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 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.
Cite
@article{arxiv.1604.07981,
title = {The Power of Arc Consistency for CSPs Defined by Partially-Ordered Forbidden Patterns},
author = {Martin C. Cooper and Stanislav Živný},
journal= {arXiv preprint arXiv:1604.07981},
year = {2023}
}