Solved: Suppose that in solving a TSP you use the nearest-neighbor algorithm and find a

Chapter 6, Problem 48

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QUESTION:

Suppose that in solving a TSP you use the nearest-neighbor algorithm and find a nearest-neighbor tour with a total length of 21,400 miles. Suppose that you later find out that the length of an optimal tour is 20,100 miles. What was the relative error of your nearest-neighbor tour? Express your answer as a percentage, rounded to the nearest tenth of a percent.

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QUESTION:

Suppose that in solving a TSP you use the nearest-neighbor algorithm and find a nearest-neighbor tour with a total length of 21,400 miles. Suppose that you later find out that the length of an optimal tour is 20,100 miles. What was the relative error of your nearest-neighbor tour? Express your answer as a percentage, rounded to the nearest tenth of a percent.

ANSWER:

Step 1 of 2

The relative error of a tour is formulated by

                          (i)

Here, is the length of the tour obtained and is the length of the optimal tour.

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