Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
A Spectral Technique for Coloring Random 3-Colorable Graphs
SIAM Journal on Computing
Analysis of low density codes and improved designs using irregular graphs
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A sharp threshold for k-colorability
Random Structures & Algorithms
A new look at survey propagation and its generalizations
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Survey propagation: An algorithm for satisfiability
Random Structures & Algorithms
Counting independent sets up to the tree threshold
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Lifts, Discrepancy and Nearly Optimal Spectral Gap
Combinatorica
Loopy belief propagation and Gibbs measures
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
Complete convergence of message passing algorithms for some satisfiability problems
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
On belief propagation guided decimation for random k-SAT
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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Belief propagation (BP) is a message-passing algorithm that computes the exact marginal distributions at every vertex of a graphical model without cycles. While BP is designed to work correctly on trees, it is routinely applied to general graphical models that may contain cycles, in which case neither convergence, nor correctness in the case of convergence is guaranteed. Nonetheless, BP has gained popularity as it seems to remain effective in many cases of interest, even when the underlying graph is ‘far’ from being a tree. However, the theoretical understanding of BP (and its new relative survey propagation) when applied to CSPs is poor. Contributing to the rigorous understanding of BP, in this paper we relate the convergence of BP to spectral properties of the graph. This encompasses a result for random graphs with a ‘planted’ solution; thus, we obtain the first rigorous result on BP for graph colouring in the case of a complex graphical structure (as opposed to trees). In particular, the analysis shows how belief propagation breaks the symmetry between the 3! possible permutations of the colour classes.