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....
View
Full Document
 Spring '11
 Estie
 Graph Theory, Spanning tree, following order, Estie Arkin, ﬁnal pred labels

Click to edit the document details