Abstract
We prove that hull consistency for a system of equations or inequalities can be achieved in polynomial time providing that the underlying functions are monotone with respect to each variable. This result holds including when variables have multiple occurrences in the expressions of the functions, which is usually a pitfall for interval-based contractors. For a given constraint, an optimal contractor can thus be enforced quickly under monotonicity and the practical significance of this theoretical result is illustrated on a simple example.
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References
Alefeld, G., Mayer, G.: Interval Analysis: Theory and Applications. J. Comput. Appl. Math. 121(1-2), 421–464 (2000)
Benhamou, F., Goualard, F., Granvilliers, L., Puget, J.-F.: Revising Hull and Box Consistency. In: ICLP, pp. 230–244 (1999)
Benhamou, F., Granvilliers, L.: Continuous and interval constraints. In: Handbook of Constraint Programming, ch. 16, pp. 571–604. Elsevier, Amsterdam (2006)
Benhamou, F., McAllester, D., Van Hentenryck, P.: CLP(intervals) revisited. In: International Symposium on Logic programming, pp. 124–138. MIT Press, Cambridge (1994)
Benhamou, F., Older, W.J.: Applying Interval Arithmetic to Real, Integer and Boolean Constraints. Journal of Logic Programming 32, 1–24 (1997)
Cleary, J.G.: Logical Arithmetic. Future Computing Systems 2(2), 125–149 (1987)
Collavizza, H.: A Note on Partial Consistencies over Continuous Domains Solving Techniques. In: Maher, M.J., Puget, J.-F. (eds.) CP 1998. LNCS, vol. 1520, pp. 147–161. Springer, Heidelberg (1998)
Delobel, F., Collavizza, H., Rueher, M.: Comparing Partial Consistencies. Reliable Computing 5(3), 213–228 (1999)
Granvilliers, L., Benhamou, F.: Progress in the Solving of a Circuit Design Problem. Journal of Global Optimization 20(2), 155–168 (2001)
Hansen, E.R.: Global Optimization using Interval Analysis. Marcel Dekker, New York (1992)
Hyvönen, E.: Constraint Reasoning Based on Interval Arithmetic. In: IJCAI, pp. 1193–1198 (1989)
Hyvönen, E.: Constraint Reasoning Based on Interval Arithmetic—The Tolerance Propagation Approach. Artificial Intelligence 58, 71–112 (1992)
Jaulin, L., Kieffer, M., Didrit, O., Walter, E.: Applied Interval Analysis. Springer, Heidelberg (2001)
Kreinovich, V., Lakeyev, A., Rohn, J., Kahl, P.: Computational complexity and feasibility of data processing and interval computations. Kluwer, Dordrecht (1997)
Lhomme, O.: Consistency Techniques for Numeric CSPs. In: IJCAI, pp. 232–238 (1993)
Moore, R.: Interval Analysis. Prentice-Hall, Englewood Cliffs (1966)
Older, W.J., Vellino, A.: Extending Prolog with Constraint Arithmetic on Real Intervals. In: IEEE Canadian Conf. on Elec. and Comp. Engineering (1990)
Van Hentenryck, P., McAllester, D., Kapur, D.: Solving Polynomial Systems Using a Branch and Prune Approach. SIAM J. Numer. Anal. 34(2), 797–827 (1997)
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Chabert, G., Jaulin, L. (2009). Hull Consistency under Monotonicity. In: Gent, I.P. (eds) Principles and Practice of Constraint Programming - CP 2009. CP 2009. Lecture Notes in Computer Science, vol 5732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04244-7_17
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DOI: https://doi.org/10.1007/978-3-642-04244-7_17
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