F. Benhamou and F. Goualard. Universally quantified interval constraints. In Proc. of the Sixth Intl. Conf. on Principles and Practice of Constraint Programming (CP'2000), number 1894 in LNCS, Singapore, 2000. Springer Verlag. Home/Search Document Details and Download
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Clustering for Disconnected Solution Sets of Numerical CSPs - Vu, Sam-Haroud, Faltings (2003) (Correct)
....of the reals. The real set, R, is in practice approximated by a finite set = F# #, # , where F is a finitely many set of reals usually corresponding to the floating point numbers. In this paper, we restrict the notion of interval to refer to real intervals no matter they are open or closed [11]. The set of intervals , denoted by I, is partially ordered by the relation on reals. Our previous results in [12, 13] can be easily extended to accept this notion. An interval box, or a box for short, B = I 1 . I n is a Cartesian product of n intervals in I. The projection of B on ....
....may consider the computation of inner and outer approximations in the form of unions of disjoint boxes, they are therefore called the inner and outer union approximations [12, 13] respectively. Various dichotomous techniques were described in [14] to compute outer union approximations. Recently, [11] has computed inner union approximations for universally quantified constraints by using the negation test, 15] has used the negation test in combination with enhanced splitting strategies to compute outer union approximations for NCSPs. Finally, the work in [12, 13] gives an improvement on the ....
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Benhamou, F., Goualard, F.: Universally Quantified Interval Constraints. In: Proceedings of the 6th International Conference on Principles and Practice of Constraint Programming (CP'2000). (2000) 67--82
Numerical Constraint Satisfaction Problems with.. - Vu, Sam-Haroud, Silaghi (2002) (1 citation) (Correct)
....in covering the spectrum of non isolated solutions using a reduced number of subsets of R . Usually, these subsets are chosen with known and simple properties (e.g. interval boxes, polytopes, ellipsoids) In recent years, several authors have proposed set covering algorithms with interval boxes [7 10]. Most existing box covering algorithms are however limited by their restrictive applicability conditions or by their high average time and space complexities in the general case. The enhanced set based technique we propose builds on the following observations. Firstly, the union of boxes produced ....
....not the most adapted branching strategy. It might lead to unnecessarily dividing entirely feasible regions. We propose to use another scheme based on splitting around the negation of feasible regions [4] which is an extension of the negation test proposed for universally quantified constraints in [10]. The resulting algorithm applies to general constraint systems. It produces inner and outer approximations of the feasible sets in the form of unions of interval boxes. The preliminary experiments show that it improves efficiency as well as the compactness and quality of the output ....
[Article contains additional citation context not shown here]
Benhamou, F., Goualard, F.: Universally Quantified Interval Constraints. In: Proceedings of the 6th International Conference on Principles and Practice of Constraint Programming (CP'2000). (2000) 67--82
Beyond NP: Arc-Consistency for Quantified Constraints - Bordeaux, Monfroy (2002) (2 citations) (Correct)
.... of first order, real valued constraints is indeed very di#erent from the discrete constraints discussed in this paper, since the problem is not even solvable in exponential time (at least to our knowledge) Nevertheless, recent e#ort to mix these techniques with continuous constraint satisfaction [4, 17] could help bridging the two research areas. In particular, the relaxed problem of solving quantified equations over the finite precision approximations of the real numbers induced by the floating point machine representation is obviously in PSPACE, and hence closer to our concerns. Last, ....
F. Benhamou and F. Goualard. Universally quantified interval constraints. In Proc. of the 6th Int. Conf. on Principles and Practice of Constraint Programming (CP), LNCS, pages 67--82, Singapore, 2000. Springer.
Approximation Techniques for Non-linear Problems with.. - Vu, Sam-Haroud, Silaghi (2002) (Correct)
....when applied to our target problems, the approximations they provide for the complete solution set are, in most cases, prohibitively verbose. As an example, let us consider the following NCSP with four non linear inequality constraints and three variables: P3 = z, xz [ 10, 10] . Using an efficient implementation of classical point wise techniques, the computation had to be stopped after 1 hour and produced more than 90000 small boxes. natural alternative to the point wise approach is to try to cover the spectrum of nonisolated solutions using a reduced number of ....
