Approximate Convex Hulls: sketching the convex hull using curvature

TL;DR

This paper introduces a scalable algorithm for approximating convex hulls by identifying high curvature vertices, making it practical for large datasets with few extreme points.

Contribution

The paper presents a novel sketching method that efficiently approximates convex hulls by focusing on high curvature vertices, improving scalability in high-dimensional data.

Findings

Effective approximation of convex hulls with fewer vertices

High probability of capturing key extreme points

Scalable performance on large datasets

Abstract

Convex hulls are fundamental objects in computational geometry. In moderate dimensions or for large numbers of vertices, computing the convex hull can be impractical due to the computational complexity of convex hull algorithms. In this article we approximate the convex hull in using a scalable algorithm which finds high curvature vertices with high probability. The algorithm is particularly effective for approximating convex hulls which have a relatively small number of extreme points.