R. Dechter and P. van Beek. Local and global relational consistency. Journal of Theoretical Computer Science, 173(1):283--308, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of consistency have been introduced and many consistency algorithms have been proposed and developed to remove local inconsistencies. Much work has been done on consistency in binary CSPs [14, 10, 6, 13, 8, 3, 18, 2] Several researchers have generalized consistency to apply to general CSPs [9, 5] but some functionality is lost in the generalization. Furthermore, enforcing these general consistencies is either too expensive (even intractable) or it does not remove local inconsistencies as expected. In this paper, we define a new form of consistency, called pairwise consistency, which ....

....for 1 l k. Node, arc, and path consistency can be achieved in polynomial time. Many competitive algorithms have been proposed to achieve arc and path consistency. Achieving k consistency is exponential in k. Arc, path, and k consistency are defined on binary constraints. Dechter and van Beek [5] extend arc, path, and k consistency to general constraints, which are called relational arc, path, and k consistency. Relational arc, path, and kconsistency are identical to the ordinary arc, path, and k consistency when they are applied to binary constraints. Definition3. Dechter and van Beek ....

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R. Dechter and P. van Beek. Local and global relational consistency. In Proceedings of the 1st International Conference on Principles and Practices of Constraint Programming, pages 240--257, Cassis, France, September 1995.

....for a compound constraint defined by means of the basic constraints is in general stronger than the rule consistency for the basic constraints treated separately. In fact, in the above case the equality rules for the full adder constraint yield the relational (1,5) consistency notion of (Dechter van Beek, 1997), whereas by virtue of Theorem 5.2, the equality rules for the and, or and xor constraints yield a weaker notion of arc consistency. 8 Related Work In a number of papers a link was made between constraint programming and rulebased programming. To start with, in (Montanari Rossi, 1991) a ....

Dechter, R., & van Beek, P. (1997). Local and global relational consistency. Theoretical computer science, 173(1), 283--308.

....how specific provably correct algorithms for achieving a local consistency notion can be automatically derived. As it is difficult to define local consistency formally, we illustrate the idea on an example. Example 3. 10 We consider here the notion of relational consistency proposed recently in Dechter and van Beek (1997). To define it need to introduce some auxiliary concepts first. Consider a CSP hD 1 ; Dn ; Ci. Take a scheme t : i 1 ; i l on n. We call d 2 D i 1 Theta Delta Delta Delta Theta D i l a tuple of type t and say that d is consistent if for every subsequence s of t and a ....

....reformulated for the CII algorithm, we can now use the CII algorithm to achieve relational m consistency for a CSP with finite domains by feeding into this algorithm the above defined functions. The obtained algorithm improves upon the (authors terminology) brute force algorithm proposed in Dechter and van Beek (1997) since the useless constraint modifications are avoided. As in Example 3.7, by simple properties of the 1 operation and by Note 1.2(i) we have C Pi t (1 C) Pi t (C 1 (1 C) Pi t (sol(C; C) Hence, by virtue of Example 3.6, the functions g s are all constraint reduction functions. ....

Dechter, R. and van Beek, P. (1997). Local and global relational consistency, Theoretical Computer Science 173(1): 283--308.

....6. Related Work The idea of using a restricted form of variable elimination to overcome its high space and time complexity is not new. Some forms of local consistency in constraint satisfaction are achieved with limited forms of variable elimination. The clearest example is relational consistency [12] in the CSP context, where the size of buckets and the arity of the new constraints is bounded (rendering the algorithm incomplete) Processed variables are not eliminated in order to preserve the soundness of subsequent search. Enforcing relational consistency makes explicit constraints that were ....

Dechter, R. and P. van Beek: 1997, `Local and global relational consistency'. Theoretical Computer Science 173(1), 283--308.

....we show here also fits into the framework developed by Arnborg and Proskourowski [2, 1] They present table based reductions for various NPhard graph problems such as the independent set problem, network reliability, vertex cover, graph k colorability, and Hamilton circuits. Here and elsewhere [22, 16] we extend the approach to a different set of problems. The following paragraphs summarize and generalizes the bucket elimination algorithm using two operators of combination and marginalization. The task at hand can be defined in terms of a triplet (X; D;F ) where X = fX 1 ; Xng is a set of ....

R. Dechter and P. van Beek. Local and global relational consistency. In Principles and Practice of Constraint programming (CP-95), pages 240-- 257, 1995.

....we show here fits also into the framework developed by Arnborg and Proskourowski [2, 1] They present table based reductions for various NPhard graph problems such as the independent set problem, network reliability, vertex cover, graph k colorability, and Hamilton circuits. Here and elsewhere [23, 16] we extend the approach to a different set of problems. 12 Summary and Conclusion Using the bucket elimination framework which generalizes dynamic programming, constraint processing and resolution procedures, we have presented a concise and uniform way of expressing algorithms for probabilistic ....

R. Dechter and P. van Beek. Local and global relational consistency. In Principles and Practice of Constraint programming (CP-95), pages 240-- 257, 1995.

.... such as directional resolution for propositional satisfiability, adaptive consistency for constraint satisfaction, Fourier and Gaussian elimination, for linear equalities and inequalities, and dynamic programming for combinatorial optimization, can be all accommodated within this framework [5]. It was recently demonstrated that many algorithms for probabilistic inference, such as belief updating, finding the most probable explanation, finding the maximum posteriori hypothesis and the maximum expected utility, can also be expressed as bucket elimination algorithms [3] The main virtues ....

R. Dechter and P. van Beek. Local and global relational consistency. In Principles and Practice of Constraint programming (CP-95), pages 240--257, 1995.

....developed by Arnborg and Proskourowski (Arnborg, 1985; Arnborg and Proskourowski, 1989) They present table based reductions for various NP hard graph problems such as the independent set problem, network reliability, vertex cover, graph k colorability, and Hamilton circuits. Here and elsewhere (Dechter and van Beek, 1995; Dechter, 1997) we extend the approach to a different set of problems. 4 R. DECHTER Following preliminaries (section 2) we present the bucket elimination algorithm for belief updating and analyze its performance (section 3) Then, we extend the algorithm to the tasks of finding the most ....

R. Dechter and P. van Beek. Local and global relational consistency. In Principles and Practice of Constraint programming (CP-95), pages 240--257, 1995.

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R. Dechter and P. van Beek. Local and global relational consistency. Journal of Theoretical Computer Science, 173(1):283--308, 1997.

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R. Dechter. Local and global relational consistency. Journal of Theoretical Computer Science, 1996. 13

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R. Dechter. Local and global relational consistency. Journal of Theoretical Computer Science, 1996.

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R. Dechter and P. van Beek. Local and global relational consistency. LNCS'99, 976:240257, 1995.

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Dechter, R. and van Beek, P. 1995. Local and global relational consistency. Principles and Practice of Constraint Programming - CP '95, Montanari and Rossi, eds. LNCS 976, Springer, 240--257.

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