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)

Abstract

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Fages, F., Martin, J.: From rules to constraint programs with the Rules2CP modelling language. Research Report RR-6495, INRIA Rocquencourt (2008)Google Scholar
  2. 2.
    Beldiceanu, N., Contejean, E.: Introducing global constraints in CHIP. Mathl. Comput. Modelling 20(12), 97–123 (1994)MATHCrossRefGoogle Scholar
  3. 3.
    Beldiceanu, N., Carlsson, M., Poder, E., Sadek, R., Truchet, C.: A generic geometrical constraint kernel in space and time for handling polymorphic k-dimensional objects. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 180–194. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Benedetti, M., Lallouet, A., Vautard, J.: QCSP made practical by virtue of restricted quantification. In: IJCAI 2007, Proceedings of the 20th International Joint Conference on Artificial Intelligence, pp. 38–43 (2007)Google Scholar
  5. 5.
    Van Hentenryck, P., Saraswat, V., Deville, Y.: Constraint processing in cc(FD). Computer Science Department, Brown University (unpublished manuscript) (1991)Google Scholar
  6. 6.
    Beldiceanu, N., Carlsson, M., Martin, J.: A geometric constraint over k-dimensional objects and shapes subject to business rules. SICS Technical Report T2008:04, Swedish Institute of Computer Science (2008)Google Scholar
  7. 7.
    Van Hentenryck, P., Deville, Y.: The cardinality operator: a new logical connective in constraint logic programming. In: Int. Conf. on Logic Programming (ICLP 1991). MIT Press, Cambridge (1991)Google Scholar
  8. 8.
    Eén, N., Sörensson, N.: Translating pseudo-boolean constraints into SAT. Journal on Satisfiability, Boolean Modeling and Computation 2, 1–25 (2006)MATHGoogle Scholar
  9. 9.
    Ganesh, V., Berezin, S., Hill, D.L.: Deciding presburger arithmetic by model checking and comparisons with other methods. In: Aagaard, M.D., O’Leary, J.W. (eds.) FMCAD 2002. LNCS, vol. 2517, pp. 171–186. Springer, Heidelberg (2002)Google Scholar
  10. 10.
    Pugh, W.: The Omega test: a fast and practical integer programming algorithm for dependence analysis. In: Supercomputing, pp. 4–13 (1991)Google Scholar
  11. 11.
    Lhomme, O.: Arc-consistency filtering algorithms for logical combinations of constraints. In: Régin, J.-C., Rueher, M. (eds.) CPAIOR 2004. LNCS, vol. 3011, pp. 209–224. Springer, Heidelberg (2004)Google Scholar
  12. 12.
    Codognet, P., Diaz, D.: Compiling constraints in clp(FD). Journal of Logic Programming 27(3), 185–226 (1996)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Carlsson, M., Ottosson, G., Carlson, B.: An open-ended finite domain constraint solver. In: Glaser, H., Hartel, P., Kuchen, H. (eds.) PLILP 1997. LNCS, vol. 1292, pp. 191–206. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  14. 14.
    Carlson, B.: Compiling and Executing Finite Domain Constraints. PhD thesis, Uppsala University (1995)Google Scholar
  15. 15.
    Tack, G., Schulte, C., Smolka, G.: Generating propagators for finite set constraints. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 575–589. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  16. 16.
    Cheng, K.C.K., Lee, J.H.M., Stuckey, P.J.: Box constraint collections for adhoc constraints. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 214–228. Springer, Heidelberg (2003)Google Scholar
  17. 17.
    Harvey, W., Stuckey, P.J.: Constraint representation for propagation. In: Maher, M.J., Puget, J.-F. (eds.) CP 1998. LNCS, vol. 1520, pp. 235–249. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  18. 18.
    Bacchus, F., Walsh, T.: Propagating logical combinations of constraints. In: IJCAI 2005, Proceedings of the 19th International Joint Conference on Artificial Intelligence, pp. 35–40 (2005)Google Scholar
  19. 19.
    Carlsson, M., et al.: SICStus Prolog User’s Manual, 4th edn. Swedish Institute of Computer Science, pp. 91–630 (2007) ISBN 91-630-3648-7 Google Scholar

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

Personalised recommendations