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

  • Mats Carlsson
  • Nicolas Beldiceanu
  • Julien Martin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5202)


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.


Geometric Constraint Global Constraint Logical Combination Business Rule Side Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Mats Carlsson
    • 1
  • Nicolas Beldiceanu
    • 2
  • Julien Martin
    • 3
  1. 1.SICSKistaSweden
  2. 2.École des Mines de Nantes, LINA UMR CNRS 6241NantesFrance
  3. 3.INRIA Rocquencourt, BP 105Le Chesnay CedexFrance

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