The AllDifferent Constraint with Precedences

TL;DR

The paper introduces AllDiffPrecedence, a global constraint combining AllDifferent and precedence constraints, with an efficient bounds consistency algorithm, applicable to scheduling and symmetry breaking, but NP-hard for domain consistency.

Contribution

It presents a novel global constraint, AllDiffPrecedence, with an efficient propagation algorithm and a decomposition approach, expanding the capabilities of constraint programming.

Findings

Bounds consistency enforcement is efficient for AllDiffPrecedence.

Enforcing domain consistency is NP-hard in general.

Applications include instruction scheduling and symmetry breaking.

Abstract

We propose AllDiffPrecedence, a new global constraint that combines together an AllDifferent constraint with precedence constraints that strictly order given pairs of variables. We identify a number of applications for this global constraint including instruction scheduling and symmetry breaking. We give an efficient propagation algorithm that enforces bounds consistency on this global constraint. We show how to implement this propagator using a decomposition that extends the bounds consistency enforcing decomposition proposed for the AllDifferent constraint. Finally, we prove that enforcing domain consistency on this global constraint is NP-hard in general.