This document presents an implementation of Dijkstra's algorithm to find the shortest path between computers connected by routers on a network. It introduces Dijkstra's algorithm and how it works, provides an example graph and step-by-step workings, then applies it to a problem of finding the lowest cost route between computers on an internet connection. A simulation models the network as a graph and runs Dijkstra's algorithm to determine the shortest path from computer A to G has a total cost of 70. Screenshots confirm the algorithm was implemented and found the lowest cost route.

1. WELCOME

2. Contents
Introduction
How it works
Algorithm & simulation
Problem discussion
Simulation of problem
Screen shot of Output

3. Presented by
Anika Ohab
ID:142-15-3568
Abul Hasnath
ID:142-15-3532
Umme Habiba
ID: 142-15-3677
Shahinur Rahman
ID: 142-15-3606

4. Introduction
• Dijkstra's Algorithm derived by a Dutch
computer scientist ‘Edsger Dijkstra’ in 1956 and
published in 1959.
• It’s a graph search algorithm that solves the
single-source shortest path problem for a graph
with nonnegative edge path costs, producing a
shortest path tree.
• This algorithm is often used in routing and as a
subroutine in other graph algorithms.

5. How it works ?
• This algorithm finds the path with lowest cost
(i.e. the shortest path) between that vertex and
every other vertex. For example, if the vertices
of the graph represent cities and edge path
costs represent driving distances between pairs
of cities connected by a direct road, Dijkstra's
algorithm can be used to find the shortest route
between one city and all other cities.
• According to this algorithm, to solve a given
problem, we need to solve different parts of
problems.

6. • What is shortest path ?
 shortest length between two vertices for an
unweighted graph:
 smallest cost between two vertices for a
weighted graph:B
D
C
A
E
B
D
C
A
E
200
60
130
190
450
210
weighted
graph
unweighted
graph
Shortest Path Problems

7. 7
How Dijkstra Works
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1. INITIALIZE-SINGLE-SOURCE(V,
s)
2. S ← 
3. Q ← V[G]
4. while Q  
5. do u ← EXTRACT-MIN(Q)
6. S ← S  {u}
7. for each vertex v  Adj[u]
8. do RELAX(u, v, w)

8. 8
Example
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9. Problem :-
Out Computers are connected to global through
Internet connection. The internet connection has
a lots routers for routing their packet data.
Suppose I wants to send a packet to my USA
server computer.A router can forward a packet
to its destination in a shortest path. So we can
program router for finding shortest path for
sending data to it’s destination using Dijkstra
Algorithm.

10. Graph Algorithm
• In this
interconnected
‘Vertex’ we’ll use
‘Dijkstra’s
Algorithm’.
• To use this
algorithm in this
network we have
to start from a
decided vertex
and then continue
to others.

11. Simulation Of Our problem
So, for the calculation give
infinite value to all Vertex.
And start with ‘A’ using this
table:

12. Graph Algorithm

13. Graph Algorithm

14. Graph Algorithm

15. Graph Algorithm

16. Graph Algorithm

17. Graph Algorithm

18. Graph Algorithm

19. Graph Algorithm
• So with this ‘Graph Algorithm’ we found our best
lowest cost route in this interconnected Vertex.
• And the best lowest cost path is given below:
A B F C D G
• So total cost from ‘A’ to ‘G’ vertex is ‘70’ which is
lowest cost from other Vertex.

20. Implementation Output

21. Implementation Output

22. Implementation Output

23. Implementation Output

24. http://bit.ly/Video-On-BFS

25. Hassnainjamil42@gmail.com Twitter.com/HassnainJamil