Range and Roots: Two common patterns for specifying and propagating counting and occurrence constraints

We propose Range and Roots which are two common patterns useful for specifying a wide range of counting and occurrence constraints. We design specialised propagation algorithms for these two patterns. Counting and occurrence constraints specified using these patterns thus directly inherit a propagation algorithm. To illustrate the capabilities of the Range and Roots constraints, we specify a number of global constraints taken from the literature. Preliminary experiments demonstrate that propagating counting and occurrence constraints using these two patterns leads to a small loss in performance when compared to specialised global constraints and is competitive with alternative decompositions using elementary constraints.