One established metric to classify the significance of a mountain peak is its isolation. It specifies the distance between a peak and the closest point of higher elevation. Peaks with high isolation dominate their surroundings and provide a nice view from the top. With the availability of worldwide Digital Elevation Models (DEMs), the isolation of all mountain peaks can be computed automatically. Previous algorithms run in worst case time that is quadratic in the input size. We present a novel sweep-plane algorithm that runs in time $\mathcal{O}(n\log n+p T_{NN})$ where $n$ is the input size, $p$ the number of considered peaks and $T_{NN}$ the time for a 2D nearest-neighbor query in an appropriate geometric search tree. We refine this to a two-level approach that has high locality and good parallel scalability. Our implementation reduces the time for calculating the isolation of every peak on earth from hours to minutes while improving precision.

翻译：衡量山峰重要性的一项既定指标是其孤立度，它指定了山峰与最近更高点之间的距离。孤立度高的山峰在其周围环境中占据主导地位，并能从山顶提供良好的视野。随着全球数字高程模型（DEM）的可用性，所有山峰的孤立度可以自动计算。先前的算法在最坏情况下的运行时间与输入规模成平方关系。我们提出了一种新颖的扫描面算法，其运行时间为 $\mathcal{O}(n\log n+p T_{NN})$，其中 $n$ 是输入规模，$p$ 是考虑的山峰数量，$T_{NN}$ 是在合适的几何搜索树中进行二维最近邻查询的时间。我们将其优化为一种具有高局部性和良好并行可扩展性的两层方法。我们的实现将计算地球上每一座山峰孤立度的时间从数小时缩短至数分钟，同时提高了精度。