| Summary: | 碩士 === 國立臺灣大學 === 資訊工程學研究所 === 96 === Since the development of computers and the expediency of internet, network plays an important role in the life of human beings. If there is only one computer as the server, then we use a single-source shortest-paths tree to connect the network. Maybe some line of communication is broken. Thus if we know the importance for each line, we may reduce the damage by taking care of more important lines. We de ne G = (V;E;w) to be an undirected graph with n vertices and m edges. And there is an non-negative edge weight function w : E ! R+. Let s 2 V and T be the shortest-paths tree rooted at s. We de ne the cost of T to be the total distance from s to all vertices. If we remove some edge from G, there is a substitute shortest-paths tree ^ T.
The most vital edge problem with respect to a shortest-paths tree is to nd an edge in E(G) such that the di erence between the costs of ^ T and T is the largest. In this thesis, we give an algorithm with time complexity O(m (m; n) + km + kn log n), where k is the number of internal nodes of T, and (m; n) is a functional inverse of Ackermann''s function.
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