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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.[1]

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.[2]

Mackworth, Alan K.; Mulder, Jan A.; Havens, William S. (1985-01-01). "Hierarchical arc consistency: exploiting structured domains in constraint satisfaction problems". Computational Intelligence. 1 (1): 118–126. doi:10.1111/j.1467-8640.1985.tb00064.x. ISSN 1467-8640.
Wilson, Molly; Borning, Alan (1993-07-01). "Hierarchical constraint logic programming". The Journal of Logic Programming. 16 (3–4): 277–318. doi:10.1016/0743-1066(93)90046-J. ISSN 0743-1066.

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