Related papers: The projector algorithm: a simple parallel algorit…
We introduce VoroFields, a hierarchical neural-field framework for approximating generalized Voronoi diagrams of finite geometric site sets in low-dimensional domains under arbitrary evaluable point-to-site distances. Instead of…
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…
In this paper we are concerned with finding the vertices of the Voronoi cell of a Euclidean lattice. Given a basis of a lattice, we prove that computing the number of vertices is a #P-hard problem. On the other hand we describe an algorithm…
This paper presents the Voronoi diagram-based evolutionary algorithm (VorEAl). VorEAl partitions input space in abnormal/normal subsets using Voronoi diagrams. Diagrams are evolved using a multi-objective bio-inspired approach in order to…
We study the Voronoi Diagram of Rotating Rays, a Voronoi structure where the input sites are rays and the distance function between a point and a site/ray, is the counterclockwise angular distance. This novel Voronoi diagram is motivated by…
This work addresses the collaborative multi-robot autonomous online exploration problem, particularly focusing on distributed exploration planning for dynamically balanced exploration area partition and task allocation among a team of…
Stochastic differential equations projected onto manifolds occur in physics, chemistry, biology, engineering, nanotechnology and optimization, with interdisciplinary applications. Intrinsic coordinate stochastic equations on the manifold…
The Voronoi Diagram is a geometrical structure that is widely used in scientific or technological applications where proximity is a relevant aspect to consider, and it also resembles natural phenomena such as cellular banks, rock formations…
A set S of n points in general position in R^d defines the unique Voronoi diagram of S. Its dual tessellation is the Delaunay triangulation (DT) of S. In this paper we consider the parabolic functional on the set of triangulations of S and…
We describe a simple, but efficient algorithm for the generation of dilated contours from bilevel images. The initial part of the contour extraction is explained to be a good candidate for parallel computer code generation. The remainder of…
We give a parallel $O(\log(n))$-time algorithm on a CRCW PRAM to assign vertical and horizontal segments to the vertices of any planar bipartite graph $G$ in the following manner: i) Two segments cannot share an interior point ii) Two…
In this paper we show that many sequential randomized incremental algorithms are in fact parallel. We consider algorithms for several problems including Delaunay triangulation, linear programming, closest pair, smallest enclosing disk,…
The interconnection network comprises a significant portion of the cost of large parallel computers, both in economic terms and power consumption. Several previous proposals exploit large-radix routers to build scalable low-distance…
A Voronoi diagram partitions the plane into convex cells, each containing the points closest to a single generator. Given such a tessellation, the inverse Voronoi problem seeks the generator set \( S \) that produced it. Our algorithm…
The construction of anisotropic triangulations is desirable for various applications, such as the numerical solving of partial differential equations and the representation of surfaces in graphics. To solve this notoriously difficult…
This paper introduces the `Projectron' as a new neural network architecture that uses Radon projections to both classify and represent medical images. The motivation is to build shallow networks which are more interpretable in the medical…
We describe a new data structure for dynamic nearest neighbor queries in the plane with respect to a general family of distance functions. These include $L_p$-norms and additively weighted Euclidean distances. Our data structure supports…
In our recent paper [de Lacy Costello et al. 2010] we described the formation of complex tessellations of the plane arising from the various reactions of metal salts with potassium ferricyanide and ferrocyanide loaded gels. In addition to…
An efficient numerical algorithm is presented for massively parallel simulations of dispersion-managed wavelength-division-multiplexed optical fiber systems. The algorithm is based on a weak nonlinearity approximation and independent…
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.…