constraintpropagating

Constraintpropagating (often written as constraint propagation) refers to the activity of propagating constraints through a problem representation in order to prune variable domains and reduce the search space. In a constraint satisfaction problem, a solver maintains variables with finite domains and a set of constraints. When domains change, constraintpropagating examines the constraints related to the affected variables and removes values that cannot participate in any solution, iterating until no more reductions are possible or a domain becomes empty.

Propagating constraints relies on local consistency techniques. Arc consistency enforces that every value of a variable has a compatible value in each neighboring variable. More powerful forms, such as path or domain consistency, propagate across longer constraint scopes. In modern systems, dedicated propagators monitor domain events and communicate through a propagation queue, activating only those constraints that may cause further pruning.

Many solvers implement global constraints, which encapsulate common patterns (for example AllDifferent or cumulative) with specialized propagators that can achieve strong pruning more efficiently than decomposing into binary constraints. The propagation process is typically incremental and event-driven, supporting backtracking or lifting to manage alternative search branches.

Constraintpropagating does not by itself solve a problem; it is combined with search. Strong propagation reduces the size of the search space but may increase per-step cost. The effectiveness depends on the problem structure and the strength of the available propagators.