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: 55

Answer

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.

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.
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