1. Dijkstra’s Algorithm Data structures: Notation: Path
c(x,y): link cost from node x to y; = ∞ if not direct neighbors
D(v): current value of cost of path from source to dest. v
p(v): predecessor node along path from source to v
N': set of nodes whose least cost path definitively known
Data structures:
Path
An ordered sequence of nodes
a cost to reach the end of the path
The sum of each lonk cost along the path
Candidate paths (CP)
Shortest paths (SP)

2. Dijsktra’s Algorithm Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have te same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop

3. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have te same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Initialization (Steps 2-3)
Least costs paths
Cost
Candidate paths
Cost A

4. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have te same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 5
Least costs paths
Cost
Candidate paths
Cost A
Entry with least cost

5. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have te same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 6
Least costs paths
Cost
Candidate paths
Cost A A
Move entry

6. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have te same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 7: Extend newly found least cost path
A’s neighbors are B and D
Least costs paths
Cost
Candidate paths
Cost A

7. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have te same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 7: Extend newly found least cost path
A’s neighbors are B and D
Least costs paths
Cost
Candidate paths
Cost A
A,B
0+C(A,B)

8. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have te same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 7: Extend newly found least cost path
A’s neighbors are B and D
Least costs paths
Cost
Candidate paths
Cost A
A,B
0+C(A,B)
A,D
0+C(A,D)

9. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have te same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 7: Extend newly found least cost path
A’s neighbors are B and D
Least costs paths
Cost
Candidate paths
Cost A
A,B
0+1=1
0+C(A,B)
A,D
0+12=12
0+C(A,D)

10. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have te same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 8: Nothing to do
Least costs paths
Cost
Candidate paths
Cost A
A,B 1
A,D 12

11. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have te same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 9: Nothing to do
Least costs paths
Cost
Candidate paths
Cost A
A,B 1
A,D 12

12. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have te same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 10: Keep on going
Least costs paths
Cost
Candidate paths
Cost A
A,B 1
A,D 12

13. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have te same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 5: A,B has the least cost
Least costs paths
Cost
Candidate paths
Cost A
A,B 1
A,D 12

14. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have te same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 6: Move to shortest paths
Least costs paths
Cost
Candidate paths
Cost A
A,D 12
A,B 1

15. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have te same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 7: Extend newly found least cost path
B’s neighbors are A, C, D, and E
Least costs paths
Cost
Candidate paths
Cost A
A,D 12
A,B 1

16. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have te same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 7: Extend newly found least cost path
B’s neighbors are A, C, and E
Least costs paths
Cost
Candidate paths
Cost A
A,D 12
A,B 1
A,B,A
1+C(B,A)

17. Step 7: Extend newly found least cost path 2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have te same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 7: Extend newly found least cost path
B’s neighbors are A, C, and E
Least costs paths
Cost
Candidate paths
Cost A
A,D 12
A,B 1
A,B,A
1+C(B,A)
A,B,C
1+C(B,C)

18. Dijsktra’s Algorithm from A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have te same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 7: Extend newly found least cost path
B’s neighbors are A, C, and E
Least costs paths
Cost
Candidate paths
Cost A
A,D 12
A,B 1
A,B,A
1+C(B,A)
A,B,C
1+C(B,C)
A,B,E
1+C(B,E)

19. Dijsktra’s Algorithm from A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have te same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 7: Extend newly found least cost path
B’s neighbors are A, C, and E
Least costs paths
Cost
Candidate paths
Cost A
A,D 12
A,B 1
A,B,A
1+C(B,A) 2
A,B,C 3
1+C(B,C)
A,B,E 7
1+C(B,E)

20. Dijsktra’s Algorithm from A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop. A F 2 12 D E 1
Step 8: Clean up candidate list 1:
remove candidate paths with the same end
Nothing to do
Least costs paths
Cost
Candidate paths
Cost A
A,D 12
A,B 1
A,B,A 2
A,B,C 3
A,B,E 7

21. Dijsktra’s Algorithm from A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop. A F 2 12 D E 1
Step 9: Clean up candidate list 2:
remove candidate paths with the same ends already in least cost paths
Remove A,B,A
Least costs paths
Cost
Candidate paths
Cost A
A,D 12
A,B 1
A,B,A 2
A,B,C 3
A,B,E 7

