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.)
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
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.
18.
19.
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
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