessellations (CVTs) are Voronoi tessellations of a region such that the generating points of the tessellations are also the centroids of the corresponding Voronoi regions with respect to a given probability measure. CVT is a fundamental notion that has a wide spectrum of applications in computational science and engineering. In this paper, an algorithm is given to obtain the CVTs with n-generators to level m, for any positive integers m and n, of any Cantor set generated by a pair of self-similar mappings given by S1(x) = r1x and S2(x) = r2x+(1−r2) for x ∈ R, where r1, r2 > 0 and r1+r2 < 1, with respect to any probability distribution P such that P = p1P ◦ S−1 1 + p2P ◦ S−12, where p1, p2 > 0 and p1 + p2 = 1.