Solving Functional Constraints by Variable Substitution

TL;DR

This paper introduces a variable substitution approach for solving functional constraints in Constraint Programming, offering efficient algorithms that improve problem-solving performance, especially when functional constraints form a reachability structure.

Contribution

It presents a novel variable substitution method for functional constraints, replacing traditional local consistency techniques in CSP solvers.

Findings

Variable elimination significantly improves solving efficiency.

The approach effectively handles CSPs with reachability via functional constraints.

Algorithms reduce systems with functional and bi-functional constraints efficiently.

Abstract

Functional constraints and bi-functional constraints are an important constraint class in Constraint Programming (CP) systems, in particular for Constraint Logic Programming (CLP) systems. CP systems with finite domain constraints usually employ CSP-based solvers which use local consistency, for example, arc consistency. We introduce a new approach which is based instead on variable substitution. We obtain efficient algorithms for reducing systems involving functional and bi-functional constraints together with other non-functional constraints. It also solves globally any CSP where there exists a variable such that any other variable is reachable from it through a sequence of functional constraints. Our experiments on random problems show that variable elimination can significantly improve the efficiency of solving problems with functional constraints.