Effective compilation of constraint models

Compiling solver-independent constraint models to solver input typically involves flattening, the decomposition of complex expressions into simpler expressions, introducing additional variables and constraints. In previous work [8], we have informally proposed extending flattening problem instances with common subexpression elimination(CSE), a widespread optimisation technique that has not yet been established in Constraint Programming (CP). This paper extends our previous work with three main contributions. First, we formally analyse the cost of flattening instances with CSE, comparing instance reduction and time/space complexity with standard flattening, which outlines its scope. Second, we present how to increase the number of common subexpressions in a constraint model by reformulation and include a formal cost analysis. Third, we show how to lift the approach of flattening instances to whole problem classes, an alternative, novel approach to instance-wise compilation. We formally integrate CSE into class-wise flattening,and show when class-wise compilation is preferable to instance-wise compilation. Finally, experiments confirm our theoretical findings and demonstrate the benefits of CSE-based flattening.