The Parameterized Complexity of Global Constraints

TL;DR

This paper demonstrates how parameterized complexity can analyze and improve the tractability of global constraints in constraint programming, enabling fixed-parameter tractability results and insights into symmetry breaking and approximation.

Contribution

It introduces the application of parameterized complexity to global constraints, showing how natural parameters lead to fixed-parameter tractability and new analysis methods.

Findings

Many intractable global constraints become fixed-parameter tractable with natural parameters.

Backdoors such as cycle cutsets facilitate efficient constraint propagation.

Parameterized complexity provides insights into symmetry breaking and approximation in constraint programming.

Abstract

We argue that parameterized complexity is a useful tool with which to study global constraints. In particular, we show that many global constraints which are intractable to propagate completely have natural parameters which make them fixed-parameter tractable and which are easy to compute. This tractability tends either to be the result of a simple dynamic program or of a decomposition which has a strong backdoor of bounded size. This strong backdoor is often a cycle cutset. We also show that parameterized complexity can be used to study other aspects of constraint programming like symmetry breaking. For instance, we prove that value symmetry is fixed-parameter tractable to break in the number of symmetries. Finally, we argue that parameterized complexity can be used to derive results about the approximability of constraint propagation.