计算复杂性、相变和社区检测的消息传递
Computational Complexity, Phase Transitions, and Message-Passing for Community Detection
摘要：
我们将对计算机科学和统计物理学边界上的问题和技术进行旋风式的浏览。我们首先简要描述P、NP和NP完全性。然后，我们讨论随机图，包括出现的巨人组成部分和k-核心，使用技术从分支过程和微分方程。利用这些工具以及二阶矩方法，我们给出了随机k-SAT的临界子句密度的上界和下界。最后，我们在网络中的社区检测，变分方法，贝特自由能，信念传播，可检测性转变，和非回溯矩阵。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
