SAT encodings for sorting networks, single-exception sorting networks and $\epsilon-$halvers

TL;DR

This paper introduces new SAT encodings for sorting networks and related structures, enabling more efficient proofs of optimality and extending to broader problem classes like single-exception networks and epsilon-halvers.

Contribution

It presents novel SAT encodings that reduce complexity and apply to a wider range of sorting network problems, including optimal single-exception networks and epsilon-halvers.

Findings

Optimal single-exception sorting networks for n ≤ 10 inputs

Reduced variables and clauses in SAT encodings

Extended applicability to epsilon-halvers

Abstract

Sorting networks are oblivious sorting algorithms with many practical applications and rich theoretical properties. Propositional encodings of sorting networks are a key tool for proving concrete bounds on the minimum number of comparators or depth (number of parallel steps) of sorting networks. In this paper, we present new SAT encodings that reduce the number of variables and clauses of the sorting constraint of optimality problems. Moreover, the proposed SAT encodings can be applied to a broader class of problems, such as the search of optimal single-exception sorting networks and $\epsilon-$halvers. We obtain optimality results for single-exception sorting networks on $n \le 10$ inputs.