Question
Consider the undirected complete graph having the following cost matrix: 1 2 3 4 5 6 X 3 9 8 7 5 1 3 X
Consider the undirected complete graph having the following cost matrix:
1 2 3 4 5 6
X | 3 | 9 | 8 | 7 | 5 | 1 |
3 | X | 8 | 1 | 11 | 7 | 2 |
9 | 8 | X | 6 | 4 | 7 | 3 |
8 | 1 | 6 | X | 9 | 8 | 4 |
7 | 11 | 4 | 9 | X | 10 | 5 |
5 | 7 | 7 | 8 | 10 | X | 6 |
a) The Nearest Neighbor Method is a greedy scheme that works on a complete graph as follows:The Traveling Salesman Problem is to find the cheapest possible tour in the graph. That is, a single simple cycle that starts at node 1, visits every node exactly once, and returns to node 1.
Start at node 1
For steps := 1 to n-1
Travel on the cheapest link from the present node to an unvisited node
3. Travel on the link from the last node to node 1
Perform this method to obtain a solution for the compete graph above and give its total cost.
b) Using any other method, find a different tour. Does it have a cheaper total cost?
c) "Starting the Nearest Neighbor Method algorithm from a different node may result in a solution having a different cost." True or False? Why?
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