J.-F. Puget. A fast algorithm for the bound consistency of alldi# constraints. In Proceedings of the AAAI '98, pages 359--366, 1998.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....propagation over domain propagation may not seem significant, for more complex constraints there can be significant di#erences in e#ciency of domain and bounds propagation. For example, domain propagation for alldifferent on n variables is O(n 2. 5 ) 16] while bounds propagation is O(n log n) [15] and even O(n) in common cases [13] Similarly, domain propagation for a linear equation on n variables is exponential while bounds propagation is O(n) In this paper we investigate when bounds and domain propagation will lead to the same search space. The contributions of this paper are: We ....

....for CLP(FD) programs that determines where we can replace domain propagators with bounds propagators without increasing the search space. We show examples where our analysis detects search space equivalent replacements and show the possible performance benefits that arise. Previous authors [13, 15] have noted the di#erence in e#ciency in bounds and domain propagation, for particular primitive constraints but not considered when di#erent propagators lead to the same search space. The closest related work is that of Harvey and Stuckey [7] who consider the relative propagation strengths of ....

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J.-F. Puget. A fast algorithm for the bound consistency of alldi# constraints. In Proceedings of the 15th National Conference on Artificial Intelligence (AAAI-98), pages 359--366, Madison, WI, USA, July 1998. AAAI Press/The MIT Press.

....is the alldifferent constraint, which states that all variables in this constraint must be pairwise di#erent. In Example 1, a scheduling problem is modeled using the alldifferent constraint. Example 1 (Scheduling of speeches) Consider the following simple scheduling problem, adapted from Puget [17], where a set of speeches must be scheduled during one day. Each speech lasts exactly one hour (including questions and a co#ee break) and only one conference room is available. Furthermore, each speaker has other commitments, and is available only for a limited fraction of the day. A particular ....

....) whereas the hyper arc consistency algorithms are around O(dn 1. 5 ) where d is the maximum cardinality of the domains and n is the number of variables involved [12, 18] Nevertheless, this filtering algorithm applies quite well to several problems, such as the n queens problem (n 200) [12, 17]. Other work on the comparison of the alldifferent constraints and the corresponding decomposition has for instance been done in [20] and [8] 4 Bound Consistency The notion of bound consistency for the alldifferent constraint was introduced by Puget [17] We summarize his method in this ....

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J.-F. Puget. A fast algorithm for the bound consistency of alldi# constraints. In Proceedings of the AAAI '98, pages 359--366, 1998.

....(see e.g. 2] for an overview) Special algorithms were being developed that are able to exploit the global information of the constraints. For the alldifferent constraint at least five di#erent filtering algorithms exist, each achieving a di#erent kind of consistency, or achieving it faster [28, 20, 26, 23]. Although the constraint is mentioned more or less deeply in a variety of papers and books (e.g. 27, 15, 22] to our knowledge there is no work that collects all e#ort that has been put into this constraint. This paper therefore tries to give an overview of the alldifferent constraint, which ....

....O(n whereas the hyper arc consistency algorithms are around O(dn 1. 5 where d is the maximum cardinality of the domains and n is the number of variables involved [20, 28] Nevertheless, this filtering algorithm applies quite well to several problems, such as the n queens problem (n 200) [20, 26]. Other work on the comparison of the alldifferent constraints and the corresponding decomposition has for instance been done in [31] and [11] 4.2. Bounds consistency The notion of bounds consistency for the alldifferent constraint was introduced by Puget [26] We summarize his method in this ....

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J.-F. Puget. A fast algorithm for the bound consistency of alldi# constraints. In Proceedings of the Fifteenth National Conference on Artificial Intelligence (AAAI '98), pages 359 -- 366, 1998.

....to make a gcc locally consistent. The ubc is a generalization of the well studied alldi erent constraint (in the alldi erent constraint u v = 1, for each value v) Some previous algorithms for bounds consistency of the alldi erent constraint have been based on the concept of Hall intervals [3, 5, 6]. A Hall interval is an interval H D such that there are jHj variables whose domains are contained in H. The de nition of a Hall interval can be generalized to sets by using the notion of maximal capacity. Let C(S) S D, be the number of variables whose domains are contained in S. The maximal ....

