The Power of Arc Consistency for CSPs Defined by Partially-Ordered Forbidden Patterns

TL;DR

This paper characterizes certain forbidden patterns in CSPs that ensure arc consistency alone can decide their satisfiability, expanding the known tractable classes beyond the broken-triangle pattern.

Contribution

It identifies five simple partially-ordered forbidden patterns with arc consistency solvability, including four new tractable classes.

Findings

BTP is one of five AC-solvable patterns.

Four new tractable classes are identified.

Arc consistency suffices for these classes.

Abstract

Characterising tractable fragments of the constraint satisfaction problem (CSP) is an important challenge in theoretical computer science and artificial intelligence. Forbidding patterns (generic sub-instances) provides a means of defining 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 five such AC-solvable patterns. The four other patterns allow us to exhibit new tractable classes.