Lightweight approximate selection

Abstract

Given a relative rank r ε(0,1) (e.g., r=1/2 refers to the median), we show how to efficiently sample with high probability an element with rank very close to r from any probability distribution that supports efficient sampling (e.g., elements stored in an array). A primary feature of our methods is their elegance and ease of implementation - they can be coded in less space than is occupied by this abstract, and their lightweight footprint makes them ideally suited for highly resource-constrained computing environments. We demonstrate through empirical testing that these methods perform well in practice, and provide a complete theoretical analysis for our methods that offers valuable insight into the performance of a natural class of approximate selection algorithms based on hierarchical random sampling. © 2014 Springer-Verlag Berlin Heidelberg.