....operation using the interval union nd data structure [2] Using the same 1 1 2 3 N . 1 1 2 3 N N . NewMin[1] 2 NewMin[2] 1 NewMin[3] 3 . 1 1 2 3 4 1 . N . NewMin[5] 4 NewMin[6] 4 Fig. 1. Trace of Algorithm 1 data structure for the failure ags, the stable sets Stable, and the potential stable sets PS the algorithm takes O(t jXj) steps. Although the interval union nd data structure gives the best theoretical time complexity, we found that it did not result in the ....

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J.-F. Puget. A fast algorithm for the bound consistency of alldi constraints. In AAAI-1998, pages 359-366.

....on relating alldi#erent constraints to matchings (see the next section for the definitions of the di#erent forms of consistency) Leconte [4] gives an O(n ) algorithm for range consistency, a weaker form of consistency than domain consistency, that is based on identifying Hall intervals. Puget [7], building upon the work of Leconte [4] gives an O(n log n) # School of Computer Science, University of Waterloo, 200 University Ave. W. N2L 3G1, Waterloo, Ontario, Canada, e mail: alopez o,cquimper,vanbeek uwaterloo.ca. CWI, P.O. Box 94079, 1090 GB Amsterdam, Netherlands, e mail: ....

....in C. ii) range consistent if for each x dom(x) has an interval support in C. iii) domain consistent if for each x dom(x) has a domain support in C. A CSP can be made locally consistent by repeatedly removing unsupported values from the domains of its variables. Example 1 (Puget [7]) Consider the CSP with six variables x 1 , x 6 ; with the following domains, x 1 [3, 6] and x 6 [1, 6] and a single constraint alldi#erent(x 1 , x 6 ) Enforcing bounds consistency on the constraint reduces the domains of the variables as follows: x 1 ....

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J.-F. Puget. A fast algorithm for the bound consistency of alldi# constraints. In Proceedings of the Fifteenth National Conference on Artificial Intelligence, pages 359--366, Madison, Wisconsin, 1998. 13

....to make a gcc locally consistent. The ubc is a generalization of the well studied alldi#erent constraint (in the alldi#erent constraint u v = 1, for each value v) Some previous algorithms for bounds consistency of the alldi#erent constraint have been based on the concept of Hall intervals [3, 5, 6]. A Hall interval is an interval H D such that there are H variables whose domains are contained in H . The definition of a Hall interval can be generalized to sets by using the notion of maximal capacity. Let C(S) S D, be the number of variables whose domains are contained in S. The ....

....for domain consistency which runs in O( D X ) 8] 6 Experimental Results We implemented our new bounds consistency algorithm for the generalized cardinality constraint (denoted hereafter as BC) using the ILOG Solver C library, Version 4. 2 [4] Following a suggestion by Puget [6] adapted to the gcc, the range of applicability of BC can be extended by combining bounds consistency with the removal of a value when the number of times it has been assigned reaches its upper bound (denoted BC ) The ILOG Solver library already provides implementations of Regin s [8] domain ....

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J.-F. Puget. A fast algorithm for the bound consistency of alldi# constraints. In AAAI-1998, pages 359--366.

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J.-F. Puget. A fast algorithm for the bound consistency of alldi# constraints. In Proceedings of the AAAI '98, pages 359--366, 1998.

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J.-F. Puget. A fast algorithm for the bound consistency of alldi# constraints. In Proceedings of the fifteenth national/tenth conference on Artificial intelligence /Innovative applications of artificial intelligence, pages 359--366, July 1998.

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Puget, J.-F. 1998. A fast algorithm for the bound consistency of alldi# constraints. Proceedings of AAAI-98 . 359--366.

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J.-F. Puget. A fast algorithm for the bound consistency of alldi constraints. In Proceedings of the fteenth national/tenth conference on Arti cial intelligence /Innovative applications of arti cial intelligence, pages 359-366, July 1998.

No context found.

J.-F. Puget. A fast algorithm for the bound consistency of alldi constraints. In Proceedings of the fteenth national/tenth conference on Arti cial intelligence /Innovative applications of arti cial intelligence, pages 359-366, July 1998.

No context found.

J.-F. Puget. A fast algorithm for the bound consistency of alldi# constraints. In AAAI-1998, pages 359--366.

No context found.

Puget, J.-F. A fast algorithm for the bound consistency of alldi# constraints. In Proceedings of the National Conference on Artificial Intelligence (AAAI98) (Menlo Park, 1998), AAAI Press, pp. 359--366.

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