Hierarchical constraint satisfaction

In artificial intelligence and operations research, hierarchical constraint satisfaction (HCS) is a method of handling constraint satisfaction problems where the variables have large domains by exploiting their internal structure.{{Cite journal|last=Mackworth|first=Alan K.|last2=Mulder|first2=Jan A.|last3=Havens|first3=William S.|date=1985-01-01|title=Hierarchical arc consistency: exploiting structured domains in constraint satisfaction problems|journal=Computational Intelligence|language=en|volume=1|issue=1|pages=118–126|doi=10.1111/j.1467-8640.1985.tb00064.x|issn=1467-8640}}

For many real-world problems the domain elements cluster together into sets with common properties and relations. This structure can be represented as a hierarchy and is partially ordered on the subset of a relation. The expectation is that the domains are structured so that the elements of a set frequently share consistency properties permitting them to be retained or eliminated as a unit. Thus, if some elements of a set satisfy a constraint, but not all, the subsets of the set are considered. In this way, if no elements of a set can satisfy the constraint the whole set can be discarded. Thus, structuring the domain helps in considering sets of elements all at a time and hence helps in pruning the search space more quickly.{{Cite journal|date=1993-07-01|title=Hierarchical constraint logic programming|journal=The Journal of Logic Programming|language=en|volume=16|issue=3–4|pages=277–318|doi=10.1016/0743-1066(93)90046-J|issn=0743-1066|last1=Wilson|first1=Molly|last2=Borning|first2=Alan|doi-access=free}}