constraintpruning

Constraint pruning is a set of techniques used in constraint programming and related fields to reduce the search space by discarding values, variable assignments, or branches that cannot lead to feasible or optimal solutions. The aim is to accelerate solving by focusing effort on viable regions of the search space.

Techniques include domain pruning through constraint propagation and enforcing consistency, such as arc-consistency and bounds consistency, which remove inconsistent values from variable domains. Forward checking and maintaining arc consistency accumulate pruning during search. For some problems, global constraints enable stronger pruning. Additionally, redundant or subsumed constraints can be identified and removed to simplify the model, and bound tightening reduces variable ranges in optimization contexts. In optimization, pruning is often integrated with search strategies like branch-and-bound, where branches with bounds worse than the current best are pruned.

Applications span constraint programming, SAT solving, integer programming, scheduling, timetabling, resource allocation, and configuration problems. In classic problems such as graph coloring or the n-queens problem, pruning reduces the number of partial assignments explored. In practical systems, pruning is balanced against the cost of propagation; aggressive pruning may incur overhead that outweighs gains.

Limitations include the risk of over-pruning unintended valid solutions, the computational cost of propagation, and difficulty in designing effective pruning for complex or global constraints. The effectiveness of constraint pruning depends on problem structure and the availability of strong propagators.

See also: constraint satisfaction problem, constraint propagation, arc consistency, forward checking, branch-and-bound, global constraints.