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2,572
Strong backdoors to bounded treewidth SAT
 In 54th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2013
, 2013
"... There are various approaches to exploiting “hidden structure ” in instances of hard combinatorial problems to allow faster algorithms than for general unstructured or random instances. For SAT and its counting version #SAT, hidden structure has been exploited in terms of decomposability and strong b ..."
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Cited by 3 (2 self)
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backdoor sets. Decomposability can be considered in terms of the treewidth of a graph that is associated with the given CNF formula, for instance by considering clauses and variables as vertices of the graph, and making a variable adjacent with all the clauses it appears in. On the other hand, a strong
Solving dSAT via Backdoors to Small Treewidth
"... A backdoor set of a CNF formula is a set of variables such that fixing the truth values of the variables from this set moves the formula into a polynomialtime decidable class. In this work we obtain several algorithmic results for solving dSAT, by exploiting backdoors to dCNF formulas whose incid ..."
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is not satisfiable, or • concludes correctly that φ has no weak or strong backdoor set to treewidth t of size at most k. As a consequence of the above, we show that dSAT parameterized by the size of a smallest weak/strong backdoor set to formulas of treewidth t, is fixedparameter tractable. Prior to our work
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.
Backdoor Trees
 In Proceedings of AAAI 08, TwentyThird Conference on Artificial Intelligence
, 2008
"... The surprisingly good performance of modern satisfiability (SAT) solvers is usually explained by the existence of a certain “hidden structure ” in realworld instances. We introduce the notion of backdoor trees as an indicator for the presence of a hidden structure. Backdoor trees refine the notion ..."
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Cited by 9 (4 self)
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The surprisingly good performance of modern satisfiability (SAT) solvers is usually explained by the existence of a certain “hidden structure ” in realworld instances. We introduce the notion of backdoor trees as an indicator for the presence of a hidden structure. Backdoor trees refine
Backdoors for SAT
, 2011
"... The concept of backdoor was introduced to try to explain the good performances achieved on real world SAT instances by solvers. A backdoor is a set of variables that, once decided, makes the rest of the problem simple (i.e. polynomialtime). In this thesis we provide a comprehensive overview on th ..."
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The concept of backdoor was introduced to try to explain the good performances achieved on real world SAT instances by solvers. A backdoor is a set of variables that, once decided, makes the rest of the problem simple (i.e. polynomialtime). In this thesis we provide a comprehensive overview
Backdoors to satisfaction
 The Multivariate Algorithmic Revolution and Beyond  Essays Dedicated to Michael R. Fellows on the Occasion of His 60th Birthday, volume 7370 of Lecture
"... ar ..."
Tradeoffs in the complexity of backdoor detection
 In Principles and Practice of Constraint Programming  CP 2007
, 2007
"... Abstract. There has been considerable interest in the identification of structural properties of combinatorial problems that lead to efficient algorithms for solving them. Some of these properties are “easily ” identifiable, while others are of interest because they capture key aspects of stateoft ..."
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Cited by 23 (5 self)
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as the inconsequential sounding feature of empty clause detection (present in all modern SAT solvers) is added. More interestingly, in practice such a feature as well as polynomial time constraint propagation mechanisms often lead to much smaller backdoor sets. In fact, despite the worstcase complexity results
Backdoors to acyclic SAT
 in Proceedings of the 39th International Colloquium on Automata, Languages, and Programming (ICALP
"... Backdoor sets, a notion introduced by Williams et al. in 2003, are certain sets of key variables of a CNF formula F that make it easy to solve the formula; by assigning truth values to the variables in a backdoor set, the formula gets reduced to one or several polynomialtime solvable formulas. More ..."
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Cited by 6 (3 self)
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Backdoor sets, a notion introduced by Williams et al. in 2003, are certain sets of key variables of a CNF formula F that make it easy to solve the formula; by assigning truth values to the variables in a backdoor set, the formula gets reduced to one or several polynomialtime solvable formulas
Results 1  10
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2,572