Hull consistency under monotonicity

Authors:
Gilles Chabert;Luc Jaulin
Affiliations:
Ecole des Mines de Nantes, LINA, CNRS, UMR, Nantes, France;ENSIETA, Brest Cedex 9, France
Venue:
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Year:
2009

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Abstract

We prove that hull consistency for a system of equations or inequalities can be achieved in polynomial time providing that the underlying functions are monotone with respect to each variable. This result holds including when variables have multiple occurrences in the expressions of the functions, which is usually a pitfall for interval-based contractors. For a given constraint, an optimal contractor can thus be enforced quickly under monotonicity and the practical significance of this theoretical result is illustrated on a simple example.