Unifying and extending hybrid tractable classes of CSPs

Finding a solution to a constraint satisfaction problem (CSP) is known to be an NP-complete task. Many works have been concerned with identifying tractable classes of CSPs. Tractability is obtained by imposing specific problem structures, specific constraint relations or both. A tractable CSP class whose tractability is due to both structural and relational properties is said to be hybrid. In this article, we present a hybrid tractable CSP class that brings together and generalises many known hybrid tractable CSPs. The proposed class is characterised by means of simple but powerful notions from set theory.