1. CS4470 Computer Networking Protocols
1/12/2019
CS Computer Networking Protocols
Routing
Huiping Guo
Department of Computer Science
California State University, Los Angeles

2. Outline Routing algorithms Link State Distance Vector
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Outline
Routing algorithms
Link State
Distance Vector
11. Routing CS4470_F17

3. Routing/Forwarding Overview
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Routing/Forwarding Overview
Extract destination IP address field
Look up IP address in the routing table
Find next hop address to forward to
Send datagram to the next hop
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4. Source of Route Table Information
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Source of Route Table Information
Manual
Table created by hand
Useful in small networks
Useful if routes never change
Automatic – Routing algorithms
software creates/updates tables
Needed in large networks
Changes routes when failures occur
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5. Graph abstraction z x u y w v
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Graph abstraction u y x w v z 2 1 3 5
A graph is used to formulate routing problems
Graph: G = (N,E)
N = set of routers = { u, v, w, x, y, z }
E = set of links ={ (u,v), (u,x),(u,w), (v,x), (v,w), (x,w), (x,y), (w,y), (w,z), (y,z) }
Node y is a neighbor of node x if (x,y) is in E.
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6. Graph abstraction: costsu y x w v z 2 1 3 5
c(x,x’) = cost of link (x,x’)
- e.g., c(w,z) = 5
cost: distance, link speed, bandwidth
A path: a sequence of nodes
Cost of path (x1, x2, x3,…, xp) = c(x1,x2) + c(x2,x3) + … + c(xp-1,xp)
Question: What’s the least-cost path between u and z ?
Routing algorithm: algorithm that finds least-cost path, or the shortest path
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7. Routing Algorithm classification
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Routing Algorithm classification
Global or decentralized information?
Global:
all routers have complete knowledge of the network topology, link cost info etc
“link state” algorithms
Decentralized:
router knows physically-connected neighbors, link costs to neighbors
iterative process of computation, exchange of info with neighbors
“distance vector” algorithms
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8. Link state algorithm Each router keeps track of its links
Whether the link is up or down
The cost on the link
Each router broadcasts the link state
To give every router a complete view of the graph
Each router runs Dijkstra’s algorithm
To compute the shortest paths
… and construct the forwarding table
Example protocols
Open Shortest Path First (OSPF)
Intermediate System – Intermediate System (IS-IS)
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9. Dijkstra’s algorithm net topology, link costs known to all nodes
accomplished via “link state broadcast”
all nodes have same info
computes least cost paths from one node (‘source”) to all other nodes
gives forwarding table for that node
iterative: after k iterations, know least cost path to k dest.’s
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10. Dijkstra’s algorithm Notation:
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): previous node along path from source to v
N': set of nodes whose least cost path definitively known
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11. Dijsktra’s Algorithm 1 Initialization: 2 N' = {u} 3 for all nodes v
if v adjacent to u
then D(v) = c(u,v)
else D(v) = ∞ 7
8 Loop
9 find w not in N' such that D(w) is a minimum
10 add w to N'
11 update D(v) for all v adjacent to w and not in N' :
D(v) = min( D(v), D(w) + c(w,v) )
13 /* new cost to v is either old cost to v or known
shortest path cost to w plus cost from w to v */
15 until all nodes in N'
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12. Dijkstra’s algorithm: example
Step 1 2 3 4 5 N' u ux
uxy
uxyv
uxyvw
uxyvwz
D(v),p(v)
2,u
D(w),p(w)
5,u
4,x
3,y
D(x),p(x)
1,u
D(y),p(y) ∞
2,x
D(z),p(z) ∞
4,y u y x w v z 2 1 3 5
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13. Dijkstra’s algorithm: example
Resulting shortest-path tree from u: u y x w v z
Resulting forwarding table in u: v x y w z
(u,v)
(u,x)
destination
link
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14. Distance Vector Algorithm
Distributed
Each node receives some information from its directly attached neighbors.
Each node performs a calculation and then distributes the results back to its neighbors
Iterative
The above process continues on until no more information is exchanged between neighbors.
