Directed (Optimum Branchings), Super Dense MST: Difference between revisions
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(Created page with "{{DISPLAYTITLE:Directed (Optimum Branchings), Super Dense 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're given a directed graph with a root and $E=\Omega(V^2)$ edges, and we wish to find a spanning arborescence...") |
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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're given a directed graph with a root and $E=\Omega(V^2)$ edges, and we wish to find a spanning arborescence of minimum weight that is rooted at the root.
Related Problems
Generalizations: Directed (Optimum Branchings), General MST
Related: Undirected, General MST, Undirected, Dense MST, Undirected, Planar MST, Undirected, Integer Weights 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 |
|---|---|---|---|---|---|---|
| Tarjan (directed, dense) | 1987 | $O(V^{2})$ | $O(E)$ | Exact | Deterministic | Time & Space |
References/Citation
https://onlinelibrary-wiley-com.ezproxy.canberra.edu.au/doi/10.1002/net.3230070103