David M. Mount

collaborators

6 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…

cs.CG2026

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…

cs.CG2026

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…

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.DS2023

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…

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…