1. EE 122: Intra-domain routing: Link State
Computer Science Division
Department of Electrical Engineering and Computer Science
University of California, Berkeley,
Berkeley, CA
September 21, 2004

2. Protocol Hourglass Application Transport
Service: best-effort data delivery
Functionality: packet forwarding
and routing
Network (IP)
Link
Physical

3. Forwarding: Example Host C Host D Host A N2 N1 N3 N5 Host B N4 Host E

4. Forwarding: Examples D dst next dst next A A dst next A N1 B N4 A N2 BC N2
Host C B N5 C C D N5 C N2
Host D
Host A D N3 E N5 D D E N3 E N7 N2 N1
dst
next A N1 N3 B N4 N5 C N1
dst
next D N3 A N3 E N3
Host B B N6
dst
next N4
Host E C N3 A N1
dst
next N6 N7 D N3 B B D A N4 E E C N4 B N4 D N6 C N4 E N6 D N7 E N7

5. Forwarding: Example D dst next dst next A A dst next A N1 B N4 A N2 BC N2
Host C B N5 C C D N5 C N2
Host D
Host A D N3 E N5 D D E N3 E N7 N2 N1
dst
next A N1 N3 B N4 N5 C N1
dst
next D N3 A N3 E N3
Host B B N6
dst
next N4
Host E D C N3 A N1
dst
next N6 N7 D N3 B B A N4 E E C N4 B N4 D N6 C N4 E N6 D N7 E N7

6. Forwarding: Example D dst next dst next A A dst next A N1 B N4 A N2 BC N2
Host C B N5 C C D N5 C N2
Host D
Host A D N3 E N5 D D E N3 E N7 N2 N1
dst
next A N1 N3 B N4 N5 C N1
dst
next D N3 A N3 E N3
Host B B N6
dst
next N4
Host E C N3 A N1
dst
next N6 N7 D N3 B B D A N4 E E C N4 B N4 D N6 C N4 E N6 D N7 E N7

7. Forwarding: Example D dst next dst next A A dst next A N1 B N4 A N2 BC N2
Host C B N5 C C D N5 C N2
Host D
Host A D N3 E N5 D D E N3 E N7 N2 N1
dst
next A N1 N3 B N4 N5 C N1
dst
next D N3 A N3 E N3
Host B B N6
dst
next N4
Host E C N3 A N1
dst
next N6 N7 D N3 B B D A N4 E E C N4 B N4 D N6 C N4 E N6 D N7 E N7

8. Forwarding: Example D dst next dst next A A dst next A N1 B N4 A N2 BC N2
Host C B N5 C C D N5 C N2
Host D
Host A D N3 E N5 D D E N3 E N7 N2 N1
dst
next D A N1 N3 B N4 N5 C N1
dst
next D N3 A N3 E N3
Host B B N6
dst
next N4
Host E C N3 A N1
dst
next N6 N7 D N3 B B A N4 E E C N4 B N4 D N6 C N4 E N6 D N7 E N7

9. Routing Protocols Compute and maintain routing tables
Routing vs. forwarding tables
Routing table: table containing all information required to compute the paths to every other node
Forwarding table: table used to forward packets
Type of routing algorithms
Distance vector (see last lecture)
Path-vector: like distance vector, but the route updates contain the entire path to the destination
Link state (this lecture)

10. Link State: Node State Host A Host B Host E Host D Host C N1 N2 N3 N4

11. Distance Vector: Control Traffic
When the routing table of a node changes, the nodes send its table to the neighbors
Host A
Host B
Host E
Host D
Host C N1 N2 N3 N4 N5 N7 N6

12. Distance Vector: Control Traffic
When the routing table of a node changes, the nodes send its table to the neighbors
Host A
Host B
Host E
Host D
Host C N1 N2 N3 N4 N5 N7 N6

13. Distance Vector: Control Traffic
When the routing table of a node changes, the nodes send its table to the neighbors
Host A
Host B
Host E
Host D
Host C N1 N2 N3 N4 N5 N7 N6

14. Distance Vector: Control Traffic
When the routing table of a node changes, the nodes send its table to the neighbors
Host A
Host B
Host E
Host D
Host C N1 N2 N3 N4 N5 N7 N6

15. Distance Vector: Control Traffic
When the routing table of a node changes, the nodes send its table to the neighbors
Host A
Host B
Host E
Host D
Host C N1 N2 N3 N4 N5 N7 N6

16. Link State: Control Traffic
Each node floods its local information to every other node in the network  each node ends up knowing the entire network topology
Host A
Host B
Host E
Host D
Host C N1 N2 N3 N4 N5 N7 N6

17. Link State: Control Traffic
Each node floods its local information to every other node in the network  each node ends up knowing the entire network topology
Host A
Host B
Host E
Host D
Host C N1 N2 N3 N4 N5 N7 N6

18. Link State Protocol
Each node computes shortest path to every other node using its local view of the network topology
When a node notices a link or another node failure, it floods this information in the network
Other nodes update their network view and recompute the shortest paths

19. A Link State Routing Algorithm
Dijkstra’s algorithm
Net topology, link costs known to all nodes
Accomplished via “link state flooding”
All nodes have same info
Each node computes least cost paths from itself to all other nodes
Iterative: after k iterations, know least cost paths to k closest destinations
Notations
c(i,j): link cost from node i to j; cost infinite if not direct neighbors
D(v): current value of cost of path from source to destination v
p(v): predecessor node along path from source to v, that is next to v
S: set of nodes whose least cost path definitively known