Asynchronous
It does not require all of the nodes to operate in lockstep with each other
Example protocol
Routing Information Protocol (RIP)
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15. Distance Vector Algorithm
Bellman-Ford Equation (dynamic programming)
Define
dx(y) := cost of least-cost path from x to y
C(x,v) :=link cost between x and v
Then
dx(y) = min {c(x,v) + dv(y) }
where min is taken over all neighbors v of x
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16. Bellman-Ford example Clearly, dv(z) = 5, dx(z) = 3, dw(z) = 3u y x w v z 2 1 3 5
B-F equation says:
du(z) = min { c(u,v) + dv(z),
c(u,x) + dx(z),
c(u,w) + dw(z) }
= min {2 + 5,
1 + 3,
5 + 3} = 4
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17. Distance Vector Algorithm
Dx(y) = estimate of least cost from x to y
Distance vector: Dx = [Dx(y): y є N ]
Node x knows cost to each neighbor v: c(x,v)
Node x maintains Dx = [Dx(y): y є N ]
Node x also maintains its neighbors’ distance vectors
For each neighbor v, x maintains Dv = [Dv(y): y є N ]
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18. Distance vector algorithm
Basic idea:
Each node periodically sends its own distance vector estimate to neighbors
When a node x receives new DV estimate from neighbor, it updates its own DV using B-F equation:
Dx(y) ← minv{c(x,v) + Dv(y)} for each node y ∊ N
If node x’s distance vector has changed as a result of this update step, x will send its updated DV to each of its neighbors.
Each cost estimate Dx(y) converges to the actual cost dx(y)
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19. Distance Vector Algorithm
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Distance Vector Algorithm
Each node:
wait for (change in local link cost or message from neighbor)
recompute estimates
if DV to any destination has changed, notify neighbors
Iterative, asynchronous: each local iteration caused by:
Local link cost change
Distance vector update message from neighbor
Distributed:
Each node notifies neighbors only when its DV changes
Neighbors then notify their neighbors if necessary
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20. Distance Vector Example: Step 0
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Distance Vector Example: Step 0
Optimum 1-hop paths E F A C D B 2 3 6 4 1
Table for A
Dst
Cst
Hop A B 4 C  – D E 2 F 6
Table for B
Dst
Cst
Hop A 4 B C  – D 3 E F 1
Table for C
Dst
Cst
Hop A  – B C D 1 E F
Table for D
Dst
Cst
Hop A  – B 3 C 1 D E F
Table for E
Dst
Cst
Hop A 2 B  – C D E F 3
Table for F
Dst
Cst
Hop A 6 B 1 C D  – E 3 F
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21. Distance Vector Example: Step 2
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Distance Vector Example: Step 2
Optimum 2-hop paths
Table for A
Dst
Cst
Hop A B 4 C 7 F D E 2 5
Table for B
Dst
Cst
Hop A 4 B C 2 F D 3 E 1 A E F C D B 3 1 1 2 6 1 3 4
Table for C
Dst
Cst
Hop A 7 F B 2 C D 1 E 4
Table for D
Dst
Cst
Hop A 7 B 3 C 1 D E  – F 2
Table for E
Dst
Cst
Hop A 2 B 4 F C D  – E 3
Table for F
Dst
Cst
Hop A 5 B 1 C D 2 E 3 F
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22. Distance Vector Example: Step 3
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Distance Vector Example: Step 3
Optimum 3-hop paths
Table for A
Dst
Cst
Hop A B 4 C 6 E D 7 2 F 5
Table for B
Dst
Cst
Hop A 4 B C 2 F D 3 E 1 A E F C D B 3 1 1 2 6 1 3 4
Table for C
Dst
Cst
Hop A 6 F B 2 C D 1 E 4
Table for D
Dst
Cst
Hop A 7 B 3 C 1 D E 5 F 2
Table for E
Dst
Cst
Hop A 2 B 4 F C D 5 E 3
Table for F
Dst
Cst
Hop A 5 B 1 C D 2 E 3 F
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23. Comparison of LS and DV algorithms
The two algorithms take complementary approaches towards computing routing
Distance Vector
Each node talks to ONLY its directly connected neighbors
But it provides its neighbors with least-cost estimates from itself to ALL the notes in the network
Link State
Each node talks to ALL other notes (via broadcast)
It tells them ONLY the costs of its directly connected links
11. Routing CS4470_F17