Constraint Representation for Propagation

Propagation based nite domain solvers provide a general mechanism for solving combinatorial problems. Diierent propagation methods can be used in conjunction by communicating through the domains of shared variables. The exibility that this entails has been an important factor in the success of propagation based solving for solving hard combinatorial problems. In this paper we investigate how linear integer constraints should be represented in order that propagation can determine strong domain information. We identify two kinds of substitution which can improve propagation solvers, and can never weaken the domain information. This leads us to an alternate approach to propagation based solving where the form of constraints is modiied by substitution as computation progresses. We compare and contrast a solver using substitution against an indexical based solver, the current method of choice for implementing propagation based constraint solvers, identifying the the relative advantages and disadvantages of the two approaches.