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57
AND/OR Search Spaces for Graphical Models
, 2004
"... The paper introduces an AND/OR search space perspective for graphical models that include probabilistic networks (directed or undirected) and constraint networks. In contrast to the traditional (OR) search space view, the AND/OR search tree displays some of the independencies present in the gr ..."
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Cited by 126 (47 self)
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The paper introduces an AND/OR search space perspective for graphical models that include probabilistic networks (directed or undirected) and constraint networks. In contrast to the traditional (OR) search space view, the AND/OR search tree displays some of the independencies present in the graphical model explicitly and may sometime reduce the search space exponentially. Indeed, most
Bounded backtracking for the valued constraint satisfaction problems
 Proc. CP03 (2003
, 2003
"... Abstract. We propose a new method for solving Valued Constraint Satisfaction Problems based both on backtracking techniques branch and bound and the notion of treedecomposition of valued constraint networks. This mixed method aims to benefit from the practical efficiency of enumerative algorithms ..."
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Cited by 24 (6 self)
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Abstract. We propose a new method for solving Valued Constraint Satisfaction Problems based both on backtracking techniques branch and bound and the notion of treedecomposition of valued constraint networks. This mixed method aims to benefit from the practical efficiency of enumerative algorithms while providing a warranty of a bounded time complexity. Indeed the time complexity of our method is O(d w+ +1) with w + an approximation of the treewidth of the constraint network and d the maximum size of domains. Such a complexity is obtained by exploiting optimal bounds on the subproblems defined from the treedecomposition. These bounds associated to some partial assignments are called ”structural valued goods”. Recording and exploiting these goods may allow our method to save some time and space with respect to ones required by classical dynamic programming methods. Finally, this method is a natural extension of the BTD algorithm [1] proposed in the classical CSP framework. 1
The Impact of AND/OR Search Spaces on Constraint Satisfaction and Counting
 IN CP’04
, 2004
"... The contribution of this paper is in demonstrating the impact of AND/OR search spaces view on solutions counting. In contrast to the traditional (OR) search space view, the AND/OR search space displays independencies present in the graphical model explicitly and may sometimes reduce the search sp ..."
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Cited by 21 (6 self)
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The contribution of this paper is in demonstrating the impact of AND/OR search spaces view on solutions counting. In contrast to the traditional (OR) search space view, the AND/OR search space displays independencies present in the graphical model explicitly and may sometimes reduce the search space exponentially. Empirical
Backtracking Search Algorithms
, 2006
"... There are three main algorithmic techniques for solving constraint satisfaction problems: backtracking search, local search, and dynamic programming. In this chapter, I survey backtracking search algorithms. Algorithms based on dynamic programming [15]— sometimes referred to in the literature as var ..."
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Cited by 19 (2 self)
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There are three main algorithmic techniques for solving constraint satisfaction problems: backtracking search, local search, and dynamic programming. In this chapter, I survey backtracking search algorithms. Algorithms based on dynamic programming [15]— sometimes referred to in the literature as variable elimination, synthesis, or inference algorithms—are the topic of Chapter 7. Local or stochastic search algorithms are the topic of Chapter 5. An algorithm for solving a constraint satisfaction problem (CSP) can be either complete or incomplete. Complete, or systematic algorithms, come with a guarantee that a solution will be found if one exists, and can be used to show that a CSP does not have a solution and to find a provably optimal solution. Backtracking search algorithms and dynamic programming algorithms are, in general, examples of complete algorithms. Incomplete, or nonsystematic algorithms, cannot be used to show a CSP does not have a solution or to find a provably optimal solution. However, such algorithms are often effective at finding a solution if one exists and can be used to find an approximation to an optimal solution. Local or stochastic search algorithms are examples of incomplete algorithms. Of the two
P.: Guiding RealWorld SAT Solving with Dynamic Hypergraph Separator Decomposition
 In: Sixteenth IEEE International Conference on Tools with Artificial Intelligence
, 2004
"... The general solution of satisfiability problems is NPComplete. Although stateoftheart SAT solvers can efficiently obtain the solutions of many realworld instances, there are still a large number of realworld SAT families which cannot be solved in reasonable time. Much effort has been spent to ..."
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Cited by 17 (1 self)
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The general solution of satisfiability problems is NPComplete. Although stateoftheart SAT solvers can efficiently obtain the solutions of many realworld instances, there are still a large number of realworld SAT families which cannot be solved in reasonable time. Much effort has been spent to take advantage of the internal structure of SAT instances. Existing decomposition techniques are based on preprocessing the static structure of the original problem. We present a dynamic decomposition method based on hypergraph separators. Integrating the separator decomposition into the variable ordering of a modern SAT solver leads to speedups on large realworld satisfiability problems. Compared with a static decomposition based variable ordering, such as Dtree (Huang and Darwiche, 2003), our approach does not need time to construct the full tree decomposition, which sometimes needs more time than the solving process itself. Our primary focus is to achieve speedups on large realworld satisfiability problems. Our results show that the new solver often outperforms both regular zChaff and zChaff integrated with Dtree decomposition. The dynamic separator decomposition shows promise in that it significantly decreases the number of decisions for some realworld problems. 1.
AND/OR multivalued decision diagrams (AOMDDs) for weighted graphical models
 In Proceedings of the Twenty Third Conference on Uncertainty in Artificial Intelligence (UAI’07
, 2007
"... Inspired by the recently introduced framework of AND/OR search spaces for graphical models, we propose to augment MultiValued Decision Diagrams (MDD) with AND nodes, in order to capture function decomposition structure and to extend these compiled data structures to general weighted graphical model ..."
