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.

翻译：最小包围球问题的算法通常具有几何特性。为凸显其效率背后的度量要素，本文聚焦于一种基于测地线的特别简洁方法。近期一项基于次梯度的研究在非正曲率测地空间的广义背景下证明了该方法的复杂度结论。我们在相同背景下提出更简洁、直观且自洽的复杂度分析，同时改进了收敛速率。此外，我们首次推导出该算法在曲率上界有界的测地空间中的复杂度结果。