8 161019A2124Apply the nearest neighbor algorithm to the graph above starting at vertex A. Give your answer as a list ofvertices, starting and ending at vertex A. Example: ABCDAEnter text [more..]

Answered: 2. 16, 10 19- A B 21 24 Apply the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

16
10
19
A
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
Enter text [more..]

Expert Solution

Step 1

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 :

Choose an arbitrary vertex x as starting vertex and find all the vertices adjacent to vertex v , say v₁,v₂,........,v_n .
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 .
Select a vertex which is not selected earlier from the last traced vertex and join it in the path to extend the path .
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 .