WRS: Waiting Room Sampling for Accurate Triangle Counting in Real Graph Streams

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.