Twenty-Five Comparators Is Optimal When Sorting Nine Inputs (and Twenty-Nine for Ten)

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

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

30 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, we obtain that 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. The proof involves a combination of two methodologies: one based on exploiting the abundance of symmetries in sorting networks, and the other based on an encoding of the problem to that of satisfiability of propositional logic. We illustrate that, while each of these can single-handedly solve smaller instances of the problem, it is their combination that leads to the more efficient solution that scales to handle 9 inputs.

Original languageEnglish
Title of host publicationProceedings - 2014 IEEE 26th International Conference on Tools with Artificial Intelligence, ICTAI 2014
PublisherIEEE Computer Society
Pages186-193
Number of pages8
ISBN (Electronic)9781479965724
DOIs
StatePublished - 12 Dec 2014
Event26th IEEE International Conference on Tools with Artificial Intelligence, ICTAI 2014 - Limassol, Cyprus
Duration: 10 Nov 201412 Nov 2014

Publication series

NameProceedings - International Conference on Tools with Artificial Intelligence, ICTAI
Volume2014-December
ISSN (Print)1082-3409

Conference

Conference26th IEEE International Conference on Tools with Artificial Intelligence, ICTAI 2014
Country/TerritoryCyprus
CityLimassol
Period10/11/1412/11/14

ASJC Scopus subject areas

  • Software
  • Artificial Intelligence
  • Computer Science Applications

Fingerprint

Dive into the research topics of 'Twenty-Five Comparators Is Optimal When Sorting Nine Inputs (and Twenty-Nine for Ten)'. Together they form a unique fingerprint.

Cite this