Results 1  10
of
23
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 ..."
Abstract

Cited by 126 (47 self)
 Add to MetaCart
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
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 ..."
Abstract

Cited by 16 (3 self)
 Add to MetaCart
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.
Modelbased monitoring and diagnosis of systems with softwareextended behavior
 In Proc. 20th National Conference on Artificial Intelligence
, 2005
"... Modelbased diagnosis has largely operated on hardware systems. However, in most complex systems today, hardware is augmented with software functions that influence the system’s behavior. In this paper, hardware models are extended to include the behavior of associated embedded software, resulting i ..."
Abstract

Cited by 14 (3 self)
 Add to MetaCart
(Show Context)
Modelbased diagnosis has largely operated on hardware systems. However, in most complex systems today, hardware is augmented with software functions that influence the system’s behavior. In this paper, hardware models are extended to include the behavior of associated embedded software, resulting in more comprehensive diagnoses. Prior work introduced probabilistic, hierarchical, constraintbased automata (PHCA) to allow the uniform and compact encoding of both hardware and software behavior. This paper focuses on PHCAbased monitoring and diagnosis to ensure the robustness of complex systems. We introduce a novel approach that frames diagnosis over a finite time horizon as a soft constraint optimization problem (COP), allowing us to leverage an extensive body of efficient solution methods for COPs. The solutions to the COP correspond to the most likely evolutions of the complex system. We demonstrate our approach on a visionbased rover navigation system, and models of the SPHERES and Earth Observing One spacecraft.
Tractable optimization problems through hypergraphbased structural restrictions
 In Proceedings of ICALP (2). LNCS
, 2009
"... Abstract. Several variants of the Constraint Satisfaction Problem have been proposed and investigated in the literature for modelling those scenarios where solutions are associated with some given costs. Within these frameworks computing an optimal solution is an NPhard problem in general; yet, whe ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
(Show Context)
Abstract. Several variants of the Constraint Satisfaction Problem have been proposed and investigated in the literature for modelling those scenarios where solutions are associated with some given costs. Within these frameworks computing an optimal solution is an NPhard problem in general; yet, when restricted over classes of instances whose constraint interactions can be modelled via (nearly)acyclic graphs, this problem is known to be solvable in polynomial time. In this paper, larger classes of tractable instances are singled out, by discussing solution approaches based on exploiting hypergraph acyclicity and, more generally, structural decomposition methods, such as (hyper)tree decompositions. 1
Dynamic Management of Heuristics for Solving Structured CSPs
"... This paper deals with the problem of solving efficiently structured CSPs. It is well known that (hyper)treedecompositions offer the best approaches from a theoretical viewpoint, but from the practical viewpoint, these methods do not offer efficient algorithms. Therefore, we introduce here a framew ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
This paper deals with the problem of solving efficiently structured CSPs. It is well known that (hyper)treedecompositions offer the best approaches from a theoretical viewpoint, but from the practical viewpoint, these methods do not offer efficient algorithms. Therefore, we introduce here a framework founded on coverings of CSP by acyclic hypergraphs. We study their properties and relations, and evaluate theoretically their interest with respect to the solving of structured problems. This framework does not define a new decomposition, but makes easier a dynamic management of the CSP structure during the search, and so an exploitation of dynamic variables ordering heuristics in the solving method. Thus, we provide a new complexity result which outperforms significantly the previous one given in the literature about heuristics for solving a decomposed problem. Finally, we present experimental results to assess the practical interest of these notions.
Solving soft constraints by separating optimization and satisfiability
 In Proceedings of the Seventh International Workshop on Preferences and Soft Constraints
, 2005
"... Abstract. As many realworld problems involve user preferences, costs, or probabilities, the constraint framework has been extended from satisfaction to optimization by extending hard constraints to soft constraints. However, techniques for constraint satisfaction, such as local consistency or confl ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
