Computational Complexity, Phase Transitions, and Message-Passing for Community Detection
Abstract
We take a whirlwind tour of problems and techniques at the boundary of computer science and statistical physics. We start with a brief description of P, NP, and NP-completeness. We then discuss random graphs, including the emergence of the giant component and the k-core, using techniques from branching processes and differential equations. Using these tools as well as the second moment method, we give upper and lower bounds on the critical clause density for random k-SAT. We end with community detection in networks, variational methods, the Bethe free energy, belief propagation, the detectability transition, and the non-backtracking matrix.
Cite
@article{arxiv.1409.2290,
title = {Computational Complexity, Phase Transitions, and Message-Passing for Community Detection},
author = {Aurélien Decelle and Janina Hüttel and Alaa Saade and Cristopher Moore},
journal= {arXiv preprint arXiv:1409.2290},
year = {2014}
}
Comments
Chapter of "Statistical Physics, Optimization, Inference, and Message-Passing Algorithms", Eds.: F. Krzakala, F. Ricci-Tersenghi, L. Zdeborova, R. Zecchina, E. W. Tramel, L. F. Cugliandolo (Oxford University Press, to appear)