Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 14 - Graph Theory - 14.3 Hamilton Paths and Hamilton Circuits - Exercise Set 14.3: 56

Answer

For a graph with a small number of vertices, the Brute Force Method is a reasonable method. However, if a graph has a large number of vertices, the number of Hamilton circuits can be extremely large. Even for a super-computer, it would be impractical to list all the possible Hamilton circuits and calculate the total weight of each Hamilton circuit.

Work Step by Step

To solve a traveling salesperson problem, we need to find the shortest possible route that a traveling salesperson can follow. The shortest possible route is the Hamilton circuit with the smallest total weight. The Brute Force Method involves listing all the possible Hamilton circuits in a graph and then calculating the total weight of each Hamilton circuit. Then we can identify the Hamilton circuit with the smallest total weight. This Hamilton circuit is the shortest possible route that a traveling salesperson can follow. For a graph with a small number of vertices, the Brute Force Method is a reasonable method. However, if a graph has a large number of vertices, the number of Hamilton circuits can be extremely large. Even for a super-computer, it would be impractical to list all the possible Hamilton circuits and calculate the total weight of each Hamilton circuit.
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