### Minimum Coast Spanning Tree (MST)

• Spanning Tree of a graph

• Definition: Spanning Tree

• Spanning Tree of a graph G = a tree (= no cycles) that includes:

 All vertices of the graph G some or all of the edges of the graph G

Example:

The edges of the Spanning tree is depicted in blue

• Cost of a Tree

• Definition: cost of a tree

 Cost of a Tree = the sum of the cost of all the edges in the tree

Example:

• Minimum cost Spanning Tree (MST)

• Definition: Minimum cost Spanning Tree

 Minimum cost Spanning Tree of a graph G = a Spanning Tree of graph G that has the lowest possible cost

• One of the classic optimization problems in graph theory is:

 Finding a Minimum cost Spanning Tree of a graph G

Why is this an important problem:

 Suppose the nodes represent cities The links represent the distance/cost to travel between cities A Minimum cost Spanning Tree is a network of roads that connect all cities that has the lowest possible cost !!!

• Classic algorithms for finding MST

• There are 2 classic algorithms for finding a MST of a graph: