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Size and Treewidth Bounds for Conjunctive Queries
"... This paper provides new worstcase bounds for the size and treewith of the result Q(D) of a conjunctive query Q to a database D. We derive bounds for the result size Q(D)  in terms of structural properties of Q, both in the absence and in the presence of keys and functional dependencies. These bou ..."
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Cited by 8 (1 self)
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This paper provides new worstcase bounds for the size and treewith of the result Q(D) of a conjunctive query Q to a database D. We derive bounds for the result size Q(D)  in terms of structural properties of Q, both in the absence and in the presence of keys and functional dependencies
On Low Treewidth Approximations of Conjunctive Queries
"... We recently initiated the study of approximations of conjunctive queries within classes that admit tractable query evaluation (with respect to combined complexity). Those include classes of acyclic, bounded treewidth, or bounded hypertreewidth queries. Such approximations are always guaranteed to ..."
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Cited by 1 (1 self)
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We recently initiated the study of approximations of conjunctive queries within classes that admit tractable query evaluation (with respect to combined complexity). Those include classes of acyclic, bounded treewidth, or bounded hypertreewidth queries. Such approximations are always guaranteed
Parameterized Complexity
, 1998
"... the rapidly developing systematic connections between FPT and useful heuristic algorithms  a new and exciting bridge between the theory of computing and computing in practice. The organizers of the seminar strongly believe that knowledge of parameterized complexity techniques and results belongs ..."
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Cited by 1218 (75 self)
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the rapidly developing systematic connections between FPT and useful heuristic algorithms  a new and exciting bridge between the theory of computing and computing in practice. The organizers of the seminar strongly believe that knowledge of parameterized complexity techniques and results belongs into the toolkit of every algorithm designer. The purpose of the seminar was to bring together leading experts from all over the world, and from the diverse areas of computer science that have been attracted to this new framework. The seminar was intended as the rst larger international meeting with a specic focus on parameterized complexity, and it hopefully serves as a driving force in the development of the eld. 1 We had 49 participants from Australia, Canada, India, Israel, New Zealand, USA, and various European countries. During the workshop 25 lectures were given. Moreover, one night session was devoted to open problems and Thursday was basically used for problem discussion
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 800 (26 self)
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The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances — including the key problems of computing marginals and modes of probability distributions — are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing likelihoods, marginal probabilities and most probable configurations. We describe how a wide varietyof algorithms — among them sumproduct, cluster variational methods, expectationpropagation, mean field methods, maxproduct and linear programming relaxation, as well as conic programming relaxations — can all be understood in terms of exact or approximate forms of these variational representations. The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in largescale statistical models.
On the Tractability of Query Compilation and Bounded Treewidth
, 2012
"... We consider the problem of computing the probability of a Boolean function, which generalizes the model counting problem. Given an OBDD for such a function, its probability can be computed in linear time in the size of the OBDD. In this paper we investigate the connection between treewidth and the s ..."
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Cited by 4 (0 self)
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and the size of the OBDD. Bounded treewidth has proven to be applicable to many graph problems, which are NPhard in general but become tractable on graphs with bounded treewidth. However, it is less well understood how bounded treewidth can be used for the probability computation problem of a Boolean function
Conjunctive Query Containment Revisited
, 1998
"... We consider the problems of conjunctive query containment and minimization, which are known to be NPcomplete, and show that these problems can be solved in polynomial time for the class of acyclic queries. We then generalize the notion of acyclicity and define a parameter called query width that ca ..."
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Cited by 119 (0 self)
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generalize those for acyclic queries, and are of practical significance because many queries have small query width compared to their sizes. We show that good bounds on the query width of Q can be obtained using the treewidth of the incidence graph of Q. We then consider the problem of finding an equivalent
ConjunctiveQuery Containment and Constraint Satisfaction
 Journal of Computer and System Sciences
, 1998
"... Conjunctivequery containment is recognized as a fundamental problem in database query evaluation and optimization. At the same time, constraint satisfaction is recognized as a fundamental problem in artificial intelligence. What do conjunctivequery containment and constraint satisfaction have in c ..."
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Cited by 168 (14 self)
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Conjunctivequery containment is recognized as a fundamental problem in database query evaluation and optimization. At the same time, constraint satisfaction is recognized as a fundamental problem in artificial intelligence. What do conjunctivequery containment and constraint satisfaction have
The complexity of acyclic conjunctive queries
 Journal of the ACM
, 1998
"... This paper deals with the evaluation of acyclic Boolean conjunctive queries in relational databases. By wellknown results of Yannakakis [1981], this problem is solvable in polynomial time; its precise complexity, however, has not been pinpointed so far. We show that the problem of evaluating acyc ..."
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Cited by 98 (22 self)
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complete: The Query Output Tuple problem for conjunctive queries, Conjunctive Query Containment, Clause Subsumption, and Constraint Satisfaction. The LOGCFLcompleteness result is extended to the class of queries of bounded treewidth and to other relevant query classes which are more general than the acyclic queries.
Fast counting with bounded treewidth
 In Logic for Programming, Artificial Intelligence, and Reasoning, volume 5330 of LNCS
"... Stefan Woltran1 Abstract. Many intractable problems have been shown to become tractable if the treewidth of the underlying structure is bounded by a constant. An important tool for deriving such results is Courcelle’s Theorem, which states that all properties defined by MonadicSecond Order (MSO) se ..."
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Cited by 5 (2 self)
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Stefan Woltran1 Abstract. Many intractable problems have been shown to become tractable if the treewidth of the underlying structure is bounded by a constant. An important tool for deriving such results is Courcelle’s Theorem, which states that all properties defined by MonadicSecond Order (MSO
Results 1  10
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