Principles and Practice of Constraint Programming

Volume 5202 of the series Lecture Notes in Computer Science pp 220-234

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

  • Mats CarlssonAffiliated withSICS
  • , Nicolas BeldiceanuAffiliated withÉcole des Mines de Nantes, LINA UMR CNRS 6241
  • , Julien MartinAffiliated withINRIA Rocquencourt, BP 105

* Final gross prices may vary according to local VAT.

Get Access


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.