Prominence is one of the most important measurements in topography and mountaineering. This paper describes an efficient, almost linear time algorithm for computing mountain prominence for all peaks on Earth using digital elevation models (DEMs). It builds on top of a classic algorithm and leverages the observation that only a few peaks have their prominence determined by a relatively distant other mountain. Thus, the classic algorithm can be adapted to memorize and use less information without the loss of correctness. The algorithm is demonstrated using 3 arcsecond real-life data from SRTM datasets. Its importance is underscored by the increasing accuracy of Earth mapping methods and the corresponding growth in the amount of data that must be processed to compute prominence.

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