A Geometric Constraint over k-Dimensional Objects and Shapes Subject to Business Rules

Authors:
Mats Carlsson;Nicolas Beldiceanu;Julien Martin
Affiliations:
SICS, Kista, Sweden SE-164 29;École des Mines de Nantes, LINA UMR CNRS 6241, Nantes, France FR-44307;INRIA Rocquencourt, BP 105, Le Chesnay Cedex, France FR-78153
Venue:
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
Year:
2008

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Abstract

This paper presents a global constraint that enforces rules written in a language based on arithmetic and first-order logic to hold among a set of objects. In a first step, the rules are rewritten to Quantifier-Free Presburger Arithmetic (QFPA) formulas. Secondly, such formulas are compiled to generators of k-dimensional forbidden sets. Such generators are a generalization of the indexicals of cc(FD). Finally, the forbidden sets generated by such indexicals are aggregated by a sweep-based algorithm and used for filtering.The business rules allow to express a great variety of packing and placement constraints, while admitting effective filtering of the domain variables of the k-dimensional object, without the need to use spatial data structures.