Related papers: Distributed boundary tracking using alpha and Dela…
Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is sometimes useful or required to compute what one might call the ``shape'' of the set. For that purpose, this paper introduces the formal…
A new O(nlog(n)) algorithm is presented for performing Delaunay triangulation of sets of 2D points. The novel component of the algorithm is a radially propagating \emph{sweep-hull} (sequentially created from the radially sorted set of 2D…
Solving linear programs is often a challenging task in distributed settings. While there are good algorithms for solving packing and covering linear programs in a distributed manner (Kuhn et al.~2006), this is essentially the only class of…
We consider an extension of the triangular-distance Delaunay graphs (TD-Delaunay) on a set $P$ of points in the plane. In TD-Delaunay, the convex distance is defined by a fixed-oriented equilateral triangle $\triangledown$, and there is an…
In this work we deal with the problem of support estimation under shape restrictions. The shape restriction we deal with is an extension of the notion of convexity named alpha-convexity. Instead of assuming, as in the convex case, the…
We present a distributed optimization algorithm for solving online personalized optimization problems over a network of computing and communicating nodes, each of which linked to a specific user. The local objective functions are assumed to…
Diameter, radius and eccentricities are fundamental graph parameters, which are extensively studied in various computational settings. Typically, computing approximate answers can be much more efficient compared with computing exact…
We describe a randomized algorithm that, given a set $P$ of points in the plane, computes the best location to insert a new point $p$, such that the Delaunay triangulation of $P\cup\{p\}$ has the largest possible minimum angle. The expected…
Writing an uncomplicated, robust, and scalable three-dimensional convex hull algorithm is challenging and problematic. This includes, coplanar and collinear issues, numerical accuracy, performance, and complexity trade-offs. While there are…
We present a new and simple randomized algorithm for constructing the Delaunay triangulation using nearest neighbor graphs for point location. Under suitable assumptions, it runs in linear expected time for points in the plane with…
We propose efficient distributed algorithms to aid navigation of a user through a geographic area covered by sensors. The sensors sense the level of danger at their locations and we use this information to find a safe path for the user…
We develop a sketching algorithm to find the point on the convex hull of a dataset, closest to a query point outside it. Studying the convex hull of datasets can provide useful information about their geometric structure and their…
We envision programmable matter as a system of nano-scale agents (called particles) with very limited computational capabilities that move and compute collectively to achieve a desired goal. We use the geometric amoebot model as our…
This paper presents a new O(nlog(n)) algorithm for computing the convex hull of a set of 3 dimensional points. The algorithm first sorts the point in (x,y,z) then incrementally adds sorted points to the convex hull using the constraint that…
We consider problems where agents in a network seek a common quantity, measured independently and periodically by each agent through a local time-varying process. Numerous solvers addressing such problems have been developed in the past,…
Advanced representation learning techniques require reliable and general evaluation methods. Recently, several algorithms based on the common idea of geometric and topological analysis of a manifold approximated from the learned data…
Convex hulls are fundamental geometric tools used in a number of algorithms. This paper presents a fast, simple to implement and robust Smart Convex Hull (S-CH) algorithm for computing the convex hull of a set of points in E3. This…
We present an algorithm for boundary approximation in locally-linked sensor networks that communicate with a remote monitoring station. Delaunay triangulations and Voronoi diagrams are used to generate a sensor communication network and…
The Hilbert metric is a distance function defined for points lying within the interior of a convex body. It arises in the analysis and processing of convex bodies, machine learning, and quantum information theory. In this paper, we show how…
The structural analysis of shape boundaries leads to the characterization of objects as well as to the understanding of shape properties. The literature on graphs and networks have contributed to the structural characterization of shapes…