AMS 301.3 (Fall, 2009)Estie ArkinHomework Set # 6 – Solution NotesA: (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 from2 to 11. Will it still be part of the minimum spanning tree? Explain. No. If (A,B) remains in thetree, its cost is now 11 + 5 + 4 + 1 + 3 = 24, but removing (A,B) and including (A,D) yields a treeof 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:uAuBuCuDuEuFnode becoming perm02∞9∞12node B--791212node C---91112node D----1112node E-----12node FThe final pred labels are: pred2= 6, pred3= 2, pred4= 3, pred5= 4, pred6= 1, pred7= 6.C: Quick TSP:T1= 1T2= 1,4,1T3= 1,3,4,1T4= 1
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