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.

翻译：连通性查询处理是图处理中的一个基本问题。给定一个无向图及两个查询顶点，该问题旨在判断它们是否通过路径相连。考虑到实际图应用中频繁的边更新，本文研究了全动态图中的连通性查询处理，其中边会频繁插入或删除。一种称为D-树的最新解决方案为每个连通分量维护一棵生成树，并应用多种启发式方法来降低树的深度。为提高效率，我们提出了一种新的基于生成树的解决方案，通过同时维护一棵不相交集树来实现。通过结合两种树的优势，我们实现了恒定的查询时间复杂度，并显著改善了边插入和边删除操作的理论运行时间。此外，我们将连通性维护算法扩展至2-边连通性的维护。在真实大规模数据集上的性能研究表明，我们的算法取得了显著的改进。