A minimum spanning tree would be one with the lowest total cost.

A number of problems from graph theory are called Minimum spanning tree.

Depending on what the graph looks like, there may be more than one minimum spanning tree.

If each edge has a distinct weight then there will be only one, unique minimum spanning tree.

Research has also considered parallel algorithms for the minimum spanning tree problem.

They were used to achieve the best complexity to date for finding a minimum spanning tree.

Prim's purpose is to find a minimum spanning tree for a graph.

If the graph is connected, the forest has a single component and forms a minimum spanning tree.

This is similar to the minimum spanning tree problem which concerns undirected graphs.

Constructions based on a minimum spanning tree have an approximation ratio of 2.

This is essentially the same as Kruskal's algorithm for minimum spanning trees.

Prim's algorithm for finding the minimum spanning tree in a graph.

Like minimum spanning trees, shortest path trees in general are not unique.

This property implies the algorithm will eventually terminate with a minimum spanning tree.

Every F-heavy edge deleted is not in the minimum spanning tree by the cycle property.

In a graph where all the edges have the same weight, every tree is a minimum spanning tree.

It can be very simple to make an algorithm that will discover a minimum spanning tree:

Download the example minimum spanning tree data.

Finally F is the minimum spanning tree of the contracted graph by the inductive hypothesis.

The popular method for connecting two correlated stocks is the minimum spanning tree method.

It is also used for implementing Kruskal's algorithm to find the minimum spanning tree of a graph.

State-of-the-art algorithms for minimum spanning trees: A tutorial discussion.

Construct a minimum spanning tree for .

A minimum spanning tree is a feasible but not usually optimal solution to the Steiner tree problem.

Fortunately, some greedy algorithms (such as minimum spanning trees) are proven to lead to the optimal solution.