A Simple and Efficient Algorithm for Finding Minimum Spanning Tree Replacement Edges

Document Type

Article

Publication Date

1-1-2022

Abstract

Given an undirected, weighted graph, the minimum spanning tree (MST) is a tree that connects all of the vertices of the graph with minimum sum of edge weights. In real world applications, network designers often seek to quickly find a replacement edge for each edge in the MST. For example, when a traffic accident closes a road in a transportation network, or a line goes down in a communication net-work, the replacement edge may reconnect the MST at lowest cost. In the paper, we consider the case of finding the lowest cost replacement edge for each edge of the MST. A previous algorithm by Tarjan takes O(mα(m, n)) time and space, where α(m, n) is the inverse Ackermann’s function. Given the MST and sorted non-tree edges, our algorithm is the first practical algorithm that runs in O(m + n) time and O(m + n) space to find all replacement edges. Additionally, since the most vital edge is the tree edge whose removal causes the highest cost, our algorithm finds it in linear time.

Identifier

85146365563 (Scopus)

Publication Title

Journal of Graph Algorithms and Applications

External Full Text Location

https://doi.org/10.7155/JGAA.00609

ISSN

15261719

First Page

577

Last Page

588

Issue

4

Volume

26

Grant

2109988

Fund Ref

National Science Foundation

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