Higher-dimensional voronoi diagrams in linear expected time

Deletion in abstract Voronoi diagrams in expected linear time

Updating an abstract Voronoi diagram in linear time, after deletion of one site, has been an open problem for a long time. Similarly for various concrete Voronoi diagrams of generalized sites, other than points. In this paper we present a simple, expected linear-time algorithm to update an abstract Voronoi diagram after deletion. We introduce the concept of a Voronoi-like diagram, a relaxed ver...

Voronoi Diagrams in Linear Time ∗

Voronoi diagrams are a well-studied data structure of proximity information, and although most cases require Ω(n log n) construction time, it is interesting and useful to develop linear-time algorithms for certain Voronoi diagrams. We develop a linear-time algorithm for abstract Voronoi diagrams in a domain where each site has a unique face and no pair of bisectors intersect outside the domain....

An Expected Linear 3 - Dimensional Voronoi

Higher Order City Voronoi Diagrams

We investigate higher-order Voronoi diagrams in the city metric. This metric is induced by quickest paths in the L1 metric in the presence of an accelerating transportation network of axis-parallel line segments. For the structural complexity of k-order city Voronoi diagrams of n point sites, we show an upper bound of O(k(n − k) + kc) and a lower bound of Ω(n+ kc), where c is the complexity of ...

Forest-Like Abstract Voronoi Diagrams in Linear Time

Voronoi diagrams are a well-studied data structure of proximity information, and although most cases require Ω(n log n) construction time, it is interesting and useful to develop linear-time algorithms for certain Voronoi diagrams. For example, the Voronoi diagram of points in convex position, and the medial axis and constrained Voronoi diagram of a simple polygon are a tree or forest structure...