We present in this paper a new, complete method for distributed constraint optimization, based on dynamic programming. It is a utility propagation method, inspired by the sum-product algorithm, which is correct only for tree-shaped constraint networks. In this paper, we show how to extend that algorithm to arbitrary topologies using a pseudotree arrangement of the problem graph. Our algorithm requires a linear number of messages, whose maximal size depends on the induced width along the particular pseudotree chosen. We compare our algorithm with backtracking algorithms, and present experimental results. For some problem types we report orders of magnitude fewer messages, and the ability to deal with arbitrarily large problems. Our algorithm is formulated for optimization problems, but can be easily applied to satisfaction problems as well.

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

Abstract. We present Minion, a new constraint solver. Empirical results on standard benchmarks show orders of magnitude performance gains over state-of-the-art constraint toolkits. These gains increase with problem size – Minion delivers scalable constraint solving. Minion is a general-purpose constraint solver, with an expressive input language based on the common constraint modelling device of matrix models. Focussing on matrix models supports a highly-optimised implementation, exploiting the properties of modern processors. This contrasts with current constraint toolkits, which, in order to provide ever more modelling and solving options, have become progressively more complex at the cost of both performance and usability. Minion is a black box from the user point of view, deliberately providing few options. This, combined with its raw speed, makes Minion a substantial step towards Puget’s ‘Model and Run ’ constraint solving paradigm. 1

We present two simple search methods for computing a sample Nash equilibrium in a normal-form game: one for 2player games and one for n-player games. We test these algorithms on many classes of games, and show that they perform well against the state of the art-- the Lemke-Howson algorithm for 2-player games, and Simplicial Subdivision and Govindan-Wilson for n-player games.

We introduce a new approach to computing answer sets of logic programs, based on concepts from constraint processing (CSP) and satisfiability checking (SAT). The idea is to view inferences in answer set programming (ASP) as unit propagation on nogoods. This provides us with a uniform constraintbased framework for the different kinds of inferences in ASP. It also allows us to apply advanced techniques from the areas of CSP and SAT. We have implemented our approach in the new ASP solver clasp. Our experiments show that the approach is competitive with state-of-the-art ASP solvers. 1

We study the complexity and expressive power of conjunctive queries over unranked labeled trees, where the tree structures are represented using "axis relations" such as "child", "descendant", and "following" (we consider a superset of the XPath axes) as well as unary relations for node labels. (Cyclic) conjunctive queries over trees occur in a wide range of data management scenarios related to XML, the Web, and computational linguistics. We establish a framework for characterizing structures representing trees for which conjunctive queries can be evaluated e#- ciently. Then we completely chart the tractability frontier of the problem for our axis relations, i.e., we find all subsetmaximal sets of axes for which query evaluation is in polynomial time. All polynomial-time results are obtained immediately using the proof techniques from our framework. Finally, we study the expressiveness of conjunctive queries over trees and compare it to the expressive power of fragments of XPath. We show that for each conjunctive query, there is an equivalent acyclic positive query (i.e., a set of acyclic conjunctive queries), but that in general this query is not of polynomial size.

The paper introduces mixed networks, a new framework for expressing and reasoning with probabilistic and deterministic information. The framework combines belief networks with constraint networks, defining the semantics and graphical representation. We also introduce the AND/OR search space for graphical models, and develop a new linear space search algorithm. This provides the basis for understanding the benefits of processing the constraint information separately, resulting in the pruning of the search space. When the constraint part is tractable or has a small number of solutions, using the mixed representation can be exponentially more effective than using pure belief networks which model constraints as conditional probability tables.

We formulate dependency parsing as a graphical model with the novel ingredient of global constraints. We show how to apply loopy belief propagation (BP), a simple and effective tool for approximate learning and inference. As a parsing algorithm, BP is both asymptotically and empirically efficient. Even with second-order features or latent variables, which would make exact parsing considerably slower or NP-hard, BP needs only O(n3) time with a small constant factor. Furthermore, such features significantly improve parse accuracy over exact first-order methods. Incorporating additional features would increase the runtime additively rather than multiplicatively. 1

We study the survey propagation algorithm [19, 5, 4], which is an iterative technique that appears to be very effective in solving random k-SAT problems even with densities close to threshold. We first describe how any SAT formula can be associated with a novel family of Markov random fields (MRFs), parameterized by a real number ρ. We then show that applying belief propagation— a well-known “message-passing” technique—to this family of MRFs recovers various algorithms, ranging from pure survey propagation at one extreme (ρ = 1) to standard belief propagation on the uniform distribution over SAT assignments at the other extreme (ρ = 0). Configurations in these MRFs have a natural interpretation as generalized satisfiability assignments, on which a partial order can be defined. We isolate cores as minimal elements in this partial

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