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Higher-order Voronoi diagrams on triangulated surfaces
Cabello, Sergio ; Fort, Marta ; Sellarès, J. Antoni
We study the complexity of higher-order Voronoi diagrams on triangulated surfaces under the geodesic distance, when the sites may be polygonal regions of constant complexity. More precisely, we show ...that in a surface defined by ▫$n$▫ triangles the sum of the combinatorial complexity of the order-▫$j$▫ Voronoi diagrams, for ▫$j = 1, \dots, k$, is $O(k^2 n^2 + k^2 m + knm)$▫, which is asymptotically tight in the worst case.
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