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性质。为突出其效率背后的度量要素，本文重点关注一种特别简单的基于测地线的方法。近期一项基于次梯度的研究在非正曲率测地空间这一广泛框架下证明了该方法的复杂度结果。我们在该框架下提出一种更简单、直观且自包含的复杂度分析，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有界测地空间上的复杂度结果。