I. Rish and R. Dechter. To guess or to think? hybrid algorithms for sat. In Principles of Constraint Programming (CP-96), pages 555--556, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....understanding of the underlying parameters often suggests good general problem solving strategies. One example of such a parameter is the tree width (or band width) of a propositional formula. Inference can be performed in polynomial time for problems of bounded tree width, and Rish and Dechter [78] have shown that a estimate of the tree width of a formula can be used to control the problem decomposition strategy used by a solver. Another important line of work relates problem hardness to phase transitions in the problem distribution as the underlying parameters are varied [20, 87, 85, 69] ....

I. Rish and R. Dechter. To guess or to think? hybrid algorithms for SAT. In Proceedings of the Conference on Principles of Constraint Programming (CP-96), pages 555--556, 1996.

....than their worst case bounds. Figure 12 summarizes the properties of elimination vs. conditioning search. This complementary behavior calls for algorithms that combine the two approaches. Indeed, such algorithms are being developed for constraint satisfaction and propositional satisfiability [12, 40, 9, 15]. In the following sections we will focus in more detail on deriving bucket elimination algorithms for processing probabilistic networks. We are presenting a syntactic and uniform exposition emphasizing these algorithms form as a straightforward elimination algorithm. 3 Preliminaries for ....

....There are a variety of possible hybrids between conditioning and elimination that can refine this basic procedure. One method imposes an upper bound on the arity of functions recorded and decides dynamically, during processing, whether to process a bucket by elimination or by conditioning (see [40]) Another method which uses the super bucket approach collects a set of consecutive buckets into one super bucket that it processes by conditioning, thus avoiding recording some intermediate results [15, 24] See also [9] 11 Additional related work We have mentioned throughout this paper ....

I. Rish and R. Dechter. To guess or to think? hybrid algorithms for sat. In Principles of Constraint Programming (CP-96), pages 555--556, 1996.

....is also briefly addressed. The latter paper includes an alternative proof to the (worst case) time superiority of tree clustering over the cyclecutset method. In [19] the idea is applied to the pathfinder system, when the conditioning set is restricted to the set of diseases. Finally in [33, 34], a scheme for combining conditioning and variable elimination for propositional theories is outlined and analyzed. It is shown that although the worst case time guarantee of an hybrid cannot be superior to tree clustering (nor to a variable elimination scheme) for some problem classes a hybrid ....

I. Rish and R. Dechter. To guess or to think? hybrid algorithms for sat. In Principles of Constraint Programming (CP-96), pages 555--556, 1996.

....limited amount of preprocessing was cost effective. The presented experiments with BDRDP (i) suggest that the results in [19] were too preliminary and that the idea of preprocessing before search is viable and should be further investigated. Our second hybrid algorithm, DCDR(b) proposed first in [53], generalizes the cyclecutset approach that was presented for constraint satisfaction [13] using static variable ordering. This idea of alternating search with bounded resolution was also suggested and evaluated independently by van Gelder in [38] where a generalization of unit resolution known ....

I. Rish and R. Dechter. To guess or to think? hybrid algorithms for SAT (extended abstract). In Proceedings of the International Conference on Principles and Practice of Constraint Programming (CP96), 1996.

....better than their worst case bounds. Figure 12 summarizes the properties of elimination vs conditioning search. This complementary behavior calls for algorithms that combine the two approaches. Indeed, such algorithms are being developed for constraint satisfaction and propositional satisfiability [12, 40, 15]. In the following sections we will focus in more detail on deriving bucket elimination algorithms for processing probabilistic networks. This will allow borrowing ideas and methods already developed for constraint processing to probabilistic inference. One area is the hybrids between conditioning ....

....There are a variety of possible hybrids between conditioning and elimination that can refine this basic procedure. One method imposes an upper bound on the arity of functions recorded and decides dynamically, during processing, whether to process a bucket by elimination or by conditioning (see [40]) Another method which uses the super bucket approach collects a set of consecutive buckets into one super bucket that it processes by conditioning, thus avoiding recording some intermediate results [15, 25] The details of these approaches are universal across tasks. 45 11 Additional related ....

I. Rish and R. Dechter. To guess or to think? hybrid algorithms for sat. In Principles of Constraint Programming (CP-96), pages 555--556, 1996.

....is also briefly addressed. The latter paper includes an alternative proof to the (worst case) time superiority of tree clustering over the cycle cutset method. In [27] the idea is applied to the pathfinder system, where the conditioning set is restricted to the set of diseases. Finally in [28], a scheme that apply this idea for combining conditioning and variable elimination for propositional theories is outlined and analyzed. It is shown that although the worst case time guarantee of an hybrid cannot be superior to tree clustering (nor to a variable elimination scheme) for some ....

I. Rish and R. Dechter. To guess or to think? hybrid algorithms for sat. In Principles of Constraint Programming (CP-96), pages 555--556, 1996.

....and branch and bound may be viewed as conditioning algorithms. The complexity of conditioning algorithms is exponential in the conditioning set, however, their space complexity is only linear. Our resulting hybrid of conditioning with elimination which trade off time for space (see also (Dechter, 1996b; R. D. Shachter and Solovitz, 1991) are applicable to all algorithms expressed within this framework. The work we present here also fits into the framework developed by Arnborg and Proskourowski (Arnborg, 1985; Arnborg and Proskourowski, 1989) They present table based reductions for various ....

....variety of possible hybrids between conditioning and elimination that can refine the basic procedure in elim cond mpe. One method imposes an upper bound on the arity of functions recorded and decides dynamically, during processing, whether to process a bucket by elimination or by conditioning (see (Dechter and Rish, 1996)) Another method which uses the super bucket approach, collects a set of consecutive buckets into one super bucket that it processes by conditioning, thus avoiding recording some intermediate results (Dechter, 1996b; El Fattah and Dechter, 1996) 9. Related work We had mentioned throughout this ....

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R. Dechter and I. Rish. To guess or to think? hybrid algorithms for sat. In Principles of Constraint Programming (CP-96), 1996.

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