Minimum Spanning Tree Maintenance in Dynamic Graphs

Minimum Spanning Tree (MST) is a fundamental structure in graph analytics and can be applied in various applications. The problem of maintaining MSTs in dynamic graphs is significant, as many real-world graphs are frequently updated. Existing studies on MST maintenance primarily focus on theoretical analysis and lack practical efficiency. In this paper, we propose a novel algorithm to maintain MST in dynamic graphs, which achieves high practical efficiency. In addition to the tree structure, our main idea is to maintain a replacement edge for each tree edge. In this way, the tree structure can be immediately updated when a tree edge is deleted. We propose algorithms to maintain the replacement edge for each tree edge by sharing the computation cost in the updating process. Our performance studies on large datasets demonstrate considerable improvements over state-of-the-art solutions.