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: 57

Answer

With the Nearest Neighbor Method, we should choose the edge which has the smallest weight for each step along the path. After completing a Hamilton circuit, we can add up the weights of each edge in the Hamilton circuit to find the total weight of the Hamilton circuit. This method will approximate the optimal solution to the traveling salesperson problem.

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 Nearest Neighbor Method can give us an answer that can be found quite quickly, but this answer only approximates the optimal solution to a traveling salesperson problem. With the Nearest Neighbor Method, we should choose the edge which has the smallest weight for each step along the path. After completing a Hamilton circuit, we can add up the weights of each edge in the Hamilton circuit to find the total weight of the Hamilton circuit. This method will approximate the optimal solution to the traveling salesperson problem.
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