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. © 2008 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Carlsson, M., Beldiceanu, N., & Martin, J. (2008). A geometric constraint over k-dimensional objects and shapes subject to business rules. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5202 LNCS, pp. 220–234). https://doi.org/10.1007/978-3-540-85958-1_15
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