Undirected, Planar MST: Difference between revisions
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(Created page with "{{DISPLAYTITLE:Undirected, Planar MST (Minimum Spanning Tree (MST))}} == Description == 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 planar. == Related Problems == Generalizations: Undirected, General MST Related: Undirected, Dense...") |
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== Parameters == | == Parameters == | ||
$V$: number of vertices | |||
E: number of edges | |||
U: maximum edge weight | $E$: number of edges | ||
$U$: maximum edge weight | |||
== Table of Algorithms == | == Table of Algorithms == | ||
Latest revision as of 08:19, 10 April 2023
Description
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 planar.
Related Problems
Generalizations: Undirected, General MST
Related: Undirected, Dense MST, Undirected, Integer Weights MST, Directed (Optimum Branchings), General MST, Directed (Optimum Branchings), Super Dense MST
Parameters
$V$: number of vertices
$E$: number of edges
$U$: maximum edge weight
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Cheriton-Tarjan (planar) | 1976 | $O(V)$ | $O(V)$ auxiliary | Exact | Deterministic | Time |
References/Citation
https://epubs-siam-org.ezproxy.canberra.edu.au/doi/abs/10.1137/0205051