A polynomial-time algorithm matches two correlated stochastic block models of logarithmic average degree almost exactly for s^2 > 0.338, and exactly whenever s^2(a+b)/2 > 1.
Community Detection and Stochastic Block Models: Recent Developments
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Efficient Graph Matching for Correlated Stochastic Block Models
A polynomial-time algorithm matches two correlated stochastic block models of logarithmic average degree almost exactly for s^2 > 0.338, and exactly whenever s^2(a+b)/2 > 1.