Given two point sets in the plane, we study the minimization of the bottleneck distance between a point set B and an equallysized subset of a point set A under translations. We relate this problem to a Voronoi-type diagram and derive polynomial bounds for its complexity that are optimal in the size of A. We devise efficient algorithms for the construction of such a diagram and its lexicographic...

A protein consists of one or more chains where each chain is a linear sequence of amino acids bonded by peptide bonds. Chains in a protein interact with each other and the interaction is known to be one of the most fundamental factors which determine important physiological phenomena in the body. Hence, biologists have been investigating protein interactions since the early days of life science...

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...

We introduce a new approach to approximate generalized 3D Voronoi diagrams for different site shapes (points, spheres, segments, lines, polyhedra, etc) and different distance functions (Euclidean metrics, convex distance functions, etc). The approach is based on an octree data structure denoted Voronoi-Octree (VO) that encodes the information required to generate a polyhedral approximation of t...

The Network Voronoi diagram and its variants have been extensively used in the context of numerous applications in road networks, particularly to efficiently evaluate various spatial proximity queries such as k nearest neighbor (kNN), reverse kNN, and closest pair. Although the existing approaches successfully utilize the network Voronoi diagram as a way to partition the space for their specifi...

Despite of many important applications in various disciplines from sciences and engineering, Voronoi diagram for spheres in a 3-dimensional Euclidean distance has not been studied as much as it deserves. In this paper, we present an edge-tracing algorithm to compute the Euclidean Voronoi diagram of 3-dimensional spheres in O( ) in the worst-case, where is the number of edges of Voronoi diagram ...

We present the first time-optimal algorithm for computing the Voronoi Diagram under the metric induced by a transportation network with discrete entry and exit points. For input with n sites, k stations, and e transportation lines, the algorithm computes the Voronoi Diagram in O ( (n+ k) log(n+ k) + e ) time.

Traditional polygon-arc-node topology is standard in vector GIS, but it has its limitations. This is particularly evident at the digitizing stage, which often appears excessively complex and tedious, Other methods, however, are capable of maintaining some forms of topology “automatically”, and this paper is an overview of three approaches based on the Voronoi diagram (or the equivalent Delaunay...

We present an algorithm for computing exact shortest paths, and consequently distance functions, from a generalized source (point, segment, polygonal chain or polygonal region) on a possibly non-convex triangulated polyhedral surface. The algorithm is generalized to the case when a set of generalized sites is considered, providing their distance field that implicitly represents the Voronoi diag...

Given a set P of n point sites in the plane, the city Voronoi diagram subdivides the plane into the Voronoi regions of the sites, with respect to the city metric. This metric is induced by quickest paths according to the Manhattan metric and an accelerating transportation network that consists of c non-intersecting axis-parallel line segments. We describe an algorithm that constructs the city V...