Mining Frequent Patterns in Evolving Graphs

TL;DR

This paper introduces algorithms for approximate frequent subgraph mining in evolving graphs, efficiently handling dynamic updates and providing high-quality results with theoretical guarantees and empirical validation.

Contribution

It presents novel algorithms for approximate FSM in streaming settings that maintain high-quality samples efficiently, unlike existing methods.

Findings

Algorithms achieve high-quality approximation with high probability.

Proposed methods outperform baselines in empirical evaluations.

Theoretical analysis supports the effectiveness of the algorithms.

Abstract

Given a labeled graph, the frequent-subgraph mining (FSM) problem asks to find all the $k$-vertex subgraphs that appear with frequency greater than a given threshold. FSM has numerous applications ranging from biology to network science, as it provides a compact summary of the characteristics of the graph. However, the task is challenging, even more so for evolving graphs due to the streaming nature of the input and the exponential time complexity of the problem. In this paper, we initiate the study of the approximate FSM problem in both incremental and fully-dynamic streaming settings, where arbitrary edges can be added or removed from the graph. For each streaming setting, we propose algorithms that can extract a high-quality approximation of the frequent $k$-vertex subgraphs for a given threshold, at any given time instance, with high probability. In contrast to the existing state-of-the-art solutions that require iterating over the entire set of subgraphs for any update, our algorithms operate by maintaining a uniform sample of $k$-vertex subgraphs with optimized neighborhood-exploration procedures local to the updates. We provide theoretical analysis of the proposed algorithms and empirically demonstrate that the proposed algorithms generate high-quality results compared to baselines.