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DOI: 10.4230/LIPIcs.SEA.2017.24

Fast Deterministic Selection

Authors: Andrei Alexandrescu

Published in: LIPIcs, Volume 75, 16th International Symposium on Experimental Algorithms (SEA 2017)

Abstract

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.

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Andrei Alexandrescu. Fast Deterministic Selection. In 16th International Symposium on Experimental Algorithms (SEA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 75, pp. 24:1-24:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{alexandrescu:LIPIcs.SEA.2017.24,
  author =	{Alexandrescu, Andrei},
  title =	{{Fast Deterministic Selection}},
  booktitle =	{16th International Symposium on Experimental Algorithms (SEA 2017)},
  pages =	{24:1--24:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-036-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{75},
  editor =	{Iliopoulos, Costas S. and Pissis, Solon P. and Puglisi, Simon J. and Raman, Rajeev},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2017.24},
  URN =		{urn:nbn:de:0030-drops-76122},
  doi =		{10.4230/LIPIcs.SEA.2017.24},
  annote =	{Keywords: Selection Problem, Quickselect, Median of Medians, Algorithm Engineering, Algorithmic Libraries}
}

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Fast Deterministic Selection

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