DTC: Real-Time and Accurate Distributed Triangle Counting in Fully Dynamic Graph Streams
Wei Xuan, Yan Liang, Huawei Cao, Ning Lin, Xiaochun Ye, Dongrui Fan

TL;DR
This paper introduces DTC, a family of distributed algorithms for real-time, approximate triangle counting in fully dynamic graph streams, effectively handling edge insertions and deletions with high accuracy.
Contribution
The paper presents DTC-AR and DTC-FD algorithms that provide unbiased, accurate, and scalable triangle counting in dynamic graph streams, addressing limitations of prior methods.
Findings
DTC-AR improves accuracy by up to 2029.4 times over baselines.
DTC-FD reduces estimation errors by up to 32.5 times.
Both algorithms scale linearly with graph stream size.
Abstract
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…
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