Constraint Propagation
An algorithmic method that propagates constraints from confirmed digits to related cells, automatically narrowing down candidates.
Constraint propagation is a method that immediately updates candidates in affected rows, columns, and blocks whenever a digit is confirmed. It is essentially the same as manually updating pencil marks, but computers can propagate all effects instantly and without omission.
Role in Solvers
Constraint propagation dramatically improves backtracking efficiency. After each tentative placement, constraints are propagated; if any cell ends up with zero candidates, the solver immediately backtracks (early pruning). Cells reduced to a single candidate are automatically confirmed.
Correspondence to Human Solving
When humans find Naked Singles and update their pencil marks, they are performing manual constraint propagation. The auto-candidate-removal feature in digital apps executes constraint propagation in real time.