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

David A. Bader, Paul Burkhardt

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)577-588
Number of pages12
JournalJournal of Graph Algorithms and Applications
Issue number4
StatePublished - 2022

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science
  • Computer Science Applications
  • Geometry and Topology
  • Computational Theory and Mathematics


Dive into the research topics of 'A Simple and Efficient Algorithm for Finding Minimum Spanning Tree Replacement Edges'. Together they form a unique fingerprint.

Cite this