Related papers: Cloud computing and hyperbolic Voronoi diagrams on…
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…
Based on Welzl's algorithm for smallest circles and spheres we develop a simple linear time algorithm for finding the smallest circle enclosing a point cloud on a sphere. The algorithm yields correct results as long as the point cloud is…
1-qubit quantum states form a space called the three-dimensional Bloch ball. To compute Holevo capacity, Voronoi diagrams in the Bloch ball with respect to the quantum divergence have been used as a powerful tool. These diagrams basically…
We present a general framework for computing two-dimensional Voronoi diagrams of different classes of sites under various distance functions. The framework is sufficiently general to support diagrams embedded on a family of two-dimensional…
In this article, we propose a numerical method to solve semi-discrete optimal transport problems for gigantic pointsets (108 points and more). By pushing the limits by several orders of magnitude, it opens the path to new applications in…
Distributed cloud networking enables the deployment of a wide range of services in the form of interconnected software functions instantiated over general purpose hardware at multiple cloud locations distributed throughout the network. We…
Cloud computing has become the backbone of the computing industry and offers subscription-based on-demand services. Through virtualization, which produces a virtual instance of a computer system running in an abstracted hardware layer, it…
In quantum information theory, a geometric approach, known as "quantum information geometry," has been considered as a powerful method. In this thesis, we give a computational geometric interpretation to the geometric structure of a quantum…
In this paper, we propose to compute Voronoi diagrams over mesh surfaces driven by an arbitrary geodesic distance solver, assuming that the input is a triangle mesh as well as a collection of sites $P=\{p_i\}_{i=1}^m$ on the surface. We…
We study Voronoi diagrams for distance functions that add together two convex functions, each taking as its argument the difference between Cartesian coordinates of two planar points. When the functions do not grow too quickly, then the…
This article provides numerical evidence that under volume constraint the ball is the set which maximizes the perimeter of the least-perimeter partition into cells with prescribed areas. We introduce a numerical maximization algorithm which…
We give linear-time quasiconvex programming algorithms for finding a Moebius transformation of a set of spheres in a unit ball or on the surface of a unit sphere that maximizes the minimum size of a transformed sphere. We can also use…
Cloud Computing holds the potential to eliminate the requirements for setting up of high-cost computing infrastructure for IT-based solutions and services that the industry uses. It promises to provide a flexible IT architecture, accessible…
Cloud Computing offers virtualized computing, storage, and networking resources, over the Internet, to organizations and individual users in a completely dynamic way. These cloud resources are cheaper, easier to manage, and more elastic…
Every robotic network cloud system can be seen as a graph with nodes as hardware with independent computational processing powers and edges as data transmissions between nodes. When assigning a task to a node we may change several values…
Computing offsets of curves on parametric surfaces is a fundamental yet challenging operation in computer aided design and manufacturing. Traditional analytical approaches suffer from time-consuming geodesic distance queries and complex…
We present an analytically explicit study of optimal discrete quantization on spherical geometries equipped with the geodesic metric, focusing on highly symmetric configurations on the unit sphere $\mathbb S^2$. Three discrete uniform…
The number of mobile devices (e.g., smartphones, wearable technologies) is rapidly growing. In line with this trend, a massive amount of spatial data is being collected since these devices allow users to geo-tag user-generated content.…
The use of numerical simulations in science is ever increasing and with it the computational size. In many cases single processors are no longer adequate and simulations are run on multiple core machines or supercomputers. One of the key…
Cloud Computing holds the potential to eliminate the requirements for setting up of high-cost computing infrastructure for the IT-based solutions and services that the industry uses. It promises to provide a flexible IT architecture,…