....cover the spectrum of nonisolated solutions using a reduced number of subsets from IR . Usually, these subsets are chosen with known and simple properties (e.g. interval boxes, polytopes, ellipsoids) 7] In recent years, several authors have proposed set covering algorithms with interval boxes [7 10]. These algorithms are based on domain splitting and have one of the following limitations: they are designed for inequality constraints only [8 10] they only apply to polynomials [9] they uniformly enforce dichotomous splitting on all variables [7] Moreover, most of these techniques produce ....
[Article contains additional citation context not shown here]
Benhamou, F., Goualard, F.: Universally Quantified Interval Constraints. In: Proceedings of the 6 th International Conference on Principles and Practice of Constraint Programming (CP'2000). (2000) 67--82
Continuous First-Order Constraint Satisfaction with Equality and .. - Ratschan (2002) (2 citations) (Correct)
....for certain applications, they still su#er from problems such as unwieldy output expressions, and restriction to addition and multiplication, small number of variables and small polynomial degrees. By using interval constraint satisfaction techniques one can at least relieve some of these problems [2, 28, 29, 27]. Existence proofs for systems of equations based on interval arithmetic have been studied in detail by interval analysis [25, 16] The usual case studied has a 0 dimension solution set. Branch and bound algorithms are used to search the solution space, variants of Newton s methods are used to ....
.... The idea to apply interval techniques to real first order constraints is according to Hong [12] They also have been used for solving special cases occurring in engineering applications [13, 20] Constraint satisfaction techniques have been used for the special case with one universal quantifier [2], and for the general case [29] The content of the paper is as follows: In Section 2 we introduce the necessary preliminaries; in Section 3 we describe the main idea in an informal style; in Section 4 we give the formal details; in Section 5 we show how to use the introduced techniques within ....
[Article contains additional citation context not shown here]
F. Benhamou and F. Goualard. Universally quantified interval constraints. In Proc. of the Sixth Intl. Conf. on Principles and Practice of Constraint Programming (CP'2000), number 1894 in LNCS, Singapore, 2000. Springer Verlag.
Exploiting Solution Clusters for Coarse-Grained Distributed Search - Parkes (2001) (Correct)
....before in other contexts. Firstly, a group of solutions is naturally more robust than a single solution and so has is useful for problems with uncertainty [7] Secondly, in problems with continuous variables then solutions are described by interval constraints on variables rather than equalities [13, 12, 1] and so solutions are naturally groups of solutions rather akin to a pure cluster, but containing an infinite number of distinct models. Possibly our work on impure clusters and distributed search is also applicable to numerical CSPs, or could benefit from the existing work in that area. 6. ....
Frederic Benhamou and Frederic Goualard. Universally quantified interval constraints. In Rina Dechter, editor, proceedings of the Sixth International Conference on Principles and Practice of Constraint Programming (CP'2000). Lecture Notes in Computer Science vol. 1894, pages 67--82. SpringerVerlag, 2000.
Search Techniques for Non-Linear Constraint.. - Silaghi, Sam-Haroud.. (2001) (Correct)
....the inequalities express a set of equally relevant choices, as for example the possible moving areas for a mobile robot. In that case it is desirable to cover the large number of point wise alternatives expressed by the constraints using a reduced number of sets, as interval boxes. Several authors [2, 1, 7] have proposed set covering algorithms specific to inequality systems. In this paper we propose a lookahead backtracking algorithm for inequality and mixed equality inequality constraints. The proposed technique combines a set covering strategy for inequalities with classical interval search ....
