Network Layer - Routing Devices and Shortest Path Algorithms for Routing

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18 Ιουλ 2012 (πριν από 5 χρόνια και 1 μήνα)

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159.334 Computer Networks
159.334 Computer Networks
Network Layer

Routing Devices and
Shortest Path Algorithms for Routing
Professor Richard Harris
School of Engineering and Advanced
Technology (SEAT)
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Function of a Repeater
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Learning Bridge
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Routers
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2
131.170.16.0 131.170.16.3
Default 131.170.16.1
Routing Table
131.170.8.0 131.170.8.1
131.170.16.0 131.170.16.1
131.170.24.0 131.170.24.1
Routing Table
131.170.16.3
131.170.16.1
131.170.16.0
131.170.24.1
131.170.24.0
131.170.8.1
131.170.8.0
Router
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Routers
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A Routing Example
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Routing Algorithms
Dijkstra
and Bellman
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Ford
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Shortest Path:Example
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1
1
4
3
4
3
3
2
Problem:
Find the shortest route fromnode 1
to each of the other nodes.
Problem:
Find the shortest route fromnode 1
to each of the other nodes.
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4
5
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Shortest Path Example
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The smallest temporary label is on node 2,so we now
label it permanently (1*,1).
What is the meaning of the second field?
It means the node which determined the minimumvalue
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or
predecessor
node.
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3
2
1
3
2
4
5
(

,
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(4,1)
(

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(0,
-
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(1,1)
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Shortest Path Example
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5

Step 4:
Now,there are still nodes left in the network with temporary la
bels,so we continue
the process.The most recently assigned permanent label is node
2,so we examine
links leaving this node as before:

Node 3:
Min(4,1+3) = 4 (tie)

Node 4:
Min(

,1+2) = 3

Node 5:
Min(

,1+4) = 5
In each case,the
predecessor
node is node 2

but we shall leave node 3 alone in this
case.
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(

,
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(4,1)
(

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(0,
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(1,1)
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Application of
Dijkstra's
Algorithm
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Another Example
Consider the following
directed
network:
2
10
3
2
3
2
4
4
3
3
2
1
You give it a try now!
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Shortest Path:Example

1 (Again!)
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4
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4
3
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2
Problem:
Find the shortest route fromnode 1
to each of the other nodes.
Problem:
Find the shortest route fromnode 1
to each of the other nodes.
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2
4
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d
1
=

d
2
=

d
3
=

d
4
=

d
5
=

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Output from1
st
and 2
nd
passes
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Output fromfinal passes and solution
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Labelling after Pass#1
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4
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d
1
= 0;p
1
= 0
d
2
= 1;p
2
= 1
d
4
= 3;p
4
= 2
d
3
= 4;p
3
= 1
d
5
= 5;p
5
= 2