Minimum Spanning Tree (MST)

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.
🔥 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.
🔥 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.
🌟 Boruvka Algorithm →
🌟 Priority Queue →
Network Design →
Clustering →
Edmonds-Chu-Liu Algorithm →
Maximum Spanning Tree →
Greedy Algorithms →