View-based Propagator Derivation

TL;DR

This paper introduces a systematic approach using views to derive perfect propagator variants, significantly reducing implementation effort while maintaining efficiency and correctness in constraint programming systems.

Contribution

It presents a formal model for views and derived propagators, proving their correctness and efficiency, and offers an implementation architecture independent of specific systems.

Findings

Derived propagators are efficient with no overhead in Gecode.

Using views reduces code size for propagators by up to 1750%.

Views enable systematic derivation of propagator variants with maintained properties.

Abstract

When implementing a propagator for a constraint, one must decide about variants: When implementing min, should one also implement max? Should one implement linear constraints both with unit and non-unit coefficients? Constraint variants are ubiquitous: implementing them requires considerable (if not prohibitive) effort and decreases maintainability, but will deliver better performance than resorting to constraint decomposition. This paper shows how to use views to derive perfect propagator variants. A model for views and derived propagators is introduced. Derived propagators are proved to be indeed perfect in that they inherit essential properties such as correctness and domain and bounds consistency. Techniques for systematically deriving propagators such as transformation, generalization, specialization, and type conversion are developed. The paper introduces an implementation architecture for views that is independent of the underlying constraint programming system. A detailed evaluation of views implemented in Gecode shows that derived propagators are efficient and that views often incur no overhead. Without views, Gecode would either require 180 000 rather than 40 000 lines of propagator code, or would lack many efficient propagator variants. Compared to 8 000 lines of code for views, the reduction in code for propagators yields a 1750% return on investment.