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.

@article{paperbot89,
  title = {The Power of Arc Consistency for CSPs Defined by Partially-Ordered Forbidden Patterns},
  author = {Martin C. Cooper and Stanislav Živný},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 13, Issue 4},
  year = {2017},
  doi = {10.23638/lmcs-13(4:26)2017}
}