
TwentyFive Comparators is Optimal when Sorting Nine Inputs (and TwentyNine for Ten)Michael Codish, Luis CruzFilipe, Michael Frank and Peter SchneiderKamp
Technical Report (unpublished);
November 2014.
Abstract:This paper describes a computerassisted nonexistence proof of 9input sorting networks consisting of 24 comparators, hence showing that the 25comparator sorting network found by Floyd in 1964 is optimal. As a corollary, we obtain that the 29comparator network found by Waksman in 1969 is optimal when sorting 10 inputs. % This closes the two smallest open instances of the optimalsize 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 singlehandedly solve smaller instances of the problem, it is their combination that leads to the more efficient solution that scales to handle 9 inputs.Available: bibtex entry Related sites: eprint from arXiv.org Michael Codish The Department of Computer Science BenGurion University of the Negev PoB 653, BeerSheva, 84105, Israel mcodish@cs.bgu.ac.il
