F. Benhamou, F. Goualard, and L. Granvilliers. Programming with the DecLIC Language In proceedings of the second workshop on Interval Constraints. October 1997, Port-Jefferson, NY, USA. Home/Search Document Details and Download
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Comparing Partial Consistencies - Collavizza, Delobel, Rueher (1999) (11 citations) (Correct)
....based on a partial consistency named Arc Consistency. Assume c is a k ary constraint over variables (x 1 ; x k ) c is arc consistent if, for any value in x i , there exists at least one value in each domain x j (j 6= i) such that c holds. In the same way, many solvers over continuous domains [25, 28, 1] rely upon relaxations of Arc Consistency. A relaxation of Arc Consistency has also been used in the context of global optimization [22] 2B Consistency (also known as hull consistency) 5, 3, 14, 15] is a relaxation of Arc Consistency which only requires to check the Arc Consistency ....
....a CSP P ; C) if X X . We write P P for this relation. By convention, P ; is the smallest CSP. In the following passage, we define and discuss several kinds of consistency, and the associated filtering of a CSP P . 3. 2B Consistency Most of the CSP systems over intervals (e.g. [23, 3, 25, 1]) compute a relaxation of Arc Consistency [18] called 2B Consistency (or Hull consistency) In this section, we give the definition of 2B consistency and explain why its computation requires a relaxation of the constraint system. 3.1. Definitions 2B Consistency [15] states a local property ....
[Article contains additional citation context not shown here]
F. Benhamou, F. Goualard, and L. Granvilliers. Programming with the DecLIC Language In proceedings of the second workshop on Interval Constraints. October 1997, Port-Jefferson, NY, USA.
Chaotic Iteration for Polynomial Constraints - Monfroy (1998) (Correct)
....constraint propagation do not enforce global consistency, but local consistency (such as arc consistency [15] that approximates the global property. For solving polynomial constraints over real numbers, several consistency methods have been designed [20] In the scheme of interval constraints [13, 5, 3, 6, 21, 11, 14] propagation algorithms consist in enforcing a local consistency property during the whole reduction of CSPs (i.e. boxconsistency [5] in [23, 22] B consistency in [13] domains of variables are reduced to obtain a local property (using a single constraint or a sub set of constraints) and the ....
....designed a prototype of our solver for real constraints. Since we were more interested in the design of strategies, and in testing several domain reduction functions, we used Maple [7] as an implementation language. Hence, the performance is not really good compared to Numerica [23] and Declic [3], but we can easily and quickly compare reduction functions, and strategies for their application. We tested several domain reduction functions, based on different techniques (Taylor, Newton, but we focus here on the functions we presented in Section 4, and on the problem of getting CSPs ....
F. Benhamou, F. Goualard, and L. Granvilliers. Programming with the Declic Language. In Proceedings of the International Workshop on Interval Constraints, pages 1--13, Port Jefferson, USA, 1997.
Using "Weaker" Functions for Constraint Propagation over Real.. - Monfroy (1999) (1 citation) (Correct)
....constraint propagation do not enforce global consistency, but local consistency (such as arc consistency [14] that approximates the global property. For solving polynomial constraints over real numbers, several consistency methods have been designed [17] In the scheme of interval constraints [12, 4, 5, 18, 10, 13] propagation algorithms consist in enforcing a local consistency property during the whole reduction of CSPs (i.e. boxconsistency in [20, 19] B consistency in [12] domains of variables are reduced to obtain a local property and the modifications are propagated till a fixed point is reached. ....
F. Benhamou, F. Goualard, and L. Granvilliers. Programming with the Declic Language. In Proceedings of the International Workshop on Interval Constraints, pages 1--13, Port Jefferson, USA, 1997.
Comparing Partial Consistencies - Collavizza, Delobel, Rueher (1999) (11 citations) (Correct)
....on a partial consistency named Arc Consistency. Assume c is a k ary constraint over variables (x 1 ; x k ) c is arc consistent if, for any value in x i , there exists at least one value in each domain x j (j 6= i) such that c holds. In the same way, many solvers over continuous domains [25, 28, 1] rely upon relaxations of Arc Consistency. A relaxation of Arc Consistency has also been used in the context of global optimization [22] 2B Consistency (also known as hull consistency) 5, 3, 14, 15] is a relaxation of Arc Consistency which only requires to check the Arc Consistency property ....
....P 0 = X 0 ; C) if X 0 X. We write P P 0 for this relation. By convention, P ; is the smallest CSP. In the following passage, we define and discuss several kinds of consistency, and the associated filtering of a CSP P . 3. 2B Consistency Most of the CSP systems over intervals (e.g. [23, 3, 25, 1]) compute a relaxation of Arc Consistency [18] called 2B Consistency (or Hull consistency) In this section, we give the definition of 2B consistency and explain why its computation requires a relaxation of the constraint system. 3.1. Definitions 2B Consistency [15] states a local property on ....
[Article contains additional citation context not shown here]
F. Benhamou, F. Goualard, and L. Granvilliers. Programming with the DecLIC Language In proceedings of the second workshop on Interval Constraints. October 1997, Port-Jefferson, NY, USA.
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