Efficient Maintenance of Minimum Spanning Trees in Dynamic Weighted Undirected Graphs
MATHEMATICS(2024)
摘要
This paper presents an algorithm for effectively maintaining the minimum spanning tree in dynamic weighted undirected graphs. The algorithm efficiently updates the minimum spanning tree when the underlying graph structure changes. By identifying the portion of the original tree that can be preserved in the updated tree, our algorithm avoids recalculating the minimum spanning tree from scratch. We provide proof of correctness for the proposed algorithm and analyze its time complexity. In general scenarios, the time complexity of our algorithm is comparable to that of Kruskal's algorithm. However, the experimental results demonstrate that our algorithm outperforms the approach of recomputing the minimum spanning tree by using Kruskal's algorithm, especially in medium- and large-scale dynamic graphs where the graph undergoes iterative changes.
更多查看译文
关键词
minimum spanning tree,dynamic weighted undirected graph,fast incremental maintenance
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要