WRS：实图流中精确三角形计数的等待室抽样
WRS: Waiting Room Sampling for Accurate Triangle Counting in Real Graph Streams
摘要：
如果我们不能存储图流中的所有边，我们应该存储哪些边来准确估计三角形计数？计数三角形（即，长度为3的循环）是在社会网络分析、web挖掘、异常检测等中具有许多应用的基本图问题。最近，已经做出了很多努力来在具有有限空间的流设置中准确地估计全局和局部三角形计数。虽然现有的方法使用采样技术，而不考虑时间依赖性的边缘，我们观察到时间的局部性，在真正的动态图。也就是说，未来的边更可能与最近的边形成三角形，而不是与较旧的边形成三角形。在这项工作中，我们提出了一个单通流算法称为等候室采样（WRS）的全球和当地的三角形计数。WRS利用时间局部性，总是存储最近的边缘，未来的边缘更有可能形成三角形，在等待室，而它使用水库采样的其余边缘。我们的理论和实证分析表明，WRS是：（a）快速和“任何时间”：在线性时间内运行，总是保持和更新估计，而新的边缘到达，（b）有效的：产生高达47%的估计误差小于其最好的竞争对手，和（c）理论上的声音：给出无偏估计的时间局部性下的小方差。
英文摘要：
If we cannot store all edges in a graph stream, which edges should we store to estimate the triangle count accurately? Counting triangles (i.e., cycles of length three) is a fundamental graph problem with many applications in social network analysis, web mining, anomaly detection, etc. Recently, much effort has been made to accurately estimate global and local triangle counts in streaming settings with limited space. Although existing methods use sampling techniques without considering temporal dependencies in edges, we observe temporal locality in real dynamic graphs. That is, future edges are more likely to form triangles with recent edges than with older edges. In this work, we propose a single-pass streaming algorithm called Waiting-Room Sampling (WRS) for global and local triangle counting. WRS exploits the temporal locality by always storing the most recent edges, which future edges are more likely to form triangles with, in the waiting room, while it uses reservoir sampling for the remaining edges. Our theoretical and empirical analyses show that WRS is: (a) Fast and 'any time': runs in linear time, always maintaining and updating estimates while new edges arrive, (b) Effective: yields up to 47% smaller estimation error than its best competitors, and (c) Theoretically sound: gives unbiased estimates with small variances under the temporal locality.
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