R. Dechter. Constraint satisfaction. In In the MIT Encyclopedia of the Cognitive Sciences (MITECS). 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....11] rely upon branch and bound search with a heuristic to compute a lower bound on the quality of the best solution that can be found by extending the partial assignment associated with the current node. This is analogous to the constraint propagation step in backtracking search for classical CSP [10, 2]. However for soft constraints the operator for aggregating costs is non idempotent [1] so the task of computing a good lower bound is significantly harder. Even determining arc consistency for soft constraints is NP hard [1] Our algorithm, called semi independent partitioning, computes a lower ....

R. Dechter and F. Rossi. Constraint satisfaction. Survey ECS, 2000.

....However, in this paper we focus on the task of finding all solutions or proving that no solution exists. CSP has not only important theoretical value in Artificial Intelligence, but also many immediate applications in areas ranging from vision, language comprehension to scheduling and diagnosis [5] . In general, CSP tasks are computationally intractable (NP hard) A simple algorithm for solving a CSP is backtracking. Backtracking works with an initially empty set of compatible instantiated variables and tries to extend the set to a new variable and a value for the variable. The most basic ....

R. Dechter. Constraint satisfaction. In the MIT Encyclopedia of the Cognitive Sciences (MITECS). January, 1998 ftp://ftp.ics.uci.edu/pub/CSP-repository/papers/R68.ps

....point from this approach. In fact, SAT is a special case of the constraint satisfaction problem (CSP) CSP has not only important theoretical value in arti cial intelligence, but also many immediate applications in areas ranging from vision, language comprehension to scheduling and diagnosis (Dechter, 1998). In general, CSP tasks are computationally intractable (NP hard) Dechter, 1998) In recent years random constraint satisfaction problems have also received great attention, both from an experimental and a theoretical point of view (Achlioptas et al. 1999; Cheeseman et al. 1991; Frost ....

.... satisfaction problem (CSP) CSP has not only important theoretical value in arti cial intelligence, but also many immediate applications in areas ranging from vision, language comprehension to scheduling and diagnosis (Dechter, 1998) In general, CSP tasks are computationally intractable (NP hard) (Dechter, 1998). In recent years random constraint satisfaction problems have also received great attention, both from an experimental and a theoretical point of view (Achlioptas et al. 1999; Cheeseman et al. 1991; Frost Dechter, 1994; Gent et al. 1999; Hogg, 1996; Larrosa Meseguer, 1996; Prosser, 1996; ....

Dechter, R. (1998). Constraint satisfaction. In MIT Encyclopedia of the Cognitive Sciences (MITECS). Online at \ ftp://ftp.ics.uci.edu/pub/CSP-repository/papers/R68.ps".

....then its theory has intricacy 1. 5.4.2 Tractable Constraint Networks This section provides formal definitions concerning constraint networks and reviews some previously proposed classes of tractable constraint networks. For a more detailed description, the interested reader is referred to [Mac87, Dec91, DH91] Since we will be interested in families of constraint networks, we start with a denumerable set V of values, and a denumerable set X of variables, sometimes called nodes. Despite their name, these are not to be confused with the variables of predicate calculus. Definition 5.4 A ....

....respect to this ordering. 125 All backtrack free networks are consistent by definition, and it is known that any consistent binary network can be transformed into an equivalent (i.e. having the same solutions) backtrack free network with respect to any given ordering by adding new constraints [Dec91] The transformation from Figure 5.2 to Figure 5.3 is an example of such a transformation. It is important to remember that, as illustrated later, these new constraints may be of arbitrary arity even if we start with a binary constraint network. The Consistency Problem Instead of finding the ....

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R. Dechter. Constraint satisfaction. In S.C. Shapiro, editor, Encyclopedia of AI (2nd Edition). John Wiley and Sons, 1991.

....is a realistic measure of time complexity in our model because it pays attention to the slowest process, by ensuring that a round is completed only when all processes, including the slowest process, have made at least one move. 4 Related work In a related work, Collin, Dechter, and Katz (CDK) [5, 6] present distributed self stabilizing solutions for a class of constraint satisfaction problems. The input to a constraint satisfaction problem consists of a finite set of variables along with a finite set of constraints among subsets of variables. The solution to the problem is an assignment of ....

....either randomization or unique process ids to break the symmetry. Second, we will show in Section 6, that the time complexity of our algorithm depends on the height of the roots. By choosing centers as roots we obtain roots with minimum height and thereby provide a time optimal algorithm. 2 CDK [5, 6] also use a similar phase in their work. Program for each process i: do (i is a leaf) h(i) 6= 0) h(i) 0 (i is not a leaf) h(i) 6= 1 2ndmax(N h (i) h(i) 1 2ndmax(N h (i) od Figure 2: The center finding algorithm In phase 2, the problem P is solved on the rooted tree ....

