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You have just been hired on to be a technician for Bolts, a satellite company. You need to find the optimal route between several places within your city to decrease the time it takes to travel.

INSTRUCTIONS

Using a mapping service to obtain distances, create a weighted graph with the following locations as vertices:

  • Your place of residence
  • Your place of employment or local large business
  • City Hall or local seat of government
  • Police Station or local law enforcement office
  • Local Hospital or medical center

If there are more than one of any of these locations, choose only one of them from each bullet point to be on your graph. The edges on the graph will be labeled with the distance between each location.

Once you have created the graph, answer the following questions:

  1. Is there an Euler path in your graph? If so, provide an Euler path. If not, make sure to explain why not.
  2. Is there an Euler circuit in your graph? If so, provide an Euler path. If not, make sure to explain why not.
  3. Find the weight of the following Hamilton path: your house, your place of employment, city hall, police station, and the local hospital. Is there a way to make this a Hamilton circuit? Explain.
  4. Using the Brute Force Algorithm, find the optimal tour for your graph. How do you know it’s the optimal tour? Explain.
  5. Use the Nearest Neighbor Algorithm with your house as the reference vertex. Is this the optimal tour for our graph? Why or why not.
  6. Use the Nearest Neighbor Algorithm with your place of employment as the reference vertex. Is this the optimal tour for our graph? Why or why not.
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