Fast Deterministic Selection

Abstract

The Median of Medians (also known as BFPRT) algorithm, although a landmark theoretical achievement, is seldom used in practice because it and its variants are slower than simple approaches based on sampling. The main contribution of this paper is a fast linear-time deterministic selection algorithm QUICKSELECTADAPTIVE based on a refined definition of MEDIANOFMEDIANS. The algorithm's performance brings deterministic selection-along with its desirable properties of reproducible runs, predictable run times, and immunity to pathological inputs-in the range of practicality. We demonstrate results on independent and identically distributed random inputs and on normally-distributed inputs. Measurements show that QUICKSELECTADAPTIVE is faster than state-of-the-art baselines.