TRI\`EST: Counting Local and Global Triangles in Fully-dynamic Streams with Fixed Memory Size

TL;DR

TRI'EST introduces streaming algorithms for accurate, unbiased approximation of triangle counts in dynamic graphs, efficiently utilizing fixed memory and outperforming existing methods in large-scale experiments.

Contribution

It provides the first fully-dynamic streaming algorithms with fixed memory for unbiased triangle counting, including variance analysis and concentration bounds.

Findings

Outperforms state-of-the-art methods in accuracy

Maintains low variance and unbiased estimates

Operates efficiently with small update times

Abstract

We present TRI\`EST, a suite of one-pass streaming algorithms to compute unbiased, low-variance, high-quality approximations of the global and local (i.e., incident to each vertex) number of triangles in a fully-dynamic graph represented as an adversarial stream of edge insertions and deletions. Our algorithms use reservoir sampling and its variants to exploit the user-specified memory space at all times. This is in contrast with previous approaches which use hard-to-choose parameters (e.g., a fixed sampling probability) and offer no guarantees on the amount of memory they will use. We show a full analysis of the variance of the estimations and novel concentration bounds for these quantities. Our experimental results on very large graphs show that TRI\`EST outperforms state-of-the-art approaches in accuracy and exhibits a small update time.