Abstract. As many realworld problems involve user preferences, costs, or probabilities, the constraint framework has been extended from satisfaction to optimization by extending hard constraints to soft constraints. However, techniques for constraint satisfaction, such as local consistency or conflict learning, do not easily generalize to optimization. Thus, solving soft constraints appears more difficult than solving hard constraints. In this paper, we present an approach to solving soft constraints that exploits this disparity by reformulating soft constraints into an optimization part (with unary objective functions), and a satisfiability part. We describe a search algorithm that exploits this reformulation by enumerating subspaces with equal valuation, that is, plateaus in the search space, rather than individual elements of the space. Experimental results indicate that this hybrid approach can in some cases be more efficient than other methods for solving soft constraints. 1
Bounded Search and Symbolic Inference for Constraint Optimization
 In Proc. of IJCAI
, 2005
"... Constraint optimization underlies many problems in AI. We present a novel algorithm for finite domain constraint optimization that generalizes branchandbound search by reasoning about sets of assignments rather than individual assignments. Because in many practical cases, sets of assignments can b ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Constraint optimization underlies many problems in AI. We present a novel algorithm for finite domain constraint optimization that generalizes branchandbound search by reasoning about sets of assignments rather than individual assignments. Because in many practical cases, sets of assignments can be represented implicitly and compactly using symbolic techniques such as decision diagrams, the setbased algorithm can compute bounds faster than explicitly searching over individual assignments, while memory explosion can be avoided by limiting the size of the sets. Varying the size of the sets yields a family of algorithms that includes known search and inference algorithms as special cases. Furthermore, experiments on random problems indicate that the approach can lead to significant performance improvements. 1
Computing and exploiting treedecomposition for (Max)CSP
, 2005
"... Methods exploiting the treedecomposition notion seem to provide the best approach for solving constraint networks w.r.t. the theoretical time complexity. Nevertheless, they have not shown a real practical interest yet. So, in this paper, we first study several methods for computing an approximate o ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Methods exploiting the treedecomposition notion seem to provide the best approach for solving constraint networks w.r.t. the theoretical time complexity. Nevertheless, they have not shown a real practical interest yet. So, in this paper, we first study several methods for computing an approximate optimal treedecomposition before assessing their relevance for solving CSPs. Then, we propose and compare several strategies to achieve the best depthfirst traversal of the associated cluster tree w.r.t. CSP solving. These strategies concern the choice of the root cluster (i.e. the first visited cluster) and the order according to which we visit the sons of a given cluster. Finally, we propose a new decomposition strategy and heuristics which both rely on probabilistic criteria and which significantly improve the runtime.
Closures of uncertain constraint satisfaction problems
 In Proceedings 1st International Workshop on Quantification in Constraint Programming (at CP
, 2005
"... Abstract Data uncertainties are inherent in the real world. The uncertain CSP (UCSP) is an extension of classical CSP that models incomplete and erroneous data by coefficients in the constraints whose values are unknown but bounded, for instance by an interval. Formally, the UCSP is a tractable rest ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
Abstract Data uncertainties are inherent in the real world. The uncertain CSP (UCSP) is an extension of classical CSP that models incomplete and erroneous data by coefficients in the constraints whose values are unknown but bounded, for instance by an interval. Formally, the UCSP is a tractable restriction of the quantified CSP. The resolution of a UCSP, a set of its potential solutions called a closure, can take different forms according to the user’s requirements and the nature of data uncertainty in the problem specification. In a former paper we presented mainly the full closure, the set of all potential solutions, which finds application in diagnosis problems where the existence of any potential solutions is an objective by itself. In this paper, we develop other commonlyuseful closures such as the covering set (found in contingent planning problems) and the most robust solution (found in conformant planning problems). We formally define different closures as solutions to a UCSP model, relate them in a hierarchy, and outline means to derive them from one another. 1
Dynamic heuristics for branch and bound search on treedecomposition of Weighted CSPs
, 2006
"... This paper deals with methods exploiting treedecomposition approaches for solving weighted 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 defi ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
This paper deals with methods exploiting treedecomposition approaches for solving weighted 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)), and finally to O(exp(2(w + k))), where w denotes the ”treewidth ” of a Weighted CSP. Finally, we assess the defined theoretical extension of the time complexity bound from a practical viewpoint.