An Answer to the Bose-Nelson Sorting Problem for 11 and 12 Channels
Abstract
We show that 11-channel sorting networks have at least 35 comparators and that 12-channel sorting networks have at least 39 comparators. This positively settles the optimality of the corresponding sorting networks given in The Art of Computer Programming vol. 3 and closes the two smallest open instances of the Bose-Nelson sorting problem. We obtain these bounds by generalizing a result of Van Voorhis from sorting networks to a more general class of comparator networks. From this we derive a dynamic programming algorithm that computes the optimal size for a sorting network with a given number of channels. From an execution of this algorithm we construct a certificate containing a derivation of the corresponding lower size bound, which we check using a program formally verified using the Isabelle/HOL proof assistant.
Keywords
Cite
@article{arxiv.2012.04400,
title = {An Answer to the Bose-Nelson Sorting Problem for 11 and 12 Channels},
author = {Jannis Harder},
journal= {arXiv preprint arXiv:2012.04400},
year = {2022}
}
Comments
v1: Revised attribution of previous results in the introduction v2: Fixed labels in Figure 3