Abstract
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, E t) of G, we study the problem of finding, for every node v ∈ V, the MST of G - v = (VSHIELA{v}, E/E v), where E v 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 + nlogn)) time and O (m) space. Our solution improves on the previously known O(m logn) time bound.
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This work has been partially developed while the second author was visiting the third one, supported by the EU TMR Grant CHOROCHRONOS and by the Swiss National Science Foundation.
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Nardelli, E., Proietti, G., Widmayer, P. (2000). Maintaining a Minimum Spanning Tree under Transient Node Failures. In: Paterson, M.S. (eds) Algorithms - ESA 2000. ESA 2000. Lecture Notes in Computer Science, vol 1879. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45253-2_32
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DOI: https://doi.org/10.1007/3-540-45253-2_32
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