2026-07-23T05:04:59Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:7612 2024-03-06T10:39:50Z ddc:004 open_access

Fast Deterministic Selection Alexandrescu, Andrei Selection Problem Quickselect Median of Medians Algorithm Engineering Algorithmic Libraries The selection problem, in forms such as finding the median or choosing the k top ranked items in a dataset, is a core task in computing with numerous applications in fields as diverse as statistics, databases, Machine Learning, finance, biology, and graphics. The selection algorithm Median of Medians, although a landmark theoretical achievement, is seldom used in practice because it is slower than simple approaches based on sampling. The main contribution of this paper is a fast linear-time deterministic selection algorithm MedianOfNinthers based on a refined definition of MedianOfMedians. A complementary algorithm MedianOfExtrema is also proposed. These algorithms work together to solve the selection problem in guaranteed linear time, faster than state-of-the-art baselines, and without resorting to randomization, heuristics, or fallback approaches for pathological cases. We demonstrate results on uniformly distributed random numbers, typical low-entropy artificial datasets, and real-world data. Measurements are open-sourced alongside the implementation at https://github.com/andralex/MedianOfNinthers. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Andrei Alexandrescu 2017 Is Part Of LIPIcs, Volume 75, 16th International Symposium on Experimental Algorithms (SEA 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SEA.2017.24 urn:nbn:de:0030-drops-76122 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2017.24 eng https://creativecommons.org/licenses/by/3.0/legalcode