Fast Deterministic Selection

TL;DR

This paper introduces QuickselectAdaptive, a fast deterministic selection algorithm that improves practical performance of median-of-medians based methods, offering predictable run times and outperforming existing baselines.

Contribution

It presents a refined median-of-medians approach resulting in a linear-time deterministic selection algorithm suitable for practical use.

Findings

QuickselectAdaptive is faster than state-of-the-art baselines.

It maintains deterministic, reproducible, and predictable performance.

The algorithm performs well on various input distributions.

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.