Enclosing depth is a recently introduced depth measure which gives a lower bound to many depth measures studied in the literature. So far, enclosing depth has only been studied from a combinatorial perspective. In this work, we give the first algorithms to compute the enclosing depth of a query point with respect to a data point set in any dimension. In the plane we are able to optimize the algorithm to get a runtime of O(n log n). In constant dimension, our algorithms still run in polynomial time.

翻译：包围深度是近期提出的一种深度度量，它为文献中研究的许多深度度量提供了下界。截至目前，包围深度仅从组合学角度进行了研究。本研究首次提出了在任意维度下计算查询点相对于数据点集的包围深度算法。在平面情形下，我们通过算法优化实现了O(n log n)的运行时间。在固定维度下，我们的算法仍可在多项式时间内运行。