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Reconstructing a Minimum Spanning Tree after Deletion of Any Node

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Abstract

Abstract. Updating a minimum spanning tree (MST) is a basic problem for communication networks. In this paper we consider single node deletions in MSTs. Let G=(V,E) be an undirected graph with n nodes and m edges, and let T be the MST of G . For each node v in V , the node replacement for v is the minimum weight set of edges R(v) that connect the components of T-v .

We present a sequential algorithm and a parallel algorithm that find R(v) for all V simultaneously. The sequential algorithm takes O(m log n) time, but only O(m α (m,n)) time when the edges of E are presorted by weight. The parallel algorithm takes O(log 2 n) time using m processors on a CREW PRAM.

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Das, Loui Reconstructing a Minimum Spanning Tree after Deletion of Any Node . Algorithmica 31, 530–547 (2001). https://doi.org/10.1007/s00453-001-0061-3

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  • DOI: https://doi.org/10.1007/s00453-001-0061-3

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