Define the spanning tree. Describe Prim’s algorithm that finding minimum cost spanning tree with suitable example.
Subject Algorithm Design
NU Year Set: 3.(b) Marks: 5 Year: 2008

A spanning tree is a subset of Graph G, which has all the vertices covered with minimum possible number of edges. Hence, a spanning tree does not have cycles and it cannot be disconnected..

The cost of the spanning tree is the sum of the weights of all the edges in the tree. There can be many spanning trees. Minimum spanning tree is the spanning tree where the cost is minimum among all the spanning trees. There also can be many minimum spanning trees.

Minimum spanning tree has direct application in the design of networks. It is used in algorithms approximating the travelling salesman problem, multi-terminal minimum cut problem and minimum-cost weighted perfect matching. Other practical applications are:

  1. Cluster Analysis
  2. Handwriting recognition
  3. Image segmentation

 

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