  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.
