Artificial Intelligence
Partition search for non-binary constraint satisfaction
Information Sciences: an International Journal
QUICKXPLAIN: preferred explanations and relaxations for over-constrained problems
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
A study of residual supports in arc consistency
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
A decision support system for managing combinatorial problems in container terminals
Knowledge-Based Systems
A pattern-based knowledge editing system for building clinical Decision Support Systems
Knowledge-Based Systems
Local consistency and SAT-solvers
Journal of Artificial Intelligence Research
Structure learning for belief rule base expert system: A comparative study
Knowledge-Based Systems
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Constraint satisfaction problem has many applications in Artificial Intelligence. Its interactive applications usually require advice from a system to help a user solve the problem. Based on maximal relaxations, the CorrectiveExp algorithm is a representative method to compute explanations. However, we found that the CorrectiveRelax algorithm, used by the CorrectiveExp algorithm to compute maximal relaxations, has a defect that it executes more consistency checks than necessary. It is very important to avoid these unnecessary consistency checks because in general each consistency check needs to resort to backtrack search. To tackle this problem, this paper proposes two improved algorithms to compute maximal relaxations, called CorrectiveRelaxReduced and CorrectiveRelaxDC respectively. The former utilizes the existing results of consistency checks to shrink the search scope for some inconsistent user constraints. Furthermore, we have proved that the number of consistency checks executed by the CorrectiveRelaxReduced algorithm is always less than or equals to that of the CorrectiveRelax algorithm. The latter uses a divide-and-conquer approach to avoid unnecessary consistency checks. Our experimental results show that the two improved algorithms execute less consistency checks than CorrectiveExp while computing maximal relaxations.