# A Fast Sketch Method for Mining User Similarities over Fully Dynamic Graph Streams

## TL;DR

This paper introduces VOS, a fast and accurate sketching method for estimating user similarities in fully dynamic graph streams, addressing the bias issues of existing static graph methods.

## Contribution

The paper proposes VOS, a novel sketching technique that processes dynamic graph streams efficiently and accurately estimates user similarities over time.

## Key findings

- VOS processes each edge with O(1) time complexity.
- VOS uses small memory to build compact graph sketches.
- Experimental results show VOS's high efficiency and accuracy.

## Abstract

Many real-world networks such as Twitter and YouTube are given as fully dynamic graph streams represented as sequences of edge insertions and deletions. (e.g., users can subscribe and unsubscribe to channels on YouTube). Existing similarity estimation methods such as MinHash and OPH are customized to static graphs. We observe that they are indeed sampling methods and exhibit a sampling bias when applied to fully dynamic graph streams, which results in large estimation errors. To solve this challenge, we develop a fast and accurate sketch method VOS. VOS processes each edge in the graph stream of interest with small time complexity O(1) and uses small memory space to build a compact sketch of the dynamic graph stream over time. Based on the sketch built on-the-fly, we develop a method to estimate user similarities over time. We conduct extensive experiments and the experimental results demonstrate the efficiency and efficacy of our method.