Maintaining a Minimum Spanning Tree Under Transient Node Failures
نویسندگان
چکیده
Given a 2-node connected, undirected graph G = (V,E), with n nodes and m edges with real weights, and given a minimum spanning tree (MST) T = (V, ET ) of G, we study the problem of finding, for every node v ∈ V , the MST of G− v = (V \ {v}, E \ Ev), where Ev is the set of edges incident to v in G. We show that this problem can be solved in O(min(m ·α(n, n),m+ n log n)) time and O(m) space. Our solution improves on the previously known O(m log n) time bound.
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