Advertisement

Constraints

, Volume 19, Issue 3, pp 309–337 | Cite as

The octagon abstract domain for continuous constraints

  • Marie Pelleau
  • Charlotte Truchet
  • Frédéric Benhamou
Article

Abstract

Domains in continuous constraint programming are generally represented with intervals whose n-ary Cartesian product (box) approximates the solution space. In this article, we generalize this representation and propose a generic solver where other domains representations can be used. In this framework, we define a new representation for continuous domains based on octagons. We generalize local consistency and split to this octagon representation. Experimental results show promising performance improvements on several classical benchmarks.

Keywords

Continuous constraints Octagonal domains Abstract domains Generic solver 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Apt, K.R. (1999). The essence of constraint propagation. Theoretical Computer Science, 221.Google Scholar
  2. 2.
    Araya, I., Trombettoni, G., Neveu, B. (2010). Exploiting monotonicity in interval constraint propagation. In Proceedings of the 24th AAAI conference on artificial intelligence. AAAI.Google Scholar
  3. 3.
    Benhamou, F. (1996). Heterogeneous constraint solvings. In Proceedings of the 5th international conference on algebraic and logic programming (pp. 62–76).Google Scholar
  4. 4.
    Benhamou, F., Goualard, F., Granvilliers, L., Puget, J.F. (1999). Revisiting hull and box consistency. In Proceedings of the 16th international conference on logic programming (pp. 230–244).Google Scholar
  5. 5.
    Chabert, G., & Jaulin, L. (2009). Contractor programming. Artificial Intelligence, 173, 1079–1100.CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Chen, L., Miné, A., Wang, J., Cousot, P. (2009). Interval polyhedra: An abstract domain to infer interval linear relationships. In Proceedings of the 16th international static analysis symposium (SAS’09) (pp. 309–325).Google Scholar
  7. 7.
    Cousot, P., & Cousot, R. (1976). Static determination of dynamic properties of programs. In Proceedings of the 2nd international symposium on programming (pp. 106–130).Google Scholar
  8. 8.
    Dechter, R., Meiri, I., Pearl, J. (1989). Temporal constraint networks. In Proceedings of the first international conference on principles of knowledge representation and reasoning.Google Scholar
  9. 9.
    Floyd, R. (1962). Algorithm 97: shortest path. Communications of the ACM, 5(6).Google Scholar
  10. 10.
    Goldberg, D. (1991). What every computer scientist should know about floating point arithmetic. ACM Computing Surveys, 23(1), 5–48.CrossRefGoogle Scholar
  11. 11.
    Goldsztejn, A., & Granvilliers, L. (2010). A new framework for sharp and efficient resolution of ncsp with manifolds of solutions. Constraints, 15(2), 190–212.CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Menasche. M., & Berthomieu, B. (1983). Time petri nets for analyzing and verifying time dependent communication protocols. In Protocol specification, testing, and verification.Google Scholar
  13. 13.
    Miné, A. (2004). Domaines numériques abstraits faiblement relationnels. Ph.D. thesis, École Normale Supérieure.Google Scholar
  14. 14.
    Miné, A. (2006). The octagon abstract domain. Higher-Order and Symbolic Computation, 19(1), 31–100.CrossRefzbMATHGoogle Scholar
  15. 15.
    Régin, J.C., & Rueher, M. (2005). Inequality-sum : a global constraint capturing the objective function: RAIRO Operations Research.Google Scholar
  16. 16.
    Rossi, F., van Beek, P., Walsh, T. (2006). Handbook of constraint programming (Foundations of Artificial Intelligence). Elsevier.Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Marie Pelleau
    • 1
  • Charlotte Truchet
    • 1
  • Frédéric Benhamou
    • 1
  1. 1.LINA, UMR CNRS 6241Université de Nantes, FranceNantesFrance

Personalised recommendations