Replaceability is a form of generalized substitutability whose features make it potentially of great importance for problem simplification. It differs from simple substitutability in that it only requires that substitutable values exist for every solution containing a given value without requiring that the former always be the same. This is also the most general form of substitutability that allows inferences from local to global versions of this property. Building on earlier work, this study first establishes that algorithms for localized replaceability (called consistent neighbourhood replaceability or CNR algorithms) based on all-solutions neighbourhood search outperform other replaceability algorithms by several orders of magnitude. It also examines the relative effectiveness of different forms of depth-first CNR algorithms. Secondly, it demonstrates an apparent complexity ridge, which does not occur at the same place in the problem space as the complexity areas for consistency or full search algorithms. Thirdly, it continues the study of methods for inferring replaceability in structured problems in order to improve efficiency. This includes correcting an oversight in earlier work and extending the formal analysis. It is also shown that some strategies for inferring replaceable values can be extended to disjunctive constraints in scheduling problems.

Replaceability for constraint satisfaction problems: Algorithms, Inferences, and Complexity Patterns