Tutorial Activity 9

Tutorial Activity 9 - MH 8300 Tutorial Activity 9...

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MH 8300 Tutorial Activity 9 Travelling Salesman Problem Group Members Name NTU Email ID Marks : /2

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MH 8300 Tutorial Activity 9 Travelling Salesman Problem Figure 1: TSP graph with cities 1 - 10 City 1 2 3 4 5 6 7 8 9 10 1 0 72 40 72 26 49 39 24 66 45 2 72 0 54 22 47 22 82 54 83 26 3 40 54 0 42 25 36 28 17 34 35 4 72 22 42 0 46 27 71 49 64 30 5 26 47 25 46 0 24 43 11 59 20 6 49 22 36 27 24 0 62 32 68 4 7 39 82 28 71 43 62 0 31 31 60 8 24 54 17 49 11 32 31 0 49 29 9 66 83 34 64 59 68 31 49 0 68 10 45 26 35 30 20 4 60 29 68 0 Table 1: Distance matrix for the cities Question 1. Answer the following questions using the distance matrix for the cities given above. (a) Use nearest neighbour heuristic to determine a TSP tour starting at city 4 . (i) Determine the TSP tour. (ii) Find the length of this tour. (b) Use nearest neighbour heuristic to determine a TSP tour starting at city 6. (i) Determine the TSP tour. (ii) Find the length of this tour.
Question 2. (a) Find a minimum spanning tree (MST) using Prim’s algorithm. (b) Find the weight of this MST, denoted as W .
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