Preserving K-Connectivity in Dynamic Graphs

Edge connectivity is a crucial concept in graph theory, which often serves as a fundamental metric for analyzing and improving the robustness, efficiency, and reliability of various types of networks. A graph is k-connected if it is still connected after removing arbitrarily fewer than $k$ edges. Sparse certificate is the lossless compression of a graph in terms of k-connectivity with a bounded size, which enables processing connectivity-driven queries in a more efficient way. Existing studies mainly focus on computing a sparse certificate in static graphs. Motivated by the prevalence of highly dynamic graphs, we aim to propose algorithms to maintain a sparse certificate when an edge is in-serted or deleted. We propose efficient algorithms to significantly improve the theoretical running time for both edge insertion and edge deletion compared with the baseline. We also propose a novel strategy for the search process in edge deletion. The strategy improves the efficiency compared with other potential methods with a theoretical guarantee. Extensive performance studies have been conducted on fourteen real-world datasets. The results demonstrate the significant advantages of our algorithms.