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# sol6 - AMS 301.3(Fall 2009 Estie Arkin Homework Set 6...

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AMS 301.3 (Fall, 2009) Estie Arkin Homework Set # 6 – Solution Notes A: (a) Kruskal’s algorithms would insert the edges in the following order: (E,F) (A,B) (C,D) (C,E) (C,B). Cost of the MST 2 + 5 + 4 + 1 + 3 = 15 (b). Prim’s algorithm would insert the edges in the following order: (A,B), (B,C), (C,E), (C,D), (E,F). Cost of the MST 2 + 5 + 4 + 1 + 3 = 15 (c). Edge (A,B) is currently part of the minimum spanning tree. Suppose its cost is increased from 2 to 11. Will it still be part of the minimum spanning tree? Explain. No. If (A,B) remains in the tree, its cost is now 11 + 5 + 4 + 1 + 3 = 24, but removing (A,B) and including (A,D) yields a tree of smaller cost, 9 + 5 + 4 + 1 + 3 = 22. B: The edges in the shortest path tree are: (A,B) (B,C) (A,D) (C,E) (A,F). Here is the entire execution of the algorithm: u A u B u C u D u E u F node becoming perm 0 2 9 12 node B - - 7 9 12 12 node C - - - 9 11 12 node D - - - - 11 12 node E - - - - - 12 node F The final pred labels are: pred 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
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