20. Dijsktra’s Algorithm 1 Initialization: 2 S = {A}; 3 for all nodes v
if v adjacent to A
then D(v) = c(A,v);
else D(v) = ; 7
8 Loop
find w not in S such that D(w) is a minimum;
10 add w to S;
11 update D(v) for all v adjacent to w and not in S:
D(v) = min( D(v), D(w) + c(w,v) );
// new cost to v is either old cost to v or known
// shortest path cost to w plus cost from w to v
13 until all nodes in S;

21. Example: Dijkstra’s Algorithm
Step 1 2 3 4 5
start S A
D(B),p(B)
2,A
D(C),p(C)
5,A
D(D),p(D)
1,A
D(E),p(E)
D(F),p(F)
1 Initialization:
2 S = {A};
3 for all nodes v
if v adjacent to A
then D(v) = c(A,v);
else D(v) = ; … 5 3 B C 2 5 A 2 1 F 3 1 2 D E 1

22. Example: Dijkstra’s Algorithm
Step 1 2 3 4 5
start S A AD
D(B),p(B)
2,A
D(C),p(C)
5,A
4,D
D(D),p(D)
1,A
D(E),p(E)
2,D
D(F),p(F) …
8 Loop
find w not in S s.t. D(w) is a minimum;
10 add w to S;
update D(v) for all v adjacent
to w and not in S:
D(v) = min( D(v), D(w) + c(w,v) );
13 until all nodes in S; 5 3 B C 2 5 A 2 1 F 3 1 2 D E 1

23. Example: Dijkstra’s Algorithm
Step 1 2 3 4 5
start S A AD
ADE
D(B),p(B)
2,A
D(C),p(C)
5,A
4,D
3,E
D(D),p(D)
1,A
D(E),p(E)
2,D
D(F),p(F)
4,E …
8 Loop
find w not in S s.t. D(w) is a minimum;
10 add w to S;
update D(v) for all v adjacent
to w and not in S:
D(v) = min( D(v), D(w) + c(w,v) );
13 until all nodes in S; 5 3 B C 2 5 A 2 1 F 3 1 2 D E 1

24. Example: Dijkstra’s Algorithm
Step 1 2 3 4 5
start S A AD
ADE
ADEB
D(B),p(B)
2,A
D(C),p(C)
5,A
4,D
3,E
D(D),p(D)
1,A
D(E),p(E)
2,D
D(F),p(F)
4,E …
8 Loop
find w not in S s.t. D(w) is a minimum;
10 add w to S;
update D(v) for all v adjacent
to w and not in S:
D(v) = min( D(v), D(w) + c(w,v) );
13 until all nodes in S; 5 3 B C 2 5 A 2 1 F 3 1 2 D E 1

25. Example: Dijkstra’s Algorithm
Step 1 2 3 4 5
start S A AD
ADE
ADEB
ADEBC
D(B),p(B)
2,A
D(C),p(C)
5,A
4,D
3,E
D(D),p(D)
1,A
D(E),p(E)
2,D
D(F),p(F)
4,E …
8 Loop
find w not in S s.t. D(w) is a minimum;
10 add w to S;
update D(v) for all v adjacent
to w and not in S:
D(v) = min( D(v), D(w) + c(w,v) );
13 until all nodes in S; 5 3 B C 2 5 A 2 1 F 3 1 2 D E 1

26. Example: Dijkstra’s Algorithm
Step 1 2 3 4 5
start S A AD
ADE
ADEB
ADEBC
ADEBCF
D(B),p(B)
2,A
D(C),p(C)
5,A
4,D
3,E
D(D),p(D)
1,A
D(E),p(E)
2,D
D(F),p(F)
4,E …
8 Loop
find w not in S s.t. D(w) is a minimum;
10 add w to S;
update D(v) for all v adjacent
to w and not in S:
D(v) = min( D(v), D(w) + c(w,v) );
13 until all nodes in S; 5 3 B C 2 5 A 2 1 F 3 1 2 D E 1

27. Oscillations Assume link cost = amount of carried traffic A 1 1 D B CC 1 1
initially

28. Oscillations Assume link cost = amount of carried trafficB
2+e
1+e 1
… recompute
routing e A D C B
2+e
1+e 1
… recompute e A D C B
2+e e
1+e 1
… recompute 1
1+e D B e C 1 1 e
initially
How can you avoid oscillations?

29. Distance Vector vs. Link State
Convergence
Message & Computation complexity
Robustness

30. Convergence How much does it take the algorithm to converge?
Link State: d*l + c, where
d: diameter of the network
l: latency of a message along the link
c: computation time to run Dijkstra’s algorithm
Distance Vector:
Good news: d*(l+c’), where c’ is the time it takes a node to update rounding table
Band news: varies (e.g., count to infinity problem)

31. Message Complexity
Link State (LS): every node needs to flood its local state: n*n*e messages, where
n: number of nodes in the network
e: average degree
n*e: number of messages per link to flood the network
Distance vector (DV): assume the algorithm executes in rounds: d*n*e messages, where
d: diameter of the network; it takes d rounds to converge
n*e: number of messages during a round  each node sends its changes to all its neighbors
Note: messages in DV are larger than in LS

32. Computation Complexity
Link State: running time of Dijkstra’s algorithm
Each iteration: need to check all nodes, w, not in S
n*(n+1)/2 comparisons: O(n2)
More efficient implementations possible: O(n*log(n))
Distance vector: update routing table
n, assuming that it takes O(1) to find an entry in the table given the node

33. Robustness Link state Distance vector
Node can advertise incorrect link cost
Each node computes only its own table
Distance vector
Node can advertise incorrect path cost
Each node’s table used by others; error propagate through network