Sweep as a Generic Pruning Technique Applied to the Non-overlapping Rectangles Constraint

  • Nicolas Beldiceanu
  • Mats Carlsson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2239)


We first presen ta generic pruning technique which aggregates several constraints sharing some variables. The method is derived from an idea called sweep which is extensively used in computational geometry. A first benefit of this technique comes from the fact that it can be applied to several families of global constraints. A second advantage is that it does not lead to any memory consumption problem since it only requires temporary memory which can be reclaimed after each invocation of the method.

We then specialize this technique to the non-overlapping rectangles constraint, describe several optimizations, and give an empirical evaluation based on six sets of test instances with different characteristics.


Computational Geometry Target Property Global Constraint Placement Problem Temporary Memory 
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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  1. 1.
    A. Aggoun and N. Beldiceanu. Extending CHIP in order to solve complex scheduling and placementproblems. Mathl. Comput. Modelling, 17(7):57–73, 1993.CrossRefGoogle Scholar
  2. 2.
    N. Beldiceanu. Global constraints as graph properties on structured network of elementary constraints of the same type. SICS Technical Report T2000/01, Swedish Institute of Computer Science, 2000.Google Scholar
  3. 3.
    N. Beldiceanu and E. Contejean. Introducing global constraints in CHIP. Mathl. Comput. Modelling, 20(12):97–123, 1994.zbMATHCrossRefGoogle Scholar
  4. 4.
    M. Carlsson, G. Ottosson, and B. Carlson. An open-ended finite domain constraint solver. In H. Glaser, P. Hartel, and H. Kucken, editors, Programming Languages: Implementations, Logics, and Programming, volume 1292 of LNCS, pages 191–206. Springer, 1997.CrossRefGoogle Scholar
  5. 5.
    F.R. du Verdier. Résolution de problèmes d’aménagement spatial fondée sur la satisfaction de contraintes. Validation sur l’implantation d’équipements électroniques hyperfréquences. PhD thesis, Université Claude Bernard-Lyon I, July 1992.Google Scholar
  6. 6.
    I. Gambini. A method for cutting squares into distinct squares. Discrete Applied Mathematics, 98(1–2):65–80, 1999.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    K. Kuchciński. Synthesis of distributed embedded systems. In Proc. 25th Euromicro Conference, Workshop on Digital System Design, Milan, Italy, 1999.Google Scholar
  8. 8.
    A. Lahrichi. Scheduling: the notions of hump, compulsory parts and their use in cumulative problems. C. R. Acad. Sci., Paris, 1982.Google Scholar
  9. 9.
    P. Martin and D.B. Shmoys. A new approach to computing optimal schedules for the job-shop scheduling problem. In Proc. of the 5th International IPCO Conference, pages 389–403, 1996.Google Scholar
  10. 10.
    K. Mehlhorn. Data Structures and Algorithms 1: Sorting and Searching. EATCS Monographs. Springer, Berlin, 1984.zbMATHGoogle Scholar
  11. 11.
    F.P. Preparata and M.I. Shamos. Computational Geometry. An Introduction. Springer, 1985.Google Scholar
  12. 12.
    H. Samet. The Design and Analysis of Spatial Data Structures. Addison-Wesley, 1989.Google Scholar
  13. 13.
    P. Van Hentenryck, V. Saraswat, and Y. Deville. Design, implementation and evaluation of the constraint language cc(FD). In A. Podelski, editor, Constraints: Basics and Trends, volume 910 of LNCS. Springer, 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Nicolas Beldiceanu
    • 1
  • Mats Carlsson
    • 1
  1. 1.SICSUPPSALASweden

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