22. Dijsktra’s Algorithm from A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop. A F 2 12 D E 1
Step 9: Clean up candidate list 2:
remove candidate paths with the same ends already in least cost paths
Remove A,B,A
Least costs paths
Cost
Candidate paths
Cost A
A,D 12
A,B 1
A,B,C 3
A,B,E 7

23. Dijsktra’s Algorithm from A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 10: Keep on going
Least costs paths
Cost
Candidate paths
Cost A
A,D 12
A,B 1
A,B,C 3
A,B,E 7

24. Dijsktra’s Algorithm from A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop. A F 2 12 D E 1
Step 5: A,B,C has the lowest costc
Least costs paths
Cost
Candidate paths
Cost A
A,D 12
A,B 1
A,B,C 3
A,B,E 7

25. Dijsktra’s Algorithm from A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 6: Move path to least costs path
Least costs paths
Cost
Candidate paths
Cost A
A,D 12
A,B 1
A,B,C 3
A,B,C 3
A,B,E 7

26. Dijsktra’s Algorithm from A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop. A F 2 12 D E 1
Step 6: Move path to least costs path
Least costs paths
Cost
Candidate paths
Cost A
A,D 12
A,B 1
A,B,E 7
A,B,C 3

27. Dijsktra’s Algorithm from A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop. A F 2 12 D E 1
Step 7: Extend newly found least cost path
C’s neighbors are B, D, and F
Least costs paths
Cost
Candidate paths
Cost A
A,D 12
A,B 1
A,B,E 7
A,B,C 3
A,B,C, B
3+C(C,B)

28. Dijsktra’s Algorithm from A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop. A F 2 12 D E 1
Step 7: Extend newly found least cost path
C’s neighbors are B, D, and F
Least costs paths
Cost
Candidate paths
Cost A
A,D 12
A,B 1
A,B,E 7
A,B,C 3
A,B,C, B
3+C(C,B)
A,B,C, D
3+C(C,D)

29. Dijsktra’s Algorithm from A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 7: Extend newly found least cost path
C’s neighbors are B, D, and F
Least costs paths
Cost
Candidate paths
Cost A
A,D 12
A,B 1
A,B,E 7
A,B,C 3
A,B,C, B
3+C(C,B)
A,B,C, D
3+C(C,D)
A,B,C, F
3+C(C,F)

30. Dijsktra’s Algorithm from A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop. A F 2 12 D E 1
Step 7: Extend newly found least cost path
C’s neighbors are B, D, and F
Least costs paths
Cost
Candidate paths
Cost A
A,D 12
A,B 1
A,B,E 7
A,B,C 3
A,B,C, B 5
3+C(C,B)
A,B,C, D 9
3+C(C,D)
A,B,C, F
3+C(C,F) 4

31. Dijsktra’s Algorithm from A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop. A F 2 12 D E 1
Step 8: Clean up candidate list 1:
remove candidate paths with the same end
A,B,C,D has lower cost than A,D
Least costs paths
Cost
Candidate paths
Cost A
A,D 12
A,B 1
A,B,E 7
A,B,C 3
A,B,C, B 5
A,B,C, D 9
A,B,C, F 4

32. Dijsktra’s Algorithm from A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 8: Clean up candidate list 1:
remove candidate paths with the same end
A,B,C,D has lower cost than A,D
Least costs paths
Cost
Candidate paths
Cost A
A,B,E 7
A,B 1
A,B,C, B 5
A,B,C 3
A,B,C, D 9
A,B,C, F 4

33. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 9: Clean up candidate list 2:
remove candidate paths with the same ends already in least cost paths
Remove A,B,C,B
Least costs paths
Cost
Candidate paths
Cost A
A,B,E 7
A,B 1
A,B,C, B 5
A,B,C 3
A,B,C, D 9
A,B,C, F 4

34. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 9: Clean up candidate list 2:
remove candidate paths with the same ends already in least cost paths
Remove A,B,C,B
Least costs paths
Cost
Candidate paths
Cost A
A,B,E 7
A,B 1
A,B,C, D 9
A,B,C 3
A,B,C, F 4

35. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 10: Keep on going
Least costs paths
Cost
Candidate paths
Cost A
A,B,E 7
A,B,C, D
A,B 1 9
A,B,C 3
A,B,C, F 4

36. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 5: A,B,C,F has the least cost
Least costs paths
Cost
Candidate paths
Cost A
A,B,E 7
A,B 1
A,B,C, D 9
A,B,C 3
A,B,C, F 4

37. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 5: A,B,C,F has the least cost
Least costs paths
Cost
Candidate paths
Cost A
A,B,E 7
A,B,C, D
A,B 1 9
A,B,C 3
A,B,C, F 4
A,B,C, F 4

38. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 5: A,B,C,F has the least cost
Least costs paths
Cost
Candidate paths
Cost A
A,B,E 7
A,B,C, D 9
A,B 1
A,B,C 3
A,B,C, F 4

39. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 7: Extend newly found least cost path
F’s neighbors are C, and E
Least costs paths
Cost
Candidate paths
Cost A
A,B,E 7
A,B,C, D 9
A,B 1
A,B,C 3
A,B,C, F 4

40. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 7: Extend newly found least cost path
F’s neighbors are C, and E
Least costs paths
Cost
Candidate paths
Cost A
A,B,E 7
A,B,C, D
A,B 1 9
A,B,C 3
A,B,C, F, C
4+C(F,C)
A,B,C, F 4

41. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 7: Extend newly found least cost path
F’s neighbors are C, and E
Least costs paths
Cost
Candidate paths
Cost A
A,B,E 7
A,B,C, D
A,B 1 9
A,B,C 3
A,B,C, F, C
4+C(F,C)
A,B,C, F 4
A,B,C, F, E
4+C(F,E)

42. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 7: Extend newly found least cost path
F’s neighbors are C, and E
Least costs paths
Cost
Candidate paths
Cost A
A,B,E 7
A,B,C, D
A,B 1 9
A,B,C 3
A,B,C, F, C 5
4+C(F,C)
A,B,C, F
A,B,C, F, E 6
4+C(F,E) 4

43. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 8: Clean up candidate list 1:
remove candidate paths with the same end
A,B,C,F,E has lower cost than A,B,E
Least costs paths
Cost
Candidate paths
Cost A
A,B,E 7
A,B,C, D
A,B 1 9
A,B,C 3
A,B,C, F, C 5
A,B,C, F 4
A,B,C, F, E 6

44. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 8: Clean up candidate list 1:
remove candidate paths with the same end
A,B,C,F,E has lower cost than A,B,E
Least costs paths
Cost
Candidate paths
Cost A
A,B,C, D 9
A,B 1
A,B,C, F, C 5
A,B,C 3
A,B,C, F, E 6
A,B,C, F 4

45. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 9: Clean up candidate list 2:
remove candidate paths with the same ends already in least cost paths
Remove A,B,C,F,C
Least costs paths
Cost
Candidate paths
Cost A
A,B,C, D 9
A,B 1
A,B,C, F, C 5
A,B,C 3
A,B,C, F, E 6
A,B,C, F 4

46. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 9: Clean up candidate list 2:
remove candidate paths with the same ends already in least cost paths
Remove A,B,C,F,C
Least costs paths
Cost
Candidate paths
Cost A
A,B,C, D 9
A,B 1
A,B,C, F, E 6
A,B,C 3
A,B,C, F 4

47. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 10: Keep on going
Least costs paths
Cost
Candidate paths
Cost A
A,B,C, D 9
A,B 1
A,B,C, F, E 6
A,B,C 3
A,B,C, F 4

48. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 5: A, B, C, F, E has the least cost
Least costs paths
Cost
Candidate paths
Cost A
A,B,C, D 9
A,B 1
A,B,C, F, E 6
A,B,C 3
A,B,C, F 4

49. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 6: Move the newly found least cost path
Least costs paths
Cost
Candidate paths
Cost A
A,B,C, D 9
A,B 1
A,B,C, F, E 6
A,B,C 3
A,B,C, F 4
A,B,C, F, E 6

50. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 6: Move the newly found least cost path
Least costs paths
Cost
Candidate paths
Cost A
A,B,C, D 9
A,B 1
A,B,C 3
A,B,C, F 4
A,B,C, F, E 6

51. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 7: Extend newly found least cost path
F’s neighbors are B, D and F
Least costs paths
Cost
Candidate paths
Cost A
A,B,C, D 9
A,B 1
A,B,C 3
A,B,C, F 4
A,B,C, F, E 6

52. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 7: Extend newly found least cost path
F’s neighbors are B, D and F
Least costs paths
Cost
Candidate paths
Cost A
A,B,C, D 9
A,B,C, F, E, B
6+C(E,B)
A,B 1
A,B,C 3
A,B,C, F 4
A,B,C, F, E 6

53. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 7: Extend newly found least cost path
F’s neighbors are B, D and F
Least costs paths
Cost
Candidate paths
Cost A
A,B,C, D 9
A,B,C, F, E, B
6+C(E,B)
A,B 1
A,B,C, F, E, D
6+C(E,D)
A,B,C 3
A,B,C, F 4
A,B,C, F, E 6

54. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 7: Extend newly found least cost path
F’s neighbors are B, D and F
Least costs paths
Cost
Candidate paths
Cost A
A,B,C, D 9
A,B,C, F, E, B
6+C(E,B)
A,B 1
A,B,C, F, E, D
6+C(E,D)
A,B,C 3
A,B,C, F 4
A,B,C, F, E, F
6+C(E,F)
A,B,C, F, E 6

55. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 7: Extend newly found least cost path
F’s neighbors are B, D and F
Least costs paths
Cost
Candidate paths
Cost A
A,B,C, D 9
A,B,C, F, E, B 12
6+C(E,B)
A,B 1 3
A,B,C, F, E, D
6+C(E,D) 7
A,B,C
A,B,C, F 4
A,B,C, F, E, F
6+C(E,F) 8
A,B,C, F, E 6

56. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 8: Clean up candidate list 1:
remove candidate paths with the same end
A,B,C,F,E,D has lower cost than A,B, C, D
Least costs paths
Cost
Candidate paths
Cost A
A,B,C, D 9
A,B,C, F, E, B 12
A,B 1
A,B,C, F, E, D 7
A,B,C 3
A,B,C, F 4
A,B,C, F, E, F 8
A,B,C, F, E 6

57. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 8: Clean up candidate list 1:
remove candidate paths with the same end
A,B,C,F,E,D has lower cost than A,B, C, D
Least costs paths
Cost
Candidate paths
Cost 12 A
A,B,C, F, E, B
A,B 1
A,B,C, F, E, D 7
A,B,C 3
A,B,C, F, E, F 8
A,B,C, F 4
A,B,C, F, E 6

58. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 9: Clean up candidate list 2:
remove candidate paths with the same ends already in least cost paths
Remove A,B,C,F,E,B and A, B, C, F,E,F
Least costs paths
Cost
Candidate paths
Cost 12 A
A,B,C, F, E, B
A,B 1
A,B,C, F, E, D 7
A,B,C 3
A,B,C, F, E, F 8
A,B,C, F 4
A,B,C, F, E 6

59. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 9: Clean up candidate list 2:
remove candidate paths with the same ends already in least cost paths
Remove A,B,C,F,E,B and A, B, C, F,E,F
Least costs paths
Cost
Candidate paths
Cost A
A,B,C, F, E, D 7
A,B 1
A,B,C 3
A,B,C, F 4
A,B,C, F, E 6

60. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 10: keep on going
Least costs paths
Cost
Candidate paths
Cost A
A,B,C, F, E, D 7
A,B 1
A,B,C 3
A,B,C, F 4
A,B,C, F, E 6

61. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 5: A,B,C,F,E,D has the least cost
Least costs paths
Cost
Candidate paths
Cost A
A,B,C, F, E, D 7
A,B 1
A,B,C 3
A,B,C, F 4
A,B,C, F, E 6

62. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 6: move newly found least cost path
Least costs paths
Cost
Candidate paths
Cost A
A,B,C, F, E, D 7
A,B 1
A,B,C 3
A,B,C, F 4
A,B,C, F, E 6

63. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 6: move newly found least cost path
Least costs paths
Cost
Candidate paths
Cost A
A,B,C, F, E, D 7
A,B 1
A,B,C 3
A,B,C, F 4
A,B,C, F, E 6
A,B,C, F, E, D 7

64. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 6: move newly found least cost path
Least costs paths
Cost
Candidate paths
Cost A
A,B 1
A,B,C 3
A,B,C, F 4
A,B,C, F, E 6
A,B,C, F, E, D 7

65. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 7: Extend newly found least cost path
D’s neighbors are A, C and E
Least costs paths
Cost
Candidate paths
Cost A
A,B,C, F, E, D,A 19
A,B 1
A,B,C, F, E, D,C 13
A,B,C 3
A,B,C, F, E, D,E 8
A,B,C, F 4
A,B,C, F, E 6
A,B,C, F, E, D 7

66. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 8: Clean up candidate list 1:
Nothing to do
Least costs paths
Cost
Candidate paths
Cost A
A,B,C, F, E, D,A 19
A,B 1
A,B,C, F, E, D,C 13
A,B,C 3
A,B,C, F, E, D,E 8
A,B,C, F 4
A,B,C, F, E 6
A,B,C, F, E, D 7

67. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 9: Clean up candidate list 2:
remove candidate paths with the same ends already in least cost paths
Remove A,B,C,F,E,D,A, A, B, C, F,E,D,C and A,B,C,F,E,D,E
Least costs paths
Cost
Candidate paths
Cost A
A,B,C, F, E, D,A 19
A,B 1
A,B,C, F, E, D,C 13
A,B,C 3
A,B,C, F, E, D,E 8
A,B,C, F 4
A,B,C, F, E 6
A,B,C, F, E, D 7

68. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 9: Clean up candidate list 2:
remove candidate paths with the same ends already in least cost paths
Remove A,B,C,F,E,D,A, A, B, C, F,E,D,C and A,B,C,F,E,D,E
Least costs paths
Cost
Candidate paths
Cost A
A,B 1
A,B,C 3
A,B,C, F 4
A,B,C, F, E 6
A,B,C, F, E, D 7

69. Dijsktra’s Algorithm from Router A2
Link Costs
C(A,B)=1
C(A,D)=12
C(B,E)=6
C(B,C)=2
C(C,F)=1
C(C,D)=6
C(D,E)=1
C(E,F)=2 B C 1 1 6 6
Let u be the router running this algorithm
1 Initialization:
Candidate paths CP = [0, {u}]
Least cost paths = empty
Loop
find path [a, {u, …, w}] in CP with the least cost
Move [a, {u, …, w}] to shortest paths
Extend w and place extensions in CP: For each neighbor v of w make new candidate path [a+c(w,v), {u,…, w,v}]
Clean up candidate paths 1: if there are multiple entries in the list of candidate paths with the same destination, remove the ones with higher cost. If two have the same cost, remove one with more hops, if two have the same number of hops, remove the one with higher next hop IP address
Clean up candidate paths 2: Remove candidate paths that have a destination that is already in the list of shortest paths
If candidate paths is empty, then stop A F 2 12 D E 1
Step 10: DONE!
Least costs paths
Cost
Candidate paths
Cost A
A,B 1
A,B,C 3
A,B,C, F 4
A,B,C, F, E 6
A,B,C, F, E, D 7

70. Dijkstra’s algorithm, discussion
Algorithm complexity: n nodes
each iteration:
Need to check all entries in candidate list, at most N comparisons
Need to extend best path, at most N extensions
Need to compare each entry to all entries in the candidate list (at most N)
Need to compare each entry in candidate list to each entry in shortest paths (N/2)
3.5N each iteration, so 3.5N^2 ~ O(N^2)
more efficient implementations possible: O(nlogn)
Oscillations possible:
e.g., link cost = amount of carried traffic A D C B 1
1+e e
2+e
initially
… recompute
routing