Smallest Intersecting and Enclosing Balls

Abstract

We study the smallest intersecting and enclosing ball problems in Euclidean spaces for input objects that are compact and convex. They link and unify many problems in computational geometry and machine learning. We show that both problems can be modeled as zero-sum games, and propose an approximation algorithm for the former. Specifically, the algorithm produces the first results in high-dimensional spaces for various input objects such as convex polytopes, balls, ellipsoids, etc.