Sorting nine inputs requires twenty-five comparisons

Michael Codish; Luís Cruz-Filipe; Michael Frank; Peter Schneider-Kamp

doi:10.1016/j.jcss.2015.11.014

Sorting nine inputs requires twenty-five comparisons

Michael Codish, Luís Cruz-Filipe, Michael Frank, Peter Schneider-Kamp

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	551-563
Number of pages	13
Journal	Journal of Computer and System Sciences
Volume	82
Issue number	3
DOIs	https://doi.org/10.1016/j.jcss.2015.11.014
State	Published - 1 Jan 2016

Keywords

Computer-assisted proofs
SAT solving
Sorting networks
Symmetry breaking

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science
Computer Networks and Communications
Computational Theory and Mathematics
Applied Mathematics

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10.1016/j.jcss.2015.11.014

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AB - 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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KW - Symmetry breaking

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Sorting nine inputs requires twenty-five comparisons

Abstract

Keywords

ASJC Scopus subject areas

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