An analysis of arithmetic constraints on integer intervals

Constraints

Volumn 12, Issue 4, 2007, Pages 429-468

  Apt, Krzysztof R ^a,b   Zoeteweij, Peter ^c  

^a CWI   (Netherlands)

^b UNIVERSITY OF AMSTERDAM   (Netherlands)

^c Department of Microelectronics   (Netherlands)

Author keywords

Arithmetic constraints; Constraint propagation; Integer interval arithmetic; Local consistency

Indexed keywords

INTEGER PROGRAMMING; MATHEMATICAL MODELS; PROBLEM SOLVING; THEOREM PROVING;

ARITHMETIC CONSTRAINTS; CONSTRAINT PROPAGATION; INTEGER INTERVAL ARITHMETIC; LOCAL CONSISTENCY;

CONSTRAINT THEORY;

EID: 35148880243     PISSN: 13837133     EISSN: 15729354     Source Type: Journal    
DOI: 10.1007/s10601-007-9017-9     Document Type: Article

References (24)

1. K. R. Apt 1998 A proof theoretic view of constraint programming Fundamenta Informaticae 33 3 263 293 Available via http://arXiv.org/archive/cs/
2. Apt, K. R. (1998). A proof theoretic view of constraint programming. Fundamenta Informaticae, 33(3), 263-293. Available via http://arXiv.org/archive/ cs/.
3. Apt, K. R. (2003). Principles of constraint programming. Cambridge: Cambridge University Press.
4. Apt, K. R., & Zoeteweij, P. (2004). A comparative study of arithmetic constraints on integer intervals. In K. R. Apt, F. Fages, F. Rossi, P. Szeredi, & J. Váncza (Eds.), Recent advances in constraints. Lecture notes in artificial intelligence, vol. 3010, pp. 1-24. Available via http://xxx.lanl.gov/abs/cs.DS/0403016.
5. Benhamou, F., Goualard, F., Granvilliers, L., & Puget, J.-F. (1999). Revising hull and box consistency. In Proceedings of the 16th International Conference on Logic Programming (ICLP'99), pp. 230-244. MIT Press.
6. Benhamou, F., McAllester, D., & Van Hentenryck, P. (1994). CLP(intervals) revisited. In Proceedings of the 1994 International Symposium on Logic programming, pp. 124-138. MIT Press.
7. Benhamou, F., & Older, W. J. (1997). Applying interval arithmetic to real, integer, and Boolean constraints. Journal of Logic Programming, 32(1), 1-24.
8. e : a tutorial introduction. Available from http://www.eclipse-clp.org/.
9. Codognet, P., & Diaz, D. (1996). Compiling constraints in clp(fd). Journal of Logic Programming, 27(3), 185-226.
10. Collaviza, H., Delobel, F., & Rueher, M. (1999). Comparing partial consistencies. Reliable Computing, 5(3), 213-228.
11. Dubrovsky, V., & Shvetsov, A. (1995). Quantum Cyberteaser. Available from http://www.nsta.org/quantum/kyotoarc.asp, (May/June).
12. GNU MP: The GNU Multiple Precision Library (2006). Edition 4.2.1. Available from http://www.gmplib.org, (September).
13. Goualard, F., & Granvilliers, L. (2005). Controlled propagation in continuous numerical constraint networks. In Proceedings of the 2005 ACM Symposium on Applied Computing, pp. 377-382. ACM Press.
14. Granvilliers, L. (2004). RealPaver user's manual: Solving nonlinear constraints by interval computations. Edition 0.4, for RealPaver Version 0.4. Available from http://sourceforge.net/projects/realpaver, (August).
15. Harvey, W., & Stuckey, P. J. (2003). Improving linear constraint propagation by changing constraint representation. Constraints, 8(2), 173-207.
16. Hickey, T. J., Ju, Q., & Van Emden M. H. (2001). Interval arithmetic: From principles to implementation. Journal of the ACM, 48(5), 1038-1068.
17. Marriott, K., & Stuckey, P. (1998). Programming with constraints: An introduction. Cambridge, MA: MIT Press.
18. Moore, R. E. (1966). Interval analysis. Englewood Cliffs, NJ: Prentice-Hall.
19. Ratz, D. (1996). Inclusion isotone extended interval arithmetic: A toolbox update. Technical Report D-76128, University of Karlsruhe.
20. Schulte, C., & Smolka, G. (2002). Finite domain constraint programming in Oz. A tutorial. Available from http://www.mozart-oz.org/ documentation/fdt/, Version 1.3.1 (20040616), (August).
21. Schulte, C., & Stuckey, P. J. (2005). When do bounds and domain propagation lead to the same search space? Transactions on Programming Languages and Systems, 27(3), 388-425.
22. Van Hentenryck, P., Michel, L., & Deville, Y. (1997). Numerica: A modeling language for global optimization. Cambridge, MA: MIT Press.
23. Wallace, R. J., & Freuder, E. F. (1992). Ordering heuristics for arc consistency algorithms. Available from http://4c.ucc.ie/web/pubs.jsp.
24. Zoeteweij, P. (2003). Opensolver: A coordination-enabled abstract branch-and-prune tree search engine (abstract). In F. Rossi (Ed.), Proceedings of CP 2003. LNCS, vol. 2833, p. 1002. Springer.