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arXiv · 2603.15488

Minimal enclosing balls via geodesics

Ariel Goodwin·Adrian S. Lewis
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Abstract

Algorithms for minimal enclosing ball problems are often geometric in nature. To highlight the metric ingredients underlying their efficiency, we focus here on a particularly simple geodesic-based method. A recent subgradient-based study proved a complexity result for this method in the broad setting of geodesic spaces of nonpositive curvature. We present a simpler, intuitive and self-contained complexity analysis in that setting, which also improves the convergence rate. We furthermore derive the first complexity result for the algorithm on geodesic spaces with curvature bounded above.

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Ariel Goodwin, Adrian S. Lewis. 2026-03-16. Minimal enclosing balls via geodesics. https://arxiv.org/abs/2603.15488

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