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Unformatted text preview: 2 = 6, pred 3 = 2, pred 4 = 3, pred 5 = 4, pred 6 = 1, pred 7 = 6. C: Quick TSP: T 1 = 1 T 2 = 1 , 4 , 1 T 3 = 1 , 3 , 4 , 1 T 4 = 1 , 2 , 3 , 4 , 1 T 5 = 1 , 2 , 3 , 5 , 4 , 1 T 6 = 1 , 2 , 3 , 6 , 5 , 4 , 1, at cost 4 + 2 + 6 + 2 + 2 + 2 = 18 Using the double the MST method we get: The minimum spanning tree contains edges (3,4) (2,3) (1,4) (4,5) (5,6). Doubling it, we get an Euler cycle 14323456541. Shortcutting this by eliminating repeated nodes, we get the nal tour: 1432561 of length 2+1+2+5+2+4 = 16. Note that this solution is dierent, neither method gaurantees that we nd an optimal tour! D: Let each red edge have a cost 0 and each blue edge have cost 1. Now nd a mimimum cost spanning tree by any of the algorithms from class. It will contain as few blue edges as possible, and therefore as many red edges as possible....
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 Spring '11
 Estie

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