An Elimination Algorithm for Functional Constraints

Abstract

Functional constraints are studied in Constraint Satisfaction Problems (CSP) using consistency concepts (e.g., [1,4]). In this paper, we propose a new method – variable substitution – to process functional constraints. The idea is that if a constraint is functional on a variable, this variable in another constraint can be substituted using the functional constraint without losing any solution. We design an efficient algorithm to reduce, in $\mathcal{O}(ed^2)$, a general binary CSP containing functional constraints into a canonical form which simplifies the problem and makes the functional portion trivially solvable. When the functional constraints are also bi-functional, then the algorithm is linear in the size of the CSP.