This document summarizes research by group members M. Hamza Khan, Wajid Khan, Saqib Sarfaraz, and M. Zohaib Khan on shortest path problems. It compares the Floyd-Warshall and Dijkstra's algorithms. Floyd-Warshall finds the shortest path between all pairs of vertices in a weighted, directed graph using dynamic programming. Dijkstra's algorithm finds the single-source shortest path from a starting node to all other nodes. While Dijkstra's only works with positive edges, Floyd-Warshall can handle graphs with negative edges or weights.

1. GROUP MEMBERS:
M. HAMZA KHAN(19B-113-SE)
WAJID KHAN(19B-109-SE)
SAQIB SARFARAZ(19B-098-SE)
M. ZOHAIB KHAN(19B-090-SE)
RESEARCH TOPIC
SHORTEST PATH PROBLEMS:
COMPARISION AND THEIR SIGNIFICANCE IN
COMPUTER SCIENCE:

2. FLOYD WARSHALLALGORITHM:

3. INTRODUCTION:
In computer science, the Floyd-Warshall Algorithm is used for
finding the shortest path problems in a weighted, directed
graph.
All Pair Shortest Path: It aims to calculate the shortest path
between each vertex and every other nodes.
It uses a Dynamic Programming Approach to solve the all pair
shortest path problem.

4. ALGORITHM:

5. COMPLICATION:
We have to apply this algorithm ‘n’ times, each time
choosing a different as the source.
The total computation time is:
n * 0(n^2) = 0(n^3)
This time complication are same for the best, average and
worst case.

6. EXAMPLE:
Dij = min(Dij-1, Dik-1 + Dkj-1)
Do = D1 =
D2 = D3 =
D4 =

7. APPLICATIONS:
 Computation of path finder networks become faster.
 Ideal routing.
 All pair shortest path.
 Negative weight-cycles in graph are detected.

8. DIJKSTRA’S ALGORITHM:

9. INTRODUCTION:
Dijkstra algorithm, named after its discovery, Dutch
computer scientist Edsgar Dijkstra.
Dijkstra Algorithm is basically single source shortest path
problem. In this algorithm one source is given to find out
the shortest path from all other vertices.
FOR EXAMPLE: If the vertices of the graph represent cities
and edge weights represent driving distances between
pairs of cities connected by a direct road, Dijkstra’s
algorithm can be used to find the shortest route between
the two cities.

10. WORKING PRINCIPLE:
STEPS:
 Assign every node a tentative distance.
 Set initial node as current and mark
all nodes as unvisited.
 For current node, consider all
unvisited nodes and calculate distance.
 Compare current and calculated
distance and assign the smaller value.
 When all neighbors are considered
mark them.
 If the destination node is marked ,
Stop

11. APPLICATIONS:
 It is used in satellite navigation and in Google maps.
 It is used to determine the earliest arrival time for the
destination.
 In telephone networks, the vertices represents switching
station, the edges represents the transmission line and the
weight of edges represent the BW.

12. COMPARISION BETWEEN FLOYD-WARSHALL
AND DIJSKTRA’S ALGORITHM:
Dijsktra’s Algorithm:
 It is a single source
shortest algorithm.
 It may or may not
work on both positive
and negative edge.
Floyd-Warshall Algorithm:
 It is an example of all
pair shortest path
algorithm.
 It works both on
negative and positive
edges.

13. CONCLUSION:
As in the above discussion conclude that both
Algorithm is used to find the shortest path /
distance but their working are different one
another Dijkstra’s algorithm is a shortest as
well as Warshall algorithm. However In
practical applications these two algorithms
can’t applied directly.