Constant-time Connectivity and 2-Edge Connectivity Querying in Dynamic Graphs

2026-01-24

AI Summary

This work addresses the problem of maintaining connectivity and 2-edge connectivity in fully dynamic undirected graphs under frequent edge updates. The paper proposes a novel data structure that simultaneously maintains both a spanning forest and a disjoint-set forest—a combination not previously explored. This approach achieves constant-time connectivity queries while significantly improving the theoretical update complexity for edge insertions and deletions, and it naturally extends to support 2-edge connectivity maintenance. Experimental evaluation on large-scale real-world graphs demonstrates that the proposed method substantially outperforms existing state-of-the-art techniques in both query speed and dynamic update efficiency.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

Abstract

Connectivity query processing is a fundamental problem in graph processing. Given an undirected graph and two query vertices, the problem aims to identify whether they are connected via a path. Given frequent edge updates in real graph applications, in this paper, we study connectivity query processing in fully dynamic graphs, where edges are frequently inserted or deleted. A recent solution, called D-tree, maintains a spanning tree for each connected component and applies several heuristics to reduce the depth of the tree. To improve efficiency, we propose a new spanning-tree-based solution by maintaining a disjoint-set tree simultaneously. By combining the advantages of two trees, we achieve the constant query time complexity and also significantly improve the theoretical running time in both edge insertion and edge deletion. In addition, we extend our connectivity maintenance algorithms to maintain 2-edge connectivity. Our performance studies on real large datasets show considerable improvement of our algorithms.

Problem

• connectivity querying
• dynamic graphs
• 2-edge connectivity
• edge updates
• graph processing

Innovation

• constant-time query
• dynamic graphs
• spanning tree
• disjoint-set tree
• 2-edge connectivity