The Voronoi diagram of n distinct generating points divides the plane into cells, each of which consists of points most close to one particular generator. After introducing ‘limit Voronoi diagrams’ by analyzing diagrams of moving and coinciding points, we define compactifications of the configuration space of n distinct, labeled points. On elements of these compactifications we define Voronoi d...

Improving on the Voronoi cell based techniques of [28, 24], we give a Las Vegas Õ(2n) expected time and space algorithm for CVPP (the preprocessing version of the Closest Vector Problem, CVP). This improves on the Õ(4n) deterministic runtime of the Micciancio Voulgaris algorithm [24] (henceforth MV) for CVPP 1 at the cost of a polynomial amount of randomness (which only affects runtime, not cor...

In this paper, we propose an approximate "fuzzy Voronoi" diagram (FVD)for fuzzy numbers of dimension two (FNDT) by designing an extension of crisp Voronoi diagram for fuzzy numbers. The fuzzy Voronoi sites are defined as fuzzy numbers of dimension two. In this approach, the fuzzy numbers have a convex continuous differentiable shape. The proposed algorithm has two stages: in the first stage we ...

Voronoi diagram on the earth surface is a powerful tool to study spatial proximity at continental or global scale. However, its computation remains challenging because geospatial features have complex shapes. This paper presents a raster-based algorithm to generate Voronoi diagrams on earth's surface. The algorithm approximates the exact point-to-point geographical distances using the cell-to-c...

The Voronoi regions of a block code govern many aspects of the code’s performance on a Gaussian channel, and they are fundamental instruments in, for example, error probability analysis and soft decision decoding. This paper presents an efficient method to find the boundaries of the Voronoi regions for an arbitrary binary linear block code. Two theoretical results together lead to the Voronoi r...

Voronoi diagrams are fundamental geometric structures that have been both deeply and widely investigated since their inception in disguise by René Descartes for analyzing the gravitational influence of stars, in the 17 century. Voronoi diagrams find countless applications in science and engineering beyond graphics as attested by the long representative, and yet non-exhaustive, list of applicati...

In a paper that considered arithmetic precision as a limited resource in the design and analysis of algorithms, Liotta, Preparata and Tamassia defined an “implicit Voronoi diagram” supporting logarithmictime proximity queries using predicates of twice the precision of the input and query coordinates. They reported, however, that computing this diagram uses five times the input precision. We def...

We present a real-time algorithm for computing the Voronoi diagram of planar freeform piecewise-spiral curves. The efficiency and robustness of our algorithm is based on a simple topological structure of Voronoi cells for spirals. Using a Möbius transformation, we provide an efficient search for maximal disks. The correct topology of Voronoi diagram is computed by sampling maximal disks systema...

We consider stationary Poisson-Voronoi tessellations (PVT) in the Euclidean plane and study properties of Voronoi tessellations induced by linear Poisson processes on the edges of the PVT. We are especially interested in simulation algorithms for the typical cell. Two different simulation algorithms are introduced. The first algorithm directly simulates the typical cell whereas the second algor...

This paper applies the randomized incremental construction (RIC) framework to computing the Hausdorff Voronoi diagram of a family of k clusters of points in the plane. The total number of points is n. The diagram is a generalization of Voronoi diagrams based on the Hausdorff distance function. The combinatorial complexity of the Hausdorff Voronoi diagram is O(n + m), where m is the total number...