Undirected, Dense MST (Minimum Spanning Tree (MST))

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A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected; edge-weighted undirected graph that connects all the vertices together; without any cycles and with the minimum possible total edge weight. Here, we assume that the graph is dense (i.e. $E = \Omega(V)$).

Related Problems

Generalizations: Undirected, General MST

Related: Undirected, Planar MST, Undirected, Integer Weights MST, Directed (Optimum Branchings), General MST, Directed (Optimum Branchings), Super Dense MST


$V$: number of vertices

$E$: number of edges

$U$: maximum edge weight

Table of Algorithms

Name Year Time Space Approximation Factor Model Reference
Cheriton-Tarjan (dense) 1976 $O(E)$ $O(E)$ auxiliary? Exact Deterministic Time