1. Discrete Math 2 Weighted Graph Search Tree
2001
Discrete Math 2 Weighted Graph Search Tree
CIS112
February 5, 2007
Daniel L. Silver

2. Overview Building a search tree Step by step
Shortest path in weighted graph
Step by step
Begin with initial vertex = root node
At each step
Choose least cost node
Expand it
Add children to tree
Matching vertice? Prune vertex with greatest cost
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3. Example Graph
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4. First Steps Place starting vertex at root Expand the node
Children = vertices directly connected
Path cost = weight of edge
In this example
Seek least cost path from 7 to 12
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5. Resulting Tree #1
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6. Next Step Choose node with lowest path cost Expand it
That is the node for vertex #3
Expand it
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7. Resulting Tree #2
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8. Next Step Choose node with lowest path cost
The path costs are: 15 23 25 34
The least cost is 15
So we expand the node for vertex #10
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9. Resulting Tree #3
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10. Next Step We now have two copies of vertex #8
One has a path cost of 24
The other’s path cost is 25
So we must prune the one with the highest cost
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11. Resulting Tree #4
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12. Next Step Now it is time again to expand
The node for vertex #11 has the lowest cost
So we expand it
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13. Resulting Tree #5
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14. Comments
Even though we have reached vertex #12, we are not finished; there may be a shorter path yet to be found.
We delete the higher cost copy of #8
We remove all nodes with path cost ≥ 26 from consideration
Q: Why can we do that?
Q: Why do we not remove them?
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15. Resulting Tree #6
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16. Continuing . . We continue by expanding Node #1 And then #8 2007
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17. Resulting Tree #7
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18. Resulting Tree #8
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19. Resulting Tree #9
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20. Final Comments There are no more nodes to expand
So the process is completed
We determine the least cost path is:
7  10  11  12
The total cost is 26
2007
Kutztown University