constraintpropagation

Constraint propagation is a technique used in constraint satisfaction problems to reduce the search space by deducing and enforcing consistency across variables. In a CSP, each variable has a finite domain of possible values, and constraints specify which combinations of values are allowed. Propagation iteratively prunes values from domains whenever they cannot participate in any feasible assignment, and any domain reduction may trigger further pruning through other constraints.

Propagation relies on notions of local consistency. The most common is arc-consistency, where for every value of a variable there exists a compatible value in every connected variable’s domain. Generalized arc consistency extends this idea to arbitrary or global constraints. Numerous propagation algorithms implement these ideas, such as AC-3 and AC-4, each with different performance trade-offs. In practice, propagators run after variable assignments or during search to maintain consistency, and can cause backtracking if a domain becomes empty.

Applications of constraint propagation span scheduling, timetabling, resource allocation, configuration problems, and puzzle solving (for example, Sudoku). It is a foundational component of constraint programming systems and is often used in conjunction with global constraints that compactly represent complex requirements. Propagation can dramatically reduce search effort by pruning large portions of the domain space early, but it cannot by itself guarantee a solution and may incur significant cost on tightly connected problems or large domains. Designers balance the strength of the propagation with its computational overhead to achieve effective problem solving. See also: constraint satisfaction problem, arc consistency, constraint programming, global constraints.