A Spectral Approach to Analyzing Belief Propagation for 3-Coloring

Amin Coja-Oghlan; Elchanan Mossel; Dan Vilenchik

doi:10.1017/s096354830900981x

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arXiv · 0712.0171

A Spectral Approach to Analyzing Belief Propagation for 3-Coloring

Amin Coja-Oghlan·Elchanan Mossel·Dan Vilenchik

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Abstract

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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Amin Coja-Oghlan, Elchanan Mossel, Dan Vilenchik. 2007-12-02. A Spectral Approach to Analyzing Belief Propagation for 3-Coloring. https://doi.org/10.1017/s096354830900981x

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