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Minimum Spanning Tree (MST)
Overview
Minimum Spanning Tree (MST)
graph_theory
graph
tree
spanning_tree
spanning_subgraph
weighted_graph
undirected_graph
connected_graph
combinatorial_optimization
matroid
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Kruskal Algorithm →
Kruskal’s algorithm computes a minimum spanning tree; its goal and correctness rely on MST definitions and properties (cut and cycle), guiding edge selection and stopping criteria.
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Prim Algorithm →
Prim's algorithm uses the MST problem and its cut/cycle properties to make greedy edge selections and to define its goal of constructing a minimum spanning tree.
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Disjoint Set Union →
In Kruskal’s MST algorithm, a Disjoint Set Union is used to maintain connected components and test whether adding an edge would create a cycle; union/find with path compression and union by rank enables near-linear-time MST construction.
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Boruvka Algorithm →
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Priority Queue →
Network Design →
Clustering →
Edmonds-Chu-Liu Algorithm →
Maximum Spanning Tree →
Greedy Algorithms →