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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 Spring '08
 ARKIN
 Graph Theory, #, edges, Spanning tree, Estie Arkin

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