Higher-order Voronoi diagrams on triangulated surfaces

Abstract

We study the complexity of higher-order Voronoi diagrams on triangulated surfaces under the geodesic distance, when the sites may be polygonal domains of constant complexity. More precisely, we show that on a surface defined by n triangles the sum of the combinatorial complexities of the order-j Voronoi diagrams of m sites, for j = 1, ..., k, is O (k2n2+ k2m + k n m), which is asymptotically tight in the worst case