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.




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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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