Computational Complexity, Phase Transitions, and Message-Passing for Community Detection

Aurélien Decelle; Janina Hüttel; Alaa Saade; Cristopher Moore

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arXiv · 1409.2290

Computational Complexity, Phase Transitions, and Message-Passing for Community Detection

Aurélien Decelle·Janina Hüttel·Alaa Saade·Cristopher Moore

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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.

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cond-mat.dis-nn cond-mat.stat-mech cs.CC physics.soc-ph

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Aurélien Decelle, Janina Hüttel, Alaa Saade, Cristopher Moore. 2014-09-08. Computational Complexity, Phase Transitions, and Message-Passing for Community Detection. https://arxiv.org/abs/1409.2290

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