A presentation on Dijkstra Algorithm for my Algorithm class

1. Dijkstra Algorithm
Akash Sethiya
(as4652)
Mississippi State University
Computer Science Graduate

2. Overview
A graph search algorithm that solves the single source shortest path
problem for a graph with non negative weight edges.
This algorithm works on both directed and undirected graph.
This Algorithm can be solved by both dynamic programming and greedy
approach.

3. Single source shortest path problem
The problem of finding shortest path from source vertex to every other vertex
in a graph G.
Image credit: http://dyewrv1redcbt.cloudfront.net//wp-content/uploads/Fig-11.jpg

4. Solution Algorithm
Algorithm from: http://www.geeksforgeeks.org/greedy-algorithms-set-6-dijkstras-shortest-path-algorithm/

5. Algorithm Pseudocode
From: Class notes

6. Complexity and When to use which?
Greedy Approach: When we have to find a shortest path from source to
destination vertex in a graph.
Dynamic programming: When we have to find shortest path from source to
every other vertex in a graph with heuristics function is equal to zero.
A* : When we have to find shortest path from source to destination vertex
in a graph with some heuristics.
Using Adjacency Matrix: O(V^2)
Using Priority queue : O(ElogV)

7. Results - Dense Graph
Vertices Edges Time(ms)
10 45 0
50 1225 0
100 4950 0
250 31125 6
500 124750 9.6
750 280875 9.4
1000 499500 4.4
2000 1999000 22.4
3000 4498500 40.8
4000 7998000 80
5000 12497500 145
Vertices Edges Time(ms)
6000 17997000 192.2
7000 24496500 244
8000 31996000 354
9000 40495500 444.6
10000 49995000 520.4
11000 60494500 628.6
12000 71994000 1052.8
13000 84493500 1103.6
14000 97993000 1173.8
15000 112492500 1289.3

8. Results (Contd..)

9. Result - Sparse Graph
Vertices Edges Time(ms)
10 10 0
50 50 0
100 100 3.2
250 250 0.2
500 500 0.2
750 750 11.6
1000 1000 3.8
2000 2000 25.4
3000 3000 62.2
4000 4000 131.4
5000 5000 209.2
Vertices Edges Time(ms)
6000 6000 313
7000 7000 407
8000 8000 509.6
9000 9000 684.4
10000 10000 817
11000 11000 876.4
12000 12000 960.4
13000 13000 1136.8
14000 14000 1291
15000 15000 1517.4

10. Results (Contd..)

11. Applications
GPS Navigator
To find a network model in spreading of a infectious disease
Routing protocols

12. References
Introduction to Algorithms Book by Charles E. Leiserson, Clifford Stein,
Ronald Rivest, and Thomas H. Cormen
http://www.geeksforgeeks.org/greedy-algorithms-set-6-dijkstras-shortest-
path-algorithm/
https://www.quora.com/What-are-the-real-life-applications-of-Dijkstras-
algorithm

13. Thank you