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Author: dbader13

README.md

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+# MST-ReplacementEdges: Find Minimum Spanning Tree Replacement Edges
+
+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. This code finds the lowest cost replacement edge for each edge of
+the MST, based on this paper:
+
+David A. Bader and Paul Burkhardt, "[A Linear Time Algorithm for
+Finding Minimum Spanning Tree Replacement
+Edges](https://arxiv.org/abs/1908.03473)", arXiv:1908.03473v3, 2020.
+
+- MST-ReplacementEdges-Tarjan: This subdirectory contains a superlinear
+  implementation using the Tarjan approach for disjoint set unions.
+
+- MST-ReplacementEdges-Gabow-Tarjan: This subdirectory implements the
+  linear-time Bader-Burkhardt algorithm using the Gabow-Tarjan
+  approach for disjoint set unions when the union tree is known in
+  advance.
+
+This code can also find the most vital edge -- the tree edge whose
+removal causes the highest cost -- in linear time.
+