Thinking Mathematically (6th Edition)

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

Chapter 14 - Graph Theory - 14.4 Trees - Exercise Set 14.4: 55

Answer

The statement makes sense.

Work Step by Step

The statement makes sense. Finding the Hamilton circuit for which the sum of the weights is a minimum can require huge amounts of calculations. The Nearest Neighbor Method is a relatively quick method which helps us find a Hamilton circuit in the graph which approximates the optimal solution. Sometimes the Nearest Neighbor Method gives us the optimal solution but the method does not always give us the optimal solution. However, Kruskal's Algorithm always gives the minimum spanning tree in a graph. That is, using Kruskal's Algorithm, we can always find the spanning tree with the smallest possible total weight.
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