Consider the problem of partitioning an arbitrary metric space into pieces of diameter at most ∆, such every pair of points is separated with relatively low probability. We propose a rate-based algorithm inspired by multiplicatively-weighted Voronoi diagrams, and prove it has optimal trade-offs. This also gives us another algorithm for the 0-extension problem.

Professor Gunzburger is a preeminent computational and applied mathematician of our times with numerous groundbreaking and seminal works. He is a pioneer, leading researcher and instigator of several important research directions that include: theory and applications of centroidal Voronoi tessellations, analysis and computational methods for the control of fluids, mathematical modeling and nume...

we introduce a new feature vector for shapebased image retrieval. This feature depends on two factors: the centroidal distances of shape and correlation between neighboring edges, hence this scheme is not only effective and robust to translation, scaling, and rotation, but also has the qualities of expressing the spatial information of edges. Experimental results show the proposed method has cl...

A centroidal Voronoi tessellation is a Voronoi tessellation whose generating points are the centroids (centers of mass) of the corresponding Voronoi regions. We give some applications of such tessellations to problems in image compression, quadrature, finite difference methods, distribution of resources, cellular biology, statistics, and the territorial behavior of animals. We discuss methods f...

The Centroidal Voronoi Diagram (CVD) is a very versatile structure, well studied in Computational Geometry. It is used as the basis for a number of applications. This paper presents a deterministic algorithm, entirely computed using graphics hardware resources, based on Lloyd’s Method for computing CVDs. While the computation of the ordinary Voronoi diagram on GPU is a well explored topic, its ...

In this paper, we introduce a novel definition of the anisotropic centroidal Voronoi tessellation (ACVT) corresponding to a given Riemann metric tensor. A directional distance function is used in the definition to simplify the computation. We provide algorithms to approximate the ACVT using the Lloyd iteration and the construction of anisotropic Delaunay triangulation under the given Riemannian...

We consider the problem of optimal coverage with areaconstraints in a mobile multi-agent system. For a planar environment with an associated density function, this problem is equivalent to dividing the environment into optimal subregions such that each agent is responsible for the coverage of its own region. In this paper, we design a continuous-time distributed policy which allows a team of ag...