A polynomial relational class of binary CSP

Finding a solution to a constraint satisfaction problem (CSP) is known to be an NP-hard task. Considerable effort has been spent on identifying tractable classes of CSP, in other words, classes of constraint satisfaction problems for which there are polynomial time recognition and resolution algorithms. In this article, we present a relational tractable class of binary CSP. Our key contribution is a new ternary operation that we name mjx. We first characterize mjx-closed relations which leads to an optimal algorithm to recognize such relations. To reduce space and time complexity, we define a new storage technique for these relations which reduces the complexity of establishing a form of strong directional path consistency, the consistency level that solves all instances of the proposed class (and, indeed, of all relational classes closed under a majority polymorphism).