Z. Collin, R. Dechter, and S. Katz, Constraint satisfaction. Personal communication.

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R. Dechter. Constraint satisfaction. In In the MIT Encyclopedia of the Cognitive Sciences (MITECS). 1998.

....for inference when determinism is present, as we will demonstrate empirically and theoretically. The main motivation for our study is the similarity that exists between belief networks that exhibit many functional relationships and deterministic networks, such as constraint satisfaction problems [7, 2]. Since these belief networks have a substantial deterministic substructure beneath their probabilistic facade, it would seem logical that the sophisticated techniques developed by the constraint satisfaction community might also be leveraged to speed Bayesian inference. If the deterministic ....

R. Dechter and F. Rossi. Constraint satisfaction. Survey ECS, 2000.

.... algorithms are arc consistency (i = 2) and path consistency (i = 3) 40, 26, 14] Indeed, the recent success of constraint processing algorithms can be attributed primarily to this class of algorithms, either used as stand alone, incomplete algorithms, or incorporated within backtracking search [19, 21]. The idea, visualized in Figure 1, shows that while exact algorithms may record arbitrarily large constraints (depicted by large cliques) i consistency algorithms enforce consistency over smaller subproblems, recording constraints of size i or less. The mini bucket approximation presented in ....

R. Dechter. Constraint satisfaction. In In the MIT Encyclopedia of the Cognitive Sciences (MITECS). 1998.

....method can benefit from keeping the query distinct from the knowledgebase (the belief network) in several ways. Computationally, by facilitating constraint propagation (e.g. arc consistency or unit resolution) that proved essential for efficient processing of Boolean and constraint expressions [Dechter, 1999b] Furthermore, belief networks can stand for physical causal mechanisms having semantical significance beyond the pure numerical function they express [Pearl, 2000] Consider the simple belief network over three propositional variables A,B,C, defined by the graph in Figure 1a. The joint ....

....in practice. A brute force search approach can generate each model, one by one, and for each compute the probability of the resulting model using belief network algorithms for conjunctive queries. Clearly, a variety of improvements can be utilized using general constraint satisfaction methods [Dechter, 1999b] However, the benefits of each proposal should be evaluated empirically. This is outside the scope of the current paper. The bucket elimination methods presented here show the power of this scheme in solving a variety of queries, thus making the study of this algorithmic framework even more ....

R. Dechter. Constraint satisfaction. In The MIT Encyclopedia of Cognitive Sciences (MITECS), pages 195--197, 1999.

.... special cases are arc consistency (i = 2) and path consistency (i = 3) 31, 21, 10] Indeed, the recent success of constraint processing algorithms can be attributed primarily to this class of algorithms, either used as standalone incomplete algorithms or incorporated within backtracking search [15, 16]. The idea and benefit of local consistency algorithms is visualized in Figure 1. The figure shows that while complete algorithms deciding consistency of the whole problem may record arbitrarily large constraints (depicted by large clusters) i consistency algorithms (deciding consistency of ....

R. Dechter. Constraint satisfaction. In In the MIT Encyclopedia of the Cognitive Sciences (MITECS). 1998. 45

.... special cases are arc consistency (i = 2) and path consistency (i = 3) 31, 21, 10] Indeed, the recent success of constraint processing algorithms can be attributed primarily to this class of algorithms, either used as standalone, incomplete algorithms or incorporated within backtracking search [15, 16]. The idea and benefit of local consistency algorithms are demonstrated in Figure 1. The figure shows that while exact algorithms may record arbitrarily large constraints, i consistency algorithms decide consistency of smaller subproblems, recording constraints of size i or less. In this paper we ....

R. Dechter. Constraint satisfaction. In In the MIT Encyclopedia of the Cognitive Sciences (MITECS). 1998.

.... special cases are arc consistency (i = 2) and path consistency (i = 3) 31, 21, 10] Indeed, the recent success of constraint processing algorithms can be attributed primarily to this class of algorithms, either used as standalone, incomplete algorithms or incorporated within backtracking search [15, 16]. The idea and benefit of local consistency algorithms is visualized in Figure 1. The figure shows that while complete algorithms deciding consistency of the whole problem may record arbitrarily large constraints (depicted by large clusters) i consistency algorithms (deciding consistency of ....

R. Dechter. Constraint satisfaction. In In the MIT Encyclopedia of the Cognitive Sciences (MITECS). 1998.

.... special cases are arc consistency (i = 2) and path consistency (i = 3) 34, 22, 11] Indeed, the recent success of constraint processing algorithms can be attributed primarily to this class of algorithms, either used as stand alone, incomplete algorithms, or incorporated within backtracking search [16, 17]. The idea and benefit of local consistency algorithms are demonstrated in Figure 1. The figure shows that while exact algorithms may record arbitrarily large constraints, i consistency algorithms decide consistency of smaller subproblems, recording constraints of size i or less. In this paper we ....

R. Dechter. Constraint satisfaction. In In the MIT Encyclopedia of the Cognitive Sciences (MITECS). 1998.

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