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Constructing Free Energy Approximations and Generalized Belief Propagation Algorithms
 IEEE Transactions on Information Theory
, 2005
"... Important inference problems in statistical physics, computer vision, errorcorrecting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems t ..."
Abstract

Cited by 585 (13 self)
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Important inference problems in statistical physics, computer vision, errorcorrecting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems that is exact when the factor graph is a tree, but only approximate when the factor graph has cycles. We show that BP fixed points correspond to the stationary points of the Bethe approximation of the free energy for a factor graph. We explain how to obtain regionbased free energy approximations that improve the Bethe approximation, and corresponding generalized belief propagation (GBP) algorithms. We emphasize the conditions a free energy approximation must satisfy in order to be a “valid ” or “maxentnormal ” approximation. We describe the relationship between four different methods that can be used to generate valid approximations: the “Bethe method, ” the “junction graph method, ” the “cluster variation method, ” and the “region graph method.” Finally, we explain how to tell whether a regionbased approximation, and its corresponding GBP algorithm, is likely to be accurate, and describe empirical results showing that GBP can significantly outperform BP.
A parallelization scheme based on work stealing for a class of sat solvers
 Journal of Automated Reasoning
"... Abstract. Due to the inherent NPcompleteness of SAT, many SAT problems currently cannot be solved in a reasonable time. Usually, to tackle a new class of SAT problems, new adhoc algorithm must be designed. Another way to solve a new problem is to use a generic solver and employ parallelism to redu ..."
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Abstract. Due to the inherent NPcompleteness of SAT, many SAT problems currently cannot be solved in a reasonable time. Usually, to tackle a new class of SAT problems, new adhoc algorithm must be designed. Another way to solve a new problem is to use a generic solver and employ parallelism to reduce the solve time. In this paper we propose a parallelization scheme for a class of SAT solvers based on the DPLL procedure. The scheme uses dynamic load balancing mechanism based on the work stealing techniques to deal with the irregularity of SAT problems. We parallelize Satz, one of the best generic SAT solvers, with the scheme to obtain a parallel solver called PSatz. The first experimental results on random 3SAT and a set of wellknown structured problems show the efficiency of PSatz. PSatz is freely available and runs on any networked workstations under Unix/Linux.
Complexity Analysis of Random Massive Algebraic System
"... Abstract. We build a new kind of random polynomial model, Massive Algebraic System (MAS), which is equivalent to algebraic polynomial system in solvability. This model focused on Finite Fields, especially on Z2, is NPcomplete. By results of Population Dynamics, we find these systems undergo 1Replic ..."
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Abstract. We build a new kind of random polynomial model, Massive Algebraic System (MAS), which is equivalent to algebraic polynomial system in solvability. This model focused on Finite Fields, especially on Z2, is NPcomplete. By results of Population Dynamics, we find these systems undergo 1Replica Symmetry Breaking (1RSB) and high order Replica Symmetry Breaking. This phenomenon indicates subtle structure and profound complexity of these systems. For determining the solvability of these random systems, Moments Method provides lower bounds α ∼ 0.5 and upper bounds α = 1 of threshold value. And through the dynamical analysis of LeafRemoving algorithm, the lower bounds are improved by αl(p), for which αl(1) = 0.562 and αl(0) = 0.818. Well understanding of this brandnew random algebraic model, which brings on new ways of complexity variation, will be instructive to polynomial equations with massive variables.