This presentation discusses various graph algorithms including Hamilton paths and circuits, Edmonds Karp algorithm, traveling salesman problem, Kruskal's algorithm, Huffman algorithm, and Ford-Fulkerson algorithm. It defines Hamilton paths and circuits, notes that finding Hamilton circuits is difficult with no simple algorithm, and lists some properties to look for. It also provides overviews of the Edmonds Karp algorithm, Kruskal's algorithm, Huffman algorithm, and Ford-Fulkerson algorithm, explaining their basic approaches and purposes. The presentation was given by Md. Sohag from Daffodil International University.

1. Hello!
Welcome to my
presentation…………
..

2. Presented by:
Md . Sohag
Em@il : sohag.0315@gmail.com
Daffodil international University

3. Hamilton Paths
& Circuit

4. Definition :
– A HAMILTON PATH in graph G is a path
which visits every vertex in G exactly once
– A HAMILTON CIRCUIT is a Hamilton Path
that returns to its start.

5. Finding Hamilton Circuits
– Unlike the Euler circuit problem, finding Hamilton
circuits in hard.
– There is no simple set of necessary and sufficient
conditions, and no simple algorithm.

6. Properties to look for….
– No vertex of degree 1
– If a node has degree 2, then both edges incident
to it must be in any Hamilton circuit.
– No smaller circuits contained in any Hamilton
circuit(the start/endpoint of any smaller circuit
would have to be visited twice.)

8. Edmonds Karp
Algorithm

9. Edmonds Karp Algorithm
– This algorithm is identical to the Ford-Fulkerson Algorithm
– Search order when finding the augmenting path is defined
– The path found must be a shortest path that has available
capacity
– The augmenting path can be obtained by using Breadth First
Search Algorithm

10. Edmonds Karp Algorithm
Graph

11. Edmonds Karp Algorithm
Graph

12. Traveling Sales
Man
Algorithm

13. Traveling Sales Man
Traveling SalesMan problem:
Visit all cities Exactly once and end where you Started

16. Kruskal's
Algorithm &
Haffman
Algorithm

17. Kruskal's algorithm
– Kruskal's algorithm is a minimum-spanning-tree algorithm
– Where the algorithm finds an edge of the least possible
weight that connects any two trees in the forest
– It is a greedy algorithm in graph theory
– as it finds a minimum spanning tree for a connected
weighted graph adding increasing cost arcs at each step.

20. Haffman algorithm
– The Huffman Encoding algorithm is a greedy
Algorithm
– Data compression algorithm
– It’s works as without loss of Information
– Based on lengths of assigned codes based on
frequencies
– Variable length Codes are known as Prefix Codes

21. Example :
– We always pick the two smallest number to combine
– The Huffman Algorithm finds an Optimal Solution

22. Ford-Falcon
Algorithm

23. Ford–Fulkerson algorithm
– Ford–Fulkerson algorithm (FFA) is an algorithm that
computes the maximum flow in a flow network
– it is specified in several implementations with different
running times
– Find an augmenting path
– Compute the bottleneck capacity
– Augment each edge and the total flow

24. Ford-Falcon Algorithm

27. Thank you all…….
Daffodil International Univercity
Sec:-H
Dept.of CSE