Range and Roots: Two Common Patterns for Specifying and Propagating Counting and Occurrence Constraints

TL;DR

This paper introduces Range and Roots, two patterns for specifying counting and occurrence constraints, along with specialized algorithms, enabling efficient propagation and broad applicability in constraint programming.

Contribution

The paper presents novel Range and Roots patterns with dedicated propagation algorithms, enhancing the expressiveness and efficiency of counting and occurrence constraints.

Findings

Propagation with Range and Roots is competitive with specialized global constraints.

The patterns enable specifying a wide range of constraints from literature.

Preliminary experiments show minimal performance loss.

Abstract

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.