社区发现的计算机科学与物理学：景观、相变与硬度
The Computer Science and Physics of Community Detection: Landscapes, Phase Transitions, and Hardness
摘要：
图中的社区发现是找到比图的其余部分更密集连接的顶点组的问题。这个问题有着悠久的历史，但由于需要分析社会和生物网络，它正在重新引起人们的兴趣。虽然有很多方法可以将其形式化，但最流行的方法之一是将其作为推理问题，其中有一个以某种方式内置到图中的“地面真相”社区结构。然后，任务是恢复只知道图形的地面真相。最近，人们发现，这个问题有一个相变，在这个相变中，它突然变得不可能了，这个发现首先在物理学中得到验证，然后在概率论和计算机科学中得到严格验证。也就是说，如果图太稀疏，或者生成它的概率过程太嘈杂，那么没有算法可以找到与种植的分区相关的分区，甚至可以判断是否有社区，即，以高概率将图与纯随机图区分开。在这个信息论阈值之上，有第二个阈值，超过这个阈值，多项式时间算法就可以成功;在这两者之间，有一个机制，社区发现是可能的，但需要指数时间。对于计算机科学家来说，这个领域提供了大量的新思想和开放性问题，与概率和组合学，消息传递算法和随机矩阵理论有关。也许更重要的是，它提供了一个窗口，让我们了解统计物理和统计推断的文化，以及这些文化如何看待实例的分布、解决方案的景观和难度。
英文摘要：
Community detection in graphs is the problem of finding groups of vertices which are more densely connected than they are to the rest of the graph. This problem has a long history, but it is undergoing a resurgence of interest due to the need to analyze social and biological networks. While there are many ways to formalize it, one of the most popular is as an inference problem, where there is a "ground truth" community structure built into the graph somehow. The task is then to recover the ground truth knowing only the graph. Recently it was discovered, first heuristically in physics and then rigorously in probability and computer science, that this problem has a phase transition at which it suddenly becomes impossible. Namely, if the graph is too sparse, or the probabilistic process that generates it is too noisy, then no algorithm can find a partition that is correlated with the planted one---or even tell if there are communities, i.e., distinguish the graph from a purely random one with high probability. Above this information-theoretic threshold, there is a second threshold beyond which polynomial-time algorithms are known to succeed; in between, there is a regime in which community detection is possible, but conjectured to require exponential time. For computer scientists, this field offers a wealth of new ideas and open questions, with connections to probability and combinatorics, message-passing algorithms, and random matrix theory. Perhaps more importantly, it provides a window into the cultures of statistical physics and statistical inference, and how those cultures think about distributions of instances, landscapes of solutions, and hardness.
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。
