DTC: Real-Time and Accurate Distributed Triangle Counting in Fully Dynamic Graph Streams

Triangle counting is a fundamental problem in graph mining, essential for analyzing graph streams with arbitrary edge orders. However, exact counting becomes impractical due to the massive size of real-world graph streams. To address this, approximate algorithms have been developed, but existing distributed streaming algorithms lack adaptability and struggle with edge deletions. In this article, we propose DTC, a novel family of single-pass distributed streaming algorithms for global and local triangle counting in fully dynamic graph streams. Our DTC-AR algorithm accurately estimates triangle counts without prior knowledge of graph size, leveraging multi-machine resources. Additionally, we introduce DTC-FD, an algorithm tailored for fully dynamic graph streams, incorporating edge insertions and deletions. Using Random Pairing and future edge insertion compensation, DTC-FD achieves unbiased and accurate approximations across multiple machines. Experimental results demonstrate significant improvements over baselines. DTC-AR achieves up to 2029.4× and 27.1× more accuracy, while maintaining the best trade-off between accuracy and storage space. DTC-FD reduces estimation errors by up to 32.5× and 19.3×, scaling linearly with graph stream size. These findings highlight the effectiveness of our proposed algorithms in tackling triangle counting in real-world scenarios. The source code and datasets are released and available at https://github.com/Anonymousview/Real-Time-and-Accurate-Distributed-Triangle-Counting-in-Fully-Dynamic-Graph-Streams.