....the spectrum of solutions for inequalities using a reduced number of subsets from IR . Usually, these subsets are chosen with known and simple properties (interval boxes, polytopes, ellipsoid, 5] In recent years, several authors have proposed set covering algorithms with intervals boxes [5, 2, 7, 1]. These algorithms, except for [5] are designed for inequality systems 1 , are based on domain splitting and have one of the two following limitations. Either the constraint system is handled as an indivisible whole 2 , or the splits are performed statically which means that their results are ....
[Article contains additional citation context not shown here]
F. Benhamou and F. Goualard. Universally quantified interval constraints. In Procs. of CP'2000, pages 67--82, 2000.
Computing, 8(1):21-42, 2002. [18] Stefan Ratschan. Quantified.. - Ratschan (2002) Self-citation (Benhamou) (Correct)
....2001. Draft. 2 Bibliography Stefan Ratschan http: www.risc.uni linz.ac.at people sratscha December 12, 2001 1 Interval Methods . Pruning with decomposing: 4, 11, 12] Pruning without decomposing: 9, 2, 8] First order constraints: Special Cases: [10, 14, 3] General Case: 17, 15] Termination Numerical Stability: 18, 16] 2 Symbolic Methods Decidability: 19] Virtual substitution of parametrized test points: 20, 13, 22, 21] Quantifier elimination by cylindrical algebraic decomposition: 6, 1, 7] ....
Frederic Benhamou and Frederic Goualard. Universally quantified interval constraints. In Proc. of the Sixth Intl. Conf. on Principles and Practice of Constraint Programming (CP'
Real First-Order Inequality Constraints Are - Stable With Probability (Correct)
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F. Benhamou and F. Goualard. Universally quantified interval constraints. In Proc. of the Sixth Intl. Conf. on Principles and Practice of Constraint Programming (CP'2000), number 1894 in LNCS, Singapore, 2000. Springer Verlag.
A Constraint-Propagation Approach to Quantified Constraints - Bordeaux (Correct)
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F. Benhamou and F. Goualard. Universally quantified interval constraints. In Proc. of the 6th Int. Conf. on Principles and Practice of Constraint Programming (CP), LNCS, pages 67--82, Singapore, 2000. Springer.
Continuous First-Order Constraint Satisfaction - With Equality And (Correct)
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F. Benhamou and F. Goualard. Universally quantified interval constraints. In Proc. of the Sixth Intl. Conf. on Principles and Practice of Constraint Programming (CP'2000), number 1894 in LNCS, Singapore, 2000. Springer Verlag.
Solving Existentially Quantified Constraints with One Equality.. - Ratschan (Correct)
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F. Benhamou and F. Goualard. Universally quantified interval constraints. In Proc. of the Sixth Intl. Conf. on Principles and Practice of Constraint Programming (CP'2000), number 1894 in LNCS, Singapore, 2000. Springer Verlag.
Continuous First-Order Constraint Satisfaction - Stefan Ratschan Institut (2002) (2 citations) (Correct)
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F. Benhamou and F. Goualard. Universally quantified interval constraints. In Proc. of the Sixth Intl. Conf. on Principles and Practice of Constraint Programming (CP'2000), number 1894 in LNCS, Singapore, 2000. Springer Verlag.
A Comparison of Complete Global - Optimization Solvers Arnold (Correct)
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F. Benhamou and F. Goualard, Universally Quantified Interval Constraints. In Proceedings of the 6th International Conference on Principles and Practice of Constraint Programming (CP'2000.
Certainty Closure - Reasoning About Constraint Problems.. - Yorke-Smith, Gervet (Correct)
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F. Benhamou and F. Goualard. Universally quantified interval constraints. In CP-2000.
Using Directed Acyclic Graphs to Coordinate Propagation.. - Vu, Schichl, Sam-Haroud (2004) (Correct)
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Benhamou, F., Goualard, F.: Universally Quantified Interval Constraints. In: Proceedings of the 6th International Conference on Principles and Practice of Constraint Programming (CP'2000). (2000) 67--82
On Constraint Problems with Incomplete - Or Erroneous Data (Correct)
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Benhamou, F. and Goualard, F. Universally quantified interval constraints. In: CP-2000.
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