相关论文: On the Expected Complexity of Voronoi Diagrams on …

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…

While the standard unweighted Voronoi diagram in the plane has linear worst-case complexity, many of its natural generalizations do not. This paper considers two such previously studied generalizations, namely multiplicative and semi…

We study algorithms and combinatorial complexity bounds for \emph{stable-matching Voronoi diagrams}, where a set, $S$, of $n$ point sites in the plane determines a stable matching between the points in $\mathbb{R}^2$ and the sites in $S$…

Let $P$ be a simple polygon with $n$ vertices. For any two points in $P$, the geodesic distance between them is the length of the shortest path that connects them among all paths contained in $P$. Given a set $S$ of $m$ sites being a subset…

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…

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…

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…

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…

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.…

The Voronoi diagram is a geometric object which is widely used in many areas. Recently it has been shown that under mild conditions Voronoi diagrams have a certain continuity property: small perturbations of the sites yield small…

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 give lower bounds for the combinatorial complexity of the Voronoi diagram of polygonal curves under the discrete Frechet distance. We show that the Voronoi diagram of n curves in R^d with k vertices each, has complexity Omega(n^{dk}) for…

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…

We introduce the inverse Voronoi diagram problem in graphs: given a graph $G$ with positive edge-lengths and a collection $\mathbb{U}$ of subsets of vertices of $V(G)$, decide whether $\mathbb{U}$ is a Voronoi diagram in $G$ with respect to…

The geodesic Voronoi diagram of m point sites inside a simple polygon of n vertices is a subdivision of the polygon into m cells, one to each site, such that all points in a cell share the same nearest site under the geodesic distance. The…

We present an algorithm to compute the geodesic $L_1$ farthest-point Voronoi diagram of $m$ point sites in the presence of $n$ rectangular obstacles in the plane. It takes $O(nm+n \log n + m\log m)$ construction time using $O(nm)$ space.…

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…

Minimization diagrams encompass a large class of diagrams of interest in the literature, such as generalized Voronoi diagrams. We develop an abstract perturbation theory and perform a sensitivity analysis for functions depending on sets…