A new arc consistency algorithm for CSPs with hierarchical domains

General arc-consistency filtering techniques for constraint satisfaction problems (CSP) can be improved by considering special CSP classes. A domain hierarchical CSP is a CSP in which an intrinsic hierarchical structure of its domains is known. A.K. Mackworth et al. (1985) proposed an are consistency algorithm for domain hierarchical CSPs (HAC) whose worst-case time complexity was 0(md³) where m is the number of constraints and d is the maximal size of a domain. HAC worked only with binary tree structured domains. In this paper we present HAC-6 a new arc-consistency algorithm for domain hierarchical CSPs which works with all types of domain hierarchies (any partial ordering) and its worst-case complexity is 0(md²). HAC-6 is based on AC-6 which is the best at present, worst-case optimal arc-consistency algorithm for classical CSPs