44 citations · 44 across the 5 of their papers we have counts for
10 papers
Differentiable Approximations for Distance Queries
Ahmed Abdelkader, David M. Mount
The widespread use of gradient-based optimization has motivated the adaptation of various classical algorithms into differentiable solvers compatible with learning pipelines. In th…
Convex Approximation and the Hilbert Geometry
Ahmed Abdelkader, David M. Mount
The efficient representation of convex bodies in multi-dimensional spaces is a fundamental problem in computational geometry. Several key developments were recently brought about u…
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…
Linear-Sized Spectral Sparsifiers and the Kadison-Singer Problem
Phevos Paschalidis, Ashley Zhuang
The Kadison-Singer Conjecture, as proved by Marcus, Spielman, and Srivastava (MSS) [Ann. Math. 182, 327-350 (2015)], has been informally thought of as a strengthening of Batson, Sp…
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}…
Approximate Nearest-Neighbor Search for Line Segments
Ahmed Abdelkader, David M. Mount
Approximate nearest-neighbor search is a fundamental algorithmic problem that continues to inspire study due its essential role in numerous contexts. In contrast to most prior work…
VoroCrust: Voronoi Meshing Without Clipping
Ahmed Abdelkader, Chandrajit L. Bajaj, Mohamed S. Ebeida +4
Polyhedral meshes are increasingly becoming an attractive option with particular advantages over traditional meshes for certain applications. What has been missing is a robust poly…
Sampling Conditions for Conforming Voronoi Meshing by the VoroCrust Algorithm
Ahmed Abdelkader, Chandrajit L. Bajaj, Mohamed S. Ebeida +4
We study the problem of decomposing a volume bounded by a smooth surface into a collection of Voronoi cells. Unlike the dual problem of conforming Delaunay meshing, a principled so…
On Realistic Target Coverage by Autonomous Drones
Ahmed Saeed, Ahmed Abdelkader, Mouhyemen Khan +3
Low-cost mini-drones with advanced sensing and maneuverability enable a new class of intelligent sensing systems. To achieve the full potential of such drones, it is necessary to d…
On the Complexity of Slide-and-Merge Games
Ahmed Abdelkader, Aditya Acharya, Philip Dasler
We study the complexity of a particular class of board games, which we call `slide and merge' games. Namely, we consider 2048 and Threes, which are among the most popular games of…