Generalized Majority-Minority Operations are Tractable

TL;DR

This paper proves that CSP instances invariant under generalized majority-minority operations can be solved efficiently, significantly expanding the class of tractable problems in constraint satisfaction.

Contribution

It introduces GMM operations as a unifying framework and demonstrates polynomial-time solvability for all CSPs invariant under these operations.

Findings

CSPs with GMM-invariant relations are polynomial-time solvable

GMM operations unify near unanimity and Mal'tsev operations

Largest known tractable class of CSPs

Abstract

Generalized majority-minority (GMM) operations are introduced as a common generalization of near unanimity operations and Mal'tsev operations on finite sets. We show that every instance of the constraint satisfaction problem (CSP), where all constraint relations are invariant under a (fixed) GMM operation, is solvable in polynomial time. This constitutes one of the largest tractable cases of the CSP.