Improving Constraint Satisfaction Algorithm Efficiency for the AllDifferent Constraint
This work provides an incremental improvement in the efficiency of constraint satisfaction problem solving for researchers and practitioners working with combinatorial problems, specifically those involving the AllDifferent constraint.
This paper introduces a "Dual CSP" method for improving the efficiency of constraint satisfaction algorithms involving the AllDifferent constraint. By simultaneously applying algorithms to both the original and its complementary problem, the method demonstrates benefits in variable domain reduction compared to standard CSP approaches.
Combinatorial problems stated as Constraint Satisfaction Problems (CSP) are examined. It is shown by example that any algorithm designed for the original CSP, and involving the AllDifferent constraint, has at least the same level of efficacy when simultaneously applied to both the original and its complementary problem. The 1-to-1 mapping employed to transform a CSP to its complementary problem, which is also a CSP, is introduced. This "Dual CSP" method and its application are outlined. The analysis of several random problem instances demonstrate the benefits of this method for variable domain reduction compared to the standard approach to CSP. Extensions to additional constraints other than AllDifferent, as well as the use of hybrid algorithms, are proposed as candidates for this Dual CSP method.