research-article

Sorting nine inputs requires twenty-five comparisons

Authors:

Michael Codish,

Luís Cruz-Filipe,

Peter Schneider-KampAuthors Info & Claims

Journal of Computer and System Sciences, Volume 82, Issue 3

Pages 551 - 563

https://doi.org/10.1016/j.jcss.2015.11.014

Published: 01 May 2016 Publication History

Abstract

Twenty-five comparators are minimal to sort nine inputs.Twenty-nine comparators are minimal to sort ten inputs.New symmetry-breaking results control the growth of the search space.Optimized and parallelized algorithms for generating size-optimal sorting networks.Use of SAT-solving to speed up the last part of the computation. This paper describes a computer-assisted non-existence proof of 9-input sorting networks consisting of 24 comparators, hence showing that the 25-comparator sorting network found by Floyd in 1964 is optimal. As a corollary, the 29-comparator network found by Waksman in 1969 is optimal when sorting 10 inputs.This closes the two smallest open instances of the optimal-size sorting network problem, which have been open since the results of Floyd and Knuth from 1966 proving optimality for sorting networks of up to 8 inputs.

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Cited By

Jain TSchneider KHu KZhan N(2018)Optimal self-routing split modules for radix-based interconnection networksProceedings of the 16th ACM-IEEE International Conference on Formal Methods and Models for System Design10.5555/3343872.3343884(99-108)Online publication date: 15-Oct-2018
https://dl.acm.org/doi/10.5555/3343872.3343884
Bundala DCodish MCruz-Filipe LSchneider-Kamp PZávodný J(2017)Optimal-depth sorting networksJournal of Computer and System Sciences10.1016/j.jcss.2016.09.00484:C(185-204)Online publication date: 1-Mar-2017
https://dl.acm.org/doi/10.1016/j.jcss.2016.09.004
Cruz-Filipe LLarsen KSchneider-Kamp P(2017)Formally Proving Size Optimality of Sorting NetworksJournal of Automated Reasoning10.1007/s10817-017-9405-959:4(425-454)Online publication date: 1-Dec-2017
https://dl.acm.org/doi/10.1007/s10817-017-9405-9
Show More Cited By

Index Terms

Sorting nine inputs requires twenty-five comparisons
1. Theory of computation
  1. Design and analysis of algorithms
    1. Data structures design and analysis
      1. Sorting and searching

Index terms have been assigned to the content through auto-classification.

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Published In

cover image Journal of Computer and System Sciences

Journal of Computer and System Sciences Volume 82, Issue 3

May 2016

171 pages

ISSN:0022-0000

Issue’s Table of Contents

Copyright © Elsevier Inc.

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Academic Press, Inc.

United States

Publication History

Published: 01 May 2016

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Cited By

Jain TSchneider KHu KZhan N(2018)Optimal self-routing split modules for radix-based interconnection networksProceedings of the 16th ACM-IEEE International Conference on Formal Methods and Models for System Design10.5555/3343872.3343884(99-108)Online publication date: 15-Oct-2018
https://dl.acm.org/doi/10.5555/3343872.3343884
Bundala DCodish MCruz-Filipe LSchneider-Kamp PZávodný J(2017)Optimal-depth sorting networksJournal of Computer and System Sciences10.1016/j.jcss.2016.09.00484:C(185-204)Online publication date: 1-Mar-2017
https://dl.acm.org/doi/10.1016/j.jcss.2016.09.004
Cruz-Filipe LLarsen KSchneider-Kamp P(2017)Formally Proving Size Optimality of Sorting NetworksJournal of Automated Reasoning10.1007/s10817-017-9405-959:4(425-454)Online publication date: 1-Dec-2017
https://dl.acm.org/doi/10.1007/s10817-017-9405-9
Codish MCruz-Filipe LNebel MSchneider-Kamp P(2017)Optimizing sorting algorithms by using sorting networksFormal Aspects of Computing10.1007/s00165-016-0401-329:3(559-579)Online publication date: 1-May-2017
https://dl.acm.org/doi/10.1007/s00165-016-0401-3
Cruz-Filipe LLarsen KSchneider-Kamp P(2017)How to Get More Out of Your OraclesInteractive Theorem Proving10.1007/978-3-319-66107-0_11(164-170)Online publication date: 26-Sep-2017
https://dl.acm.org/doi/10.1007/978-3-319-66107-0_11

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