The power of arc consistency for CSPs defined by partially-ordered forbidden patterns

Abstract

Characterising tractable fragments of the constraint satisfaction problem (CSP) is an important challenge in theoretical computer science and arti ficial intelligence. Forbidding patterns (generic sub-instances) provides a means of defi ning CSP fragments which are neither exclusively language-based nor exclusively structure-based. It is known that the class of binary CSP instances in which the broken-triangle pattern (BTP) does not occur, a class which includes all tree-structured instances, are decided by arc consistency (AC), a ubiquitous reduction operation in constraint solvers. We provide a characterisation of simple partially-ordered forbidden patterns which have this AC-solvability property. It turns out that BTP is just one of fi ve such AC-solvable patterns. The four other patterns allow us to exhibit new tractable classes.