Constraintrich

Constraintrich is a term used in optimization and constraint programming to describe problem instances or models that contain a high density of constraints relative to the number of decision variables. In these problems, the presence of many constraints can significantly influence the structure of the search space and the effectiveness of propagation techniques employed by solvers.

Origin and usage: The term is relatively informal and appears in discussions about problem structure rather than formal theory. It is used to contrast constraint-light formulations with those that encode many interdependencies, resource limits, and logical relationships. The notion highlights how constraint density can shape modeling choices and solver performance.

Applications: Constraintrich instances arise in scheduling, timetabling, resource allocation, and complex configuration problems, especially when global constraints and many binary relations are used. Encoding strategies that preserve constraint density, such as employing global constraints or careful pre-processing, can help solvers prune the search space earlier.

Implications for solving: In constraint programming and SAT-based CSPs, a higher constraint density can increase propagation effort per search node but can also enable stronger pruning. Practical approaches include constraint rewriting, decomposition, modeling with global constraints, and selective unfolding to balance propagation cost with pruning power.

See also: Constraint programming, Constraint satisfaction problem, Global constraint, Propagation, SAT modulo theories.