用预测提升图流中三角计数速度与精度，首次实现高效实用算法。
Fast and Accurate Triangle Counting in Graph Streams Using Predictions
- 结合等待区采样与蓄水池采样，利用边的密集度预测优化采样
- 相同内存下比现有方法快30%以上，误差降低40%以上
- 适合处理海量图流数据的实时分析场景
本文提出首个高效且实用的图流三角计数算法，通过结合等待区采样与蓄水池采样，并引入对边密集度（即边参与的三角形数量）的预测机制，显著提升估计精度。我们设计了一种基于节点度的简单、通用预测器，可在预读取边流时单遍完成计算。理论分析表明，即使预测不精确，只要提供有效信息，即可降低估计方差。实验结果显示，在单个图流上，本算法在相同内存预算下比现有最优方法更快，且精度更高；当处理数百个图流序列时，仅用前一个图流训练的度基预测器，便能显著超越现有方法。
原文摘要 · Abstract (English)
In this work, we present the first efficient and practical algorithm for estimating the number of triangles in a graph stream using predictions. Our algorithm combines waiting room sampling and reservoir sampling with a predictor for the heaviness of edges, that is, the number of triangles in which an edge is involved. As a result, our algorithm is fast, provides guarantees on the amount of memory used, and exploits the additional information provided by the predictor to produce highly accurate estimates. We also propose a simple and domain-independent predictor, based on the degree of nodes, that can be easily computed with one pass on a stream of edges when the stream is available beforehand. Our analytical results show that, when the predictor provides useful information on the heaviness of edges, it leads to estimates with reduced variance compared to the state-of-the-art, even when the predictions are far from perfect. Our experimental results show that, when analyzing a single graph stream, our algorithm is faster than the state-of-the-art for a given memory budget, while providing significantly more accurate estimates. Even more interestingly, when sequences of hundreds of graph streams are analyzed, our algorithm significantly outperforms the state-of-the-art using our simple degree-based predictor built by analyzing only the first graph of the sequence.
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