Minimum Spanning Tree

A minimum spanning tree is a subgraph of a given undirected graph, containing all the nodes and a subset of the arcs, such that:

• All nodes are connected.
• The resulting graph is a tree, i.e. there are no cycles.
• The sum of weights on the remaining arcs is as low as possible.

Example: Connect a set of locations to the Internet using a minimum length of cable.

The minimum spanning tree may not be unique, but all MST's will have the same total cost of arcs.