A Spectral Approach to Analyzing Belief Propagation for 3-Coloring

Details A Spectral Approach to Analyzing Belief Propagation for 3-Coloring A Spectral Approach to Analyzing Belief Propagation for 3-Coloring

2007-12-02

arxiv.org/abs/0712.0171v1

Computer Science

Computational Complexity

Scientific paper

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 coloring 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 color classes.

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