View-based propagation of decomposable constraints

TL;DR

This paper introduces a view-based approach for propagating decomposable constraints in constraint programming, offering a modular, efficient, and correct alternative to traditional decomposition methods that avoids auxiliary variables.

Contribution

The paper presents a novel view-based method for propagating decomposable constraints, simplifying and improving the efficiency of constraint propagation without auxiliary variables.

Findings

View-based propagation is modular and avoids auxiliary variables.

The approach improves efficiency over traditional decomposition methods.

It maintains correctness and simplifies the implementation of propagators.

Abstract

Constraints that may be obtained by composition from simpler constraints are present, in some way or another, in almost every constraint program. The decomposition of such constraints is a standard technique for obtaining an adequate propagation algorithm from a combination of propagators designed for simpler constraints. The decomposition approach is appealing in several ways. Firstly because creating a specific propagator for every constraint is clearly infeasible since the number of constraints is infinite. Secondly, because designing a propagation algorithm for complex constraints can be very challenging. Finally, reusing existing propagators allows to reduce the size of code to be developed and maintained. Traditionally, constraint solvers automatically decompose constraints into simpler ones using additional auxiliary variables and propagators, or expect the users to perform such decomposition themselves, eventually leading to the same propagation model. In this paper we explore views, an alternative way to create efficient propagators for such constraints in a modular, simple and correct way, which avoids the introduction of auxiliary variables and propagators.