Improving Constraint Satisfaction Algorithm Efficiency for the AllDifferent Constraint

TL;DR

This paper introduces a Dual CSP method that transforms CSPs with AllDifferent constraints into complementary problems, enhancing variable domain reduction and improving algorithm efficiency.

Contribution

The paper presents a novel Dual CSP transformation technique that leverages problem complementarity to improve efficiency in solving AllDifferent constrained CSPs.

Findings

Dual CSP method reduces variable domains more effectively.

Application of the method improves efficiency over standard approaches.

Extensions to other constraints are promising for future work.

Abstract

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.