Applications of Graph Theory in Routing

8/10/2019 Applications of Graph Theory in Routing

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Applications of Graph Theory in

Routing

By

Paritosh Ramanan [2009C6PS681G]A R Pavan [2009C6PS678G]


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Routers

A router is a device used heavily in computer

networks.

It discretely distributes data packets to each

computer directly connected.

It is also responsible for communicating with

other computers on other networks in the

most optimum way.


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Routers


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The Working of Routers

The router uses the routing algorithm, stored inthe router's memory, to compute the path thatwould best serve to transport the data from thesource to the destination.

The routing protocol you choose for yournetwork determines which algorithm you willuse.

The overall performance of your networkdepends mainly on the routing algorithm.


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ROUTING PROTOCOLS


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Routing Protocols

The decision of which path to take in order tosend the data is based upon the "weights" ormetrics, which normally depend on the averagedelay time experienced by the router to

send/receive information.

Time delay can be due to the material of thecable used.

Therefore, the best possible path to take will bethe one with the lowest metric.

Contd


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The routing protocol provides the informationneeded by the routing algorithm to compute itsdecisions, through a process known as a routingupdate.

In the process it gathers information aboutnetworks and routers from the surroundingenvironment and stores the information within arouting table in the router's memory.

The routing algorithm is run using theinformation within this table to calculate the bestpath from one network to another.

Contd


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Calculating the new values within the formulathen generates a sum. The result of this

calculation is used then to determine where to

send information.

Through a series of updates, each router will

tell the other what information it has.

Eventually, an entire routing table will be built.


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ROUTING ALGORITHMS

Distance Vector Algorithm

Link-State Algorithm


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Distance vector algorithm (also called the

Ford-Fulkerson algorithm) use metrics or costs

to determine the best possible path.

The core crux of the algorithm lies in the

formula

m(i,k)=min[m(i,t)+m(t,k)]


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Illustration

Router Link Metric

A-B 2

B-C 3

A-C 6

C-D 5

A B

CD


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The router counts weights of all its direct links

and saves it to the table.

It sends this information to neighbour routers.

It in turn receives information of all itsneighbouring routers and thereby updates its

own tables.


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Illustration


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Illustration


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Drawback


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Link-State Algorithm

Identify the routers that are physically connected to them and get their IPaddresses.

Routers measure the delay time for neighbour routers by sending echo packetsover the network. Every router that receives these packets replies with an echoreply packet.

They broadcast their information over the network for other routers and receivethe other routers' information. In this step, all routers share their knowledge andbroadcast their information to each other.

In this way, every router can know the structure and status of the network.

Routers use an appropriate algorithm to identify the best route between twonodes of the network. In this step, routers choose the best route to every node.

They do this using an algorithm, such as the Dijkstra shortest path algorithm.


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DIJKSTRAS ALGORITHM


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Dijkstras Algorithm

Status record for each nodeon the network:

Predecessor field - showsthe previous node.

Length field - shows thesum of the weights fromthe source to that node.

Label field - shows thestatus of node; eachnode have one statusmode: "permanent" or"tentative."


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Finding the Shortest Path

This algorithm works well, but it is so

complicated that it may take a long time for

routers to process it.

That would cause the efficiency of the

network to fail.

If a router gives the wrong information to

other routers, all routing decisions will be

ineffective.


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Thank You

Documents

Applications of Graph Theory in Routing