EG180 Module 10 Assignment

EG180 Module 10 Assignment

Use the following graph for problems 1 and 2.

1. For the weighted graph given above, use the Brute Force Algorithm to find an optimal Hamilton Circuit stating at vertex D. Make sure to list all of your steps!

• Using the nearest-neighbor algorithm on the weighted graph above, provide the resulting Hamilton circuit depending on the starting vertex given below.
  • Using a starting vertex of A.
• Start from designated vertex ( A) i.e. home
• Move to the corresponding vertex ( or neighbor) with the smallest weight
• Each vertex is visited ones.
• Avoid passing through vertex that will create the smallest circuit
• Return to the starting vertex (home)

• Using a starting vertex of B.
• Start from designated vertex ( B) i.e. home
• Move to the corresponding vertex (neighbor) with the smallest weight
• Each vertex is visited ones.
• Avoid passing through vertex that will create the smallest circuit
• Return to the starting vertex (home)

• Which algorithm will always result in an optimal solution? Why? What are the benefits of the other algorithm?

• Suppose you are planning a trip around the world. Below is a table of the distances (in miles) between the cities you want to visit. Assume that you will start and end your trip in New York City.

	New York	London	Shanghai	Istanbul	Moscow	Cancún
New York		3459	7364	5030	4700	3391
London	3459		5715	1555	1560	4944
Shanghai	7364	5715		4960	4235	8354
Istanbul	5030	1555	4960		1090	6491
Moscow	4700	1560	4235	1090		6209
Cancún	3391	4944	8354	6491	6209

1. Find the nearest-neighbor tour with New York as the starting city.

• Find the nearest-neighbor tour with Moscow as the starting city.
• Find the total weight of both tours.

1. Tour starting New work
2. Tour starting Moscow

 

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