License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SEA.2017.24
URN: urn:nbn:de:0030-drops-76122
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7612/
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Alexandrescu, Andrei

Fast Deterministic Selection

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LIPIcs-SEA-2017-24.pdf (0.5 MB)

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.

BibTeX - Entry

@InProceedings{alexandrescu:LIPIcs:2017:7612,
  author =	{Andrei Alexandrescu},
  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 =	{Costas S. Iliopoulos and Solon P. Pissis and Simon J. Puglisi and Rajeev Raman},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7612},
  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}
}

Keywords: Selection Problem, Quickselect, Median of Medians, Algorithm Engineering, Algorithmic Libraries
Collection: 16th International Symposium on Experimental Algorithms (SEA 2017)
Issue Date: 2017
Date of publication: 07.08.2017

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