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Cited by 16 (3 self)
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Inspired by the recently introduced framework of AND/OR search spaces for graphical models, we propose to augment MultiValued Decision Diagrams (MDD) with AND nodes, in order to capture function decomposition structure and to extend these compiled data structures to general weighted graphical models (e.g., probabilistic models). We present the AND/OR MultiValued Decision Diagram (AOMDD) which compiles a graphical model into a canonical form that supports polynomial (e.g., solution counting, belief updating) or constant time (e.g. equivalence of graphical models) queries. We provide two algorithms for compiling the AOMDD of a graphical model. The first is searchbased, and works by applying reduction rules to the trace of the memory intensive AND/OR search algorithm. The second is inferencebased and uses a Bucket Elimination schedule to combine the AOMDDs of the input functions via the the APPLY operator. For both algorithms, the compilation time and the size of the AOMDD are, in the worst case, exponential in the treewidth of the graphical model, rather than pathwidth as is known for ordered binary decision diagrams (OBDDs). We introduce the concept of semantic treewidth, which helps explain why the size of a decision diagram is often much smaller than the worst case bound. We provide an experimental evaluation that demonstrates the potential of AOMDDs. 1.
Computing and exploiting treedecompositions for solving constraint networks
 IN PROCEEDINGS OF CP
, 2005
"... Methods exploiting treedecompositions seem to provide the best approach for solving constraint networks w.r.t. the theoretical time complexity. However, they have not shown a real practical interest yet. In this paper, we study several methods for computing a rough optimal treedecomposition and as ..."
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Cited by 8 (5 self)
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Methods exploiting treedecompositions seem to provide the best approach for solving constraint networks w.r.t. the theoretical time complexity. However, they have not shown a real practical interest yet. In this paper, we study several methods for computing a rough optimal treedecomposition and assess their relevance for solving CSPs.
Russian Doll Search with Tree Decomposition
"... Optimization in graphical models is an important problem which has been studied in many AI frameworks such as weighted CSP, maximum satisfiability or probabilistic networks. By identifying conditionally independent subproblems, which are solved independently and whose optimum is cached, recent Branc ..."
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Cited by 6 (6 self)
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Optimization in graphical models is an important problem which has been studied in many AI frameworks such as weighted CSP, maximum satisfiability or probabilistic networks. By identifying conditionally independent subproblems, which are solved independently and whose optimum is cached, recent Branch and Bound algorithms offer better asymptotic time complexity. But the locality of bounds induced by decomposition often hampers the practical effects of this result because subproblems are often uselessly solved to optimality. Following the Russian Doll Search (RDS) algorithm, a possible approach to overcome this weakness is to (inductively) solve a relaxation of each subproblem to strengthen bounds. The algorithm obtained generalizes both RDS and treedecomposition based algorithms such as BTD or ANDOR Branch and Bound. We study its efficiency on different problems, closing a very hard frequency assignment instance which has been open for more than 10 years. 1
Dynamic Heuristics for Backtrack Search on TreeDecomposition of CSPs
 IN PROC. OF IJCAI
, 2007
"... This paper deals with methods exploiting treedecomposition approaches for solving constraint networks. We consider here the practical efficiency of these approaches by defining five classes of variable orders more and more dynamic which preserve the time complexity bound. For that, we define extens ..."
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Cited by 5 (3 self)
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This paper deals with methods exploiting treedecomposition approaches for solving constraint networks. We consider here the practical efficiency of these approaches by defining five classes of variable orders more and more dynamic which preserve the time complexity bound. For that, we define extensions of this theoretical time complexity bound to increase the dynamic aspect of these orders. We define a constant k allowing us to extend the classical bound from O(exp(w + 1)) firstly to O(exp(w + k + 1)), and finally to O(exp(2(w + k+1)−s −)), with w the ”treewidth ” of a CSP and s − the minimum size of its separators. Finally, we assess the defined theoretical extension of the time complexity bound from a practical viewpoint.
An Algebraic Graphical Model for Decision with Uncertainties, Feasibilities, and Utilities
, 2005
"... Numerous formalisms and dedicated algorithms have been designed in the last decades to model and solve decision making problems. Some formalisms, such as constraint networks, can express “simple ” decision problems, while others are designed to take into account uncertainties, unfeasible decisions, ..."
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Cited by 5 (1 self)
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Numerous formalisms and dedicated algorithms have been designed in the last decades to model and solve decision making problems. Some formalisms, such as constraint networks, can express “simple ” decision problems, while others are designed to take into account uncertainties, unfeasible decisions, and utilities. Even in a single formalism, several variants are often proposed to model different types of uncertainty (probability, possibility...) or utility (additive or not). In this article, we introduce an algebraic graphical model that encompasses a large number of such formalisms: (1) we first adapt previous structures from Friedman, Chu and Halpern for representing uncertainty, utility, and expected utility in order to deal with generic forms of sequential decision making; (2) on these structures, we then introduce composite graphical models that express information via variables linked by “local ” functions, thanks to conditional independence; (3) on these graphical models, we finally define a simple class of queries which can represent various scenarios in terms of observabilities and controllabilities. A natural decisiontree semantics for such queries is completed by an equivalent operational semantics, which induces generic algorithms. The proposed framework, called the PlausibilityFeasibilityUtility (PFU) framework, not only provides a better understanding of the links between existing formalisms, but it also covers yet unpublished frameworks (such as possibilistic influence diagrams) and unifies formalisms such as quantified boolean formulas and influence diagrams. Our backtrack and variable elimination generic algorithms are a first step towards unified algorithms. 1.