Optimal Sorting Networks
Discrete Mathematics
2013-12-24 v2 Data Structures and Algorithms
Abstract
This paper settles the optimality of sorting networks given in The Art of Computer Programming vol. 3 more than 40 years ago. The book lists efficient sorting networks with n <= 16 inputs. In this paper we give general combinatorial arguments showing that if a sorting network with a given depth exists then there exists one with a special form. We then construct propositional formulas whose satisfiability is necessary for the existence of such a network. Using a SAT solver we conclude that the listed networks have optimal depth. For n <= 10 inputs where optimality was known previously, our algorithm is four orders of magnitude faster than those in prior work.
Cite
@article{arxiv.1310.6271,
title = {Optimal Sorting Networks},
author = {Daniel Bundala and Jakub Závodný},
journal= {arXiv preprint arXiv:1310.6271},
year = {2013}
}