Optimal point location in a monotone subdivision
SIAM Journal on Computing
A fast planar partition algorithm, I
Journal of Symbolic Computation
An optimal algorithm for the intersection radius of a set of convex polygons
Journal of Algorithms
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
Smallest Color-Spanning Objects
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
A Coarse Grained Parallel Algorithm for Hausdorff Voronoi Diagrams
ICPP '06 Proceedings of the 2006 International Conference on Parallel Processing
Farthest line segment Voronoi diagrams
Information Processing Letters
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
The geodesic farthest-site Voronoi diagram in a polygonal domain with holes
Proceedings of the twenty-fifth annual symposium on Computational geometry
Farthest voronoi diagrams under travel time metrics
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
Tight bound for farthest-color voronoi diagrams of line segments
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
Higher order city voronoi diagrams
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
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Given a family of k disjoint connected polygonal sites in general position and of total complexity n, we consider the farthest-site Voronoi diagram of these sites, where the distance to a site is the distance to a closest point on it. We show that the complexity of this diagram is O(n), and give an O(nlog^3n) time algorithm to compute it. We also prove a number of structural properties of this diagram. In particular, a Voronoi region may consist of k-1 connected components, but if one component is bounded, then it is equal to the entire region.