8 citations · 34 across the 13 of their papers we have counts for
5 papers · 1 filter
Smooth Distance Approximation
Ahmed Abdelkader, David M. Mount
Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, b…
Approximate Nearest Neighbor Searching with Non-Euclidean and Weighted Distances
Ahmed Abdelkader, Sunil Arya, Guilherme D. da Fonseca +1
We present a new approach to approximate nearest-neighbor queries in fixed dimension under a variety of non-Euclidean distances. We are given a set of points in $\mathbb{R}…
Analysis of Dynamic Voronoi Diagrams in the Hilbert Metric
Madeline Bumpus, Xufeng Caesar Dai, Auguste H. Gezalyan +4
The Hilbert metric is a projective metric defined on a convex body which generalizes the Cayley-Klein model of hyperbolic geometry to any convex set. In this paper we analyze Hilbe…
Economical Convex Coverings and Applications
Sunil Arya, Guilherme D. da Fonseca, David M. Mount
Coverings of convex bodies have emerged as a central component in the design of efficient solutions to approximation problems involving convex bodies. Intuitively, given a convex b…
Optimal Volume-Sensitive Bounds for Polytope Approximation
Sunil Arya, David M. Mount
Approximating convex bodies is a fundamental question in geometry, which has a wide variety of applications. Given a convex body in for fixed , the objective…