algorithm distributed bellman ford - computer...

Distributed Bellman Ford Algorithm

Studying the effects of deletion of nodes over a graph

Overview

Distributed Bellman Ford also known as Distance Vector Routing Algorithmis a well known shortest path routing algorithm with time complexity of O(|V||E|) where,V - verticesE - edges

We want to simulate Distance Vector over a graph and show that the running time increases with the percentage of increase in deletion of nodes.

Overview

● In this project we would vary the no of nodes in a graph from 100-10,000.

● At every n node graph we would delete x% of nodes in a graph where x would vary between 1% to 40%.

● We would study the effects of increasing the deletion of nodes in each graph.

● We feel that increasing the no of deletions would increase the response time of the algorithm making is slower

Hypothesis

Deletion of nodes in a graph simulating Bellman Ford Algorithm causes the response time to find the shortest path to increase.

Algorithm

n1 n2 n3

n4 n5

1 2

3 4 5

6

Node n1 sends the vector table to n2 and n4

from n2 Link Cost

n1 n1 1

n2 _ 0

from n4 Link Cost

n1 n1 3

n4 _ 0

A loop-free Extended Bellman-Ford Routing Protocol without Bouncing Effect,

SIGCOMM '89 Symposium proceedings on Communications architectures & protocols

Algorithm

n1 n2 n3

n4 n5

1 2

3 4 5

6

Node n2 sends the vector table to n1, n3 and n5

from node n1

Link Cost

n1 _ 0

n2 n2 1

from Link n3

Link Cost

n1 n2 3

n2 n2 2

n3 _ 0

From node n5 Link Cost

n1 n2 5

n2 n2 4

n5 _ 0

Algorithm

n1 n2 n3

n4 n5

1 2

3 4 5

6


from node n1

Link Cost

n1 _ 0

n2 n2 1

n4 n4 3

from Node n5 Link Cost

n1 n2 5

n2 n2 4

n4 n4 6

n5 _ 0

Algorithm

n1 n2 n3

n4 n5

1 2

3 4 5

6


from n2 Link Cost

n1 n1 1

n2 _ 0

n4 n1 4

from n4 Link Cost

n1 n1 1

n2 n1 4

n4 _ 0

Algorithm

n1 n2 n3

n4 n5

1 2

3 4 5

6


from node n2

Link Cost

n1 n1 1

n2 _ 0

n3 n3 2

n4 n1 4

from node n5 Link Cost

n1 n2 5

n2 n2 4

n3 n3 5

n4 n4 6

n5 _ 0

Algorithm

n1 n2 n3

n4 n5

1 2

3 4 5

6


from node n2

Link Cost

n1 n1 1

n2 _ 0

n3 n3 2

n4 n1 4

n5 n5 4

from node n3

Link Cost

n1 n2 3

n2 n2 2

n3 _ 0

n4 n5 11

n5 n5 5

from node n4

Link Cost

n1 n1 3

n2 n1 4

n3 n5 11

n4 _ 0

n5 n5 6

from n1

Link Cost

n1 _ 0

n2 n2 1

n3 n2 3

n4 n4 3

n5 n2 5

from n4

Link Cost

n1 n1 3

n2 n1 4

n3 n1 6

n4 _ 0

n5 n5 6

from n5

Link Cost

n1 n2 5

n2 n3 4

n3 n3 5

n4 n4 6

n5 _ 0

from n2

Link Cost

n1 n1 1

n2 _ 0

n3 n3 2

n4 n1 4

n5 n5 4

from n3

Link Cost

n1 n2 3

n2 n2 2

n3 _ 0

n4 n2 6

n5 n5 5

Problems in Bellman Ford Algorithm● Bouncing Effect● Count to Infinity● Looping

Bouncing Effect

100 1

1

n1

n3 n2

● edge n1-n2 fail● n1 is the destination node

from n3● n2 is the prefered

neighbour according to the routing table

● n3 is the prefered neighbour for n2 because n1-n2 link failed

● Nodes n2 and n3 have distance 2 and 3 respectively now. This is less than 100

● This stops when the value of link n3-n2 becomes greater than 100

Count to Infinity

100 1

1

n1

n3 n2

● link n1-n3 also fail along with link n1-n2

● The bouncing effect between link n2-n3 continues till infinity

● It does not stop at a value just greater than 100.



Looping

n1

n2n5 n4

n3

5 1

5

1

13

● If link n1-n5 and n3-n5 break.

● n1 and n3 will send their updated vectors to the neighbours

● for instance the message delay for clockwise is very small in comparison to the counter clockwise.

● the prefered neighbour for both n2 and n4 remain same.

● causing looping or delay for the packets which have arrived to be transferred.



Progress

● We understood the routing algorithm and its drawbacks.

● We studied some ways of improving the algorithm to avoid Count to Infinity.

● We implemented node sensitive graphs.● We simulated Bellman Ford Algorithm over

the built graph.

Software DesignDistanceVector Node

- Graph g- Node [] nodeArray- LinkedList <Integer> myqueue

-byte distanceVector-int nodeId-Set <Integer> notification-Set <Integer> neighbours-boolean changeInDv-static Node NodeArray[] +addToQueue()

+calculateQueueDV()+displayDV()+mian()

+static Node[] initializeNode(Graph g)+Set<Integer> recalculateDV()+Set<Integer>notifyNeighbours()

Graph

-static final byte INFINITY-long seed-int E-int N-byte maxDistanceBetweenTwoNodes-byte AdjacencyMatrix[][]

+int getNumberOfObjects()+byte[] getDistanceVector(int index)+Set<Integer>getNeighbours(int index)

1

*1

1

1 *

Usagejava DistanceVector <seed> <noOfNodes> <noOfEdges> <maxDistance>

seed: This is a no. which is used to create a random no.noOfNodes: This defines the no of nodes in a graphnoOfEdges: defines the no of edges in a graphmaxDistance: The max. distance between two connected nodes

Demonstration

algorithm distributed bellman ford - computer...

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