S. Arya

activity

20162026

ε

-Kernel Construction and Related Problems

8 citations · 32 across the 12 of their papers we have counts for

collaborators

13 papers

math.MG2026

Duality Bounds for Convexified Packing in Hilbert Geometry

Sunil Arya, David M. Mount

Let $G$ and $K$ be convex bodies in $R^{d}$ , where $0 \in int G$ and $G \subset int K$ . Given $α > 0$ , the Hilbert packing number $M_{H} (G, K; α)$ is the maximum…

math.MG2026

On the Duality of Coverings in Hilbert Geometry

Sunil Arya, David M. Mount

We prove polarity duality for covering problems in Hilbert geometry. Let $G$ and $K$ be convex bodies in $R^{d}$ where $G \subset int (K)$ and $\operatorname{i…

cs.CG2026

Cauchy's Surface Area Formula in the Funk Geometry

Sunil Arya, David M. Mount

Cauchy's surface area formula expresses the surface area of a convex body as the average area of its orthogonal projections over all directions. While this tool is fundamental in E…

cs.CG2023

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 $S$ of $n$ points in $\mathbb{R}…

cs.CG2023

Optimal Area-Sensitive Bounds for Polytope Approximation

Sunil Arya, Guilherme D. da Fonseca, David M. Mount

Approximating convex bodies is a fundamental problem in geometry. Given a convex body $K$ in $R^{d}$ for a fixed dimension $d$ , the objective is to minimize the number of fa…

cs.CG2023

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…