Routing Algorithm

Network Layer 4-11
1
23
IP destination address in
arriving packet’s header
routing algorithm
local forwarding table
dest address output link
address-range 1
address-range 2
address-range 3
address-range 4
3
2
2
1
Interplay between routing, forwarding
routing algorithm determines
end-end-path through network
forwarding table determines
local forwarding at this router

Network Layer 4-12
Routing algorithm classification
Q: global or decentralized
information?
global:
• all routers have complete
topology, link cost info
• “link state” algorithms
decentralized:
• router knows physically-
connected neighbors, link
costs to neighbors
• iterative process of
computation, exchange of
info with neighbors
Q: static or dynamic?
static:
 routes change slowly over
time
dynamic:
 routes change more
quickly
 periodic update
 in response to link cost
changes

Network Layer 4-13
A Link-State Routing Algorithm
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
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): predecessor node
along path from source to v
• N': set of nodes whose
least cost path definitively
known

Network Layer 4-14
Routing algorithm classification
Q: global or decentralized
information?
global:
• all routers have complete
topology, link cost info
• “link state” algorithms
decentralized:
• router knows physically-
connected neighbors, link
costs to neighbors
• iterative process of
computation, exchange of
info with neighbors
Q: static or dynamic?
static:
 routes change slowly over
time
dynamic:
 routes change more
quickly
 periodic update
 in response to link cost
changes

Network Layer 4-15
w3
4
v
x
u
5
3
7 4
y
8
z
2
7
9
Dijkstra’s algorithm: example
Step N'
D(v)
p(v)
0
1
2
3
4
5
D(w)
p(w)
D(x)
p(x)
D(y)
p(y)
D(z)
p(z)
u ∞∞7,u 3,u 5,u
uw ∞11,w6,w 5,u
14,x11,w6,wuwx
uwxv 14,x10,v
uwxvy 12,y
notes:
 construct shortest path tree
by tracing predecessor
nodes
 ties can exist (can be broken
arbitrarily)
uwxvyz

Network Layer 4-16
Dijkstra’s algorithm: another example
Step
0
1
2
3
4
5
N'
u
ux
uxy
uxyv
uxyvw
uxyvwz
D(v),p(v)
2,u
2,u
2,u
D(w),p(w)
5,u
4,x
3,y
3,y
D(x),p(x)
1,u
D(y),p(y)
∞
2,x
D(z),p(z)
∞
∞
4,y
4,y
4,y
u
yx
wv
z
2
2
1
3
1
1
2
5
3
5

Network Layer 4-17
Dijkstra’s algorithm: example (2)
u
yx
wv
z
resulting shortest-path tree from u:
v
x
y
w
z
(u,v)
(u,x)
(u,x)
(u,x)
(u,x)
destination link
resulting forwarding table in u:

Network Layer 4-18
Distance vector algorithm
Bellman-Ford equation (dynamic
programming)
let
dx(y) := cost of least-cost path from x to y
then
dx(y) = min {c(x,v) + dv(y) }
v
cost to neighbor v
min taken over all neighbors v of x
cost from neighbor v to destination y

Network Layer 4-19
Bellman-Ford example
u
yx
wv
z
2
2
1
3
1
1
2
5
3
5
clearly, dv(z) = 5, dx(z) = 3, dw(z) = 3
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
B-F equation says:

Network Layer 4-20
key idea:
from time-to-time, each node sends its
own distance vector estimate to neighbors
when 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
 under minor, natural conditions, the estimate
Dx(y) converge to the actual least cost dx(y)

Network Layer 4-21
iterative, asynchronous:
each local iteration
caused by:
• local link cost change
• DV update message from
neighbor
distributed:
• each node notifies
neighbors only when its
DV changes
– neighbors then notify their
neighbors if necessary
wait for (change in local link
cost or msg from neighbor)
recompute estimates
if DV to any dest has changed,
notify neighbors
each node:

Network Layer 4-22
x y z
x
y
z
0 2 7
∞∞ ∞
∞∞ ∞
from
cost to
fromfrom
x y z
x
y
z
0
x y z
x
y
z
∞ ∞
∞∞ ∞
cost to
x y z
x
y
z
∞∞ ∞
7 1 0
cost to
∞
2 0 1
∞ ∞ ∞
2 0 1
7 1 0
time
x z
12
7
y
node x
table
Dx(y) = min{c(x,y) + Dy(y), c(x,z) + Dz(y)}
= min{2+0 , 7+1} = 2
Dx(z) = min{c(x,y) +
Dy(z), c(x,z) + Dz(z)}
= min{2+1 , 7+0} = 3
32
node y
table
node z
table
cost to
from

Network Layer 4-23
x y z
x
y
z
0 2 3
from
cost to
x y z
x
y
z
0 2 7
from
cost to
x y z
x
y
z
0 2 3
from
cost to
x y z
x
y
z
0 2 3
from
cost to
x y z
x
y
z
0 2 7
from
cost to
2 0 1
7 1 0
2 0 1
3 1 0
2 0 1
3 1 0
2 0 1
3 1 0
2 0 1
3 1 0
time
x y z
x
y
z
0 2 7
∞∞ ∞
∞∞ ∞
from
cost to
fromfrom
x y z
x
y
z
0
x y z
x
y
z
∞ ∞
∞∞ ∞
cost to
x y z
x
y
z
∞∞ ∞
7 1 0
cost to
∞
2 0 1
∞ ∞ ∞
2 0 1
7 1 0
time
x z
12
7
y
node x
table
Dx(y) = min{c(x,y) + Dy(y), c(x,z) + Dz(y)}
= min{2+0 , 7+1} = 2
Dx(z) = min{c(x,y) +
Dy(z), c(x,z) + Dz(z)}
= min{2+1 , 7+0} = 3
32
node y
table
node z
table
cost to
from

Routing Algorithm

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