2. 16, 10 19- A B 21 24 Apply the nearest neighbor algorithm to the graph above starting at vertex A. Give your answer as a list of vertices, starting and ending at vertex A. Example: ABCDA

In the graphical representation of Travelling Salesman Problem vertices corresponds to the cities and weights of the edges denotes the distance between the cities .

Nearest Neighbour Algorithm :

1. Choose an arbitrary vertex x as starting vertex and find all the vertices adjacent to vertex v , say v₁,v₂,........,v_n .
2. Find the vertex v_k that is closet to vertex v w(v,v_k) = min { w(v,v₁),w(v,v₂),......,w(v,v_i)} , 1<= k <=1 join the two vertices v and v_k to form a path of length one say p .
3. Select a vertex which is not selected earlier from the last traced vertex and join it in the path to extend the path .
4. If the path contains all vertices of the graph . Then we are done . Now to obtain Hamiltonian circuit join the terminal vertices of the path by edge of minimum weight existing between the two vertices . Otherwise repeat steps 2 and 3 .