SIAM Journal on Computing
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Order-k Voronoi Diagrams, k-Sections, and k-Sets
JCDCG '98 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
The Clarkson–Shor Technique Revisited and Extended
Combinatorics, Probability and Computing
Proceedings of the twenty-second annual symposium on Computational geometry
Generalized Higher-Order Voronoi Diagrams on Polyhedral Surfaces
ISVD '07 Proceedings of the 4th International Symposium on Voronoi Diagrams in Science and Engineering
On k-Nearest Neighbor Voronoi Diagrams in the Plane
IEEE Transactions on Computers
Discrete construction of order-k voronoi diagram
ICICA'10 Proceedings of the First international conference on Information computing and applications
Discrete construction of power network voronoi diagram
ICICA'11 Proceedings of the Second international conference on Information Computing and Applications
The complexity of geodesic Voronoi diagrams on triangulated 2-manifold surfaces
Information Processing Letters
| Hi-index | 0.89 |
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(k^2n^2+k^2m+knm), which is asymptotically tight in the worst case.