Given a graph stream, how can we estimate the number of triangles in it using multiple machines with limited storage? Specifically, how should edges be processed and sampled across the machines for rapid and accurate estimation? The count of triangles (i.e., cliques of size three) has proven useful in numerous applications, including anomaly detection, community detection, and link recommendation. For triangle counting in large and dynamic graphs, recent work has focused largely on streaming algorithms and distributed algorithms but little on their combinations for “the best of both worlds.” In this work, we propose CoCoS , a fast and accurate distributed streaming algorithm for estimating the counts of global triangles (i.e., all triangles) and local triangles incident to each node. Making one pass over the input stream, CoCoS carefully processes and stores the edges across multiple machines so that the redundant use of computational and storage resources is minimized. Compared to baselines, CoCoS is: (a) accurate: giving up to smaller estimation error; (b) fast : up to faster, scaling linearly with the size of the input stream; and (c) theoretically sound : yielding unbiased estimates.

中文翻译：

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CoCoS：图流中快速准确的分布式三角形计数

给定一个图流，我们如何使用多台存储有限的机器来估计其中的三角形数量？具体来说，应该如何在机器上处理和采样边缘以进行快速准确的估计？三角形的计数（即大小为 3 的团）已被证明在许多应用中很有用，包括异常检测、社区检测和链接推荐。对于大型动态图中的三角形计数，最近的工作主要集中在流式算法和分布式算法上，但很少关注它们的组合以实现“两全其美”。在这项工作中，我们建议CoCoS，一种快速准确的分布式流算法，用于估计全局三角形（即所有三角形）和入射到每个节点的局部三角形的计数。对输入流进行一次传递，CoCoS在多台机器上仔细处理和存储边缘，以便最大限度地减少计算和存储资源的冗余使用。与基线相比，CoCoS是：(a) 准确：放弃 较小的估计误差；(b) 快速： 取决于 更快，随着输入流的大小线性缩放；和(c) 理论上合理: 产生无偏估计。