# Directed (Optimum Branchings), Super Dense MST (Minimum Spanning Tree (MST))

Jump to navigation
Jump to search

## 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 |