Improving Constraint Satisfaction Algorithm Efficiency for the
  AllDifferent Constraint
  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.
