Decomposition and Preprocessing of Ternary Constraint Networks

TL;DR

This paper introduces a formal decomposition method for transforming general constraint networks into ternary constraint networks (TCNs) to optimize their execution on GPU hardware, focusing on efficient data layout and preprocessing.

Contribution

It formally specifies the decomposition function of discrete constraint networks into TCNs and details preprocessing steps for GPU-based constraint propagation.

Findings

Formal decomposition function defined for TCN conversion

Preprocessing enhances GPU execution efficiency

Provides a basis for implementing TCN-based constraint solvers

Abstract

Constraint programming is a general and exact method based on constraint propagation and backtracking search. We provide a function decomposing a constraint network into a ternary constraint network (TCN) with a reduced number of operators. TCNs are not new and have been used since the inception of constraint programming, notably in constraint logic programming systems. This work aims to specify formally the decomposition function of discrete constraint network into TCN and its preprocessing. We aim to be self-contained and descriptive enough to serve as the basis of an implementation. Our primary usage of TCN is to obtain a regular data layout of constraints to efficiently execute propagators on graphics processing unit (GPU) hardware.