Related papers: Stable-Matching Voronoi Diagrams: Combinatorial Co…

Surprisingly, the order-$k$ Voronoi diagram of line segments had received no attention in the computational-geometry literature. It illustrates properties surprisingly different from its counterpart for points; for example, a single…

We study the amortized number of combinatorial changes (edge insertions and removals) needed to update the graph structure of the Voronoi diagram $\mathcal{V}(S)$ (and several variants thereof) of a set $S$ of $n$ sites in the plane as…

We present a simple wavefront-like approach for computing multiplicatively weighted Voronoi diagrams of points and straight-line segments in the Euclidean plane. If the input sites may be assumed to be randomly weighted points then the use…

We study the problem of computing the Voronoi diagram of a set of $n^2$ points with $O(\log n)$-bit coordinates in the Euclidean plane in a substantially sublinear in $n$ number of rounds in the congested clique model with $n$ nodes.…

We investigate the combinatorial complexity of geodesic Voronoi diagrams on polyhedral terrains using a probabilistic analysis. Aronov etal [ABT08] prove that, if one makes certain realistic input assumptions on the terrain, this complexity…

Voronoi diagrams are a fundamental geometric data structure for obtaining proximity relations. We consider collections of axis-aligned orthogonal polyhedra in two and three-dimensional space under the max-norm, which is a particularly…

Let $P$ be a planar set of $n$ sites in general position. For $k\in\{1,\dots,n-1\}$, the Voronoi diagram of order $k$ for $P$ is obtained by subdividing the plane into cells such that points in the same cell have the same set of nearest $k$…

Voronoi diagrams appear in many areas in science and technology and have numerous applications. They have been the subject of extensive investigation during the last decades. Roughly speaking, they are a certain decomposition of a given…

In this paper, we provide an $O(n \mathrm{polylog} n)$ bound on the expected complexity of the randomly weighted Voronoi diagram of a set of $n$ sites in the plane, where the sites can be either points, interior-disjoint convex sets, or…

Given a set of sites in a simple polygon, a geodesic Voronoi diagram of the sites partitions the polygon into regions based on distances to sites under the geodesic metric. We present algorithms for computing the geodesic nearest-point,…

The Hilbert metric is a distance function defined for points lying within a convex body. It generalizes the Cayley-Klein model of hyperbolic geometry to any convex set, and it has numerous applications in the analysis and processing of…

A Voronoi diagram is a basic geometric structure that partitions the space into regions associated with a given set of sites, such that all points in a region are closer to the corresponding site than to all other sites. While being…

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…

We study a general family of facility location problems defined on planar graphs and on the 2-dimensional plane. In these problems, a subset of $k$ objects has to be selected, satisfying certain packing (disjointness) and covering…

We describe a new algorithm for computing the Voronoi diagram of a set of $n$ points in constant-dimensional Euclidean space. The running time of our algorithm is $O(f \log n \log \Delta)$ where $f$ is the output complexity of the Voronoi…

We present an explicit and efficient construction of additively weighted Voronoi diagrams on planar graphs. Let $G$ be a planar graph with $n$ vertices and $b$ sites that lie on a constant number of faces. We show how to preprocess $G$ in…

Let $G=(V,E)$ be a graph with unit-length edges and nonnegative costs assigned to its vertices. Being given a list of pairwise different vertices $S=(s_1,s_2,\ldots,s_p)$, the {\em prioritized Voronoi diagram} of $G$ with respect to $S$ is…

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…

Let $S$ be a planar $n$-point set. A triangulation for $S$ is a maximal plane straight-line graph with vertex set $S$. The Voronoi diagram for $S$ is the subdivision of the plane into cells such that all points in a cell have the same…

Given a set of point sites in a simple polygon, the geodesic farthest-point Voronoi diagram partitions the polygon into cells, at most one cell per site, such that every point in a cell has the same farthest site with respect to the…