The table shows driving times in hours between cities. City | A | B | C | D | E --- | --- | --- | --- | --- | --- A | * | 9 | 8 | 5 | 13 B | 9 | * | 12 | 4 | 6 C | 8 | 12 | * | 7 | 10 D | 5 | 4 | 7 | * | 17 E | 13 | 6 | 10 | 17 | * 8. Draw a graph of these travel options where the vertices are the cities and two vertices are connected by an edge if a trip can be made between the two cities. Indicate the weight of the appropriate edge also. 9. A recruiting agent is required to drive to interview prospects. They live in city A. How many different ways can the agent visit each city and return to his starting point in city A? 10. Use the nearest neighbor algorithm to find the Hamiltonian circuit starting at A in the graph below. Make sure to list the edges chosen in order, give the cheapest circuit starting in city A and its weight.
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The driving times between cities are as follows: - A to B: 13 hours - A to C: 12 hours - A to D: 5 hours - A to E: 12 hours - B to C: 10 hours - B to D: 13 hours - B to E: 10 hours Now, let's find the number of different ways the agent can visit each city and Show more…
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Let the following graph also represent a map of towns (represented by the letters A, B, C, D, E) with connecting roads. But now, each edge connecting the towns has a weight; and this number could be thought of as the time it takes to travel that segment of road. For instance, the route B, C, D has a total travel time of 1 + 3 = 4. Suppose you want to travel from town A to town E, passing through each town exactly once along the way: List all the different routes you could take (there are six of them), along with the total time it would take to travel each route. Which of these routes takes the least time? Which takes the most time? Find a walk that starts at vertex a, passes through each edge exactly once, and then ends at vertex a. (This is an example of what is called an Euler Tour.) There are many possible answers; just write one. Note that you are allowed to pass through some vertices more than once.
Adi S.
Problem I: Route Planning A company representative lives in Louisville, Kentucky and needs to visit offices in five different Indiana cities over the next few days. The representative wants to drive between cities and return to Louisville at the end of the trip. The estimated driving times, in hours, between cities are given in the table below (along with a map of Indiana): a) Represent the driving times by a weighted graph. b) Use the greedy algorithm to design an efficient route for the representative to follow. How many hours does this route require? c) Use the edge-picking algorithm to design an efficient route for the representative to follow. How many hours does this route require? d) Which of the two previous routes best minimizes the representative's total driving time?
Madhur L.
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