# PES: Priority Edge Sampling in Streaming Triangle Estimation

## TL;DR

PES is a new streaming algorithm that efficiently estimates the number of triangles in large graphs by combining edge and reservoir sampling, outperforming existing methods especially on very large datasets.

## Contribution

The paper introduces PES, a novel streaming algorithm that improves triangle estimation accuracy and efficiency, with proven unbiasedness and variance analysis.

## Key findings

- PES outperforms state-of-the-art algorithms in large real-world networks.
- Performance ratio of PES can be as high as 11, growing exponentially with data size.
- PES is unbiased and its variance is analytically derived.

## Abstract

The number of triangles (hereafter denoted by $\Delta$) is an important metric to analyze massive graphs. It is also used to compute clustering coefficient in networks. This paper proposes a new algorithm called PES (Priority Edge Sampling) to estimate the number of triangles in the streaming model where we need to minimize the memory window. PES combines edge sampling and reservoir sampling. Compared with the state-of-the-art streaming algorithms, PES outperforms consistently. The results are verified extensively in 48 large real-world networks in different domains and structures. The performance ratio can be as large as 11. More importantly, the ratio grows with data size almost exponentially. This is especially important in the era of big data--while we can tolerate existing algorithms for smaller datasets, our method is indispensable when sampling very large data. In addition to empirical comparisons, we also proved that the estimator is unbiased, and derived the variance.