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Analysis of Algorithm
1.
Approximation Algorithms Presented
By Ahlam Ansari
2.
3.
4.
Approximation Algorithm
5.
6.
7.
8.
Performance ratios of
Approximation Algorithm
9.
10.
11.
12.
Examples of Approximation
Algorithm
13.
14.
The vertex-cover problem
15.
16.
17.
Example Fig: 1
The vertex-cover problem Optimal Size=3 Near Optimal size=6
18.
19.
20.
21.
22.
23.
24.
Contd… Fig: 2
The vertex-cover problem
25.
26.
27.
28.
Contd… The vertex-cover
problem
29.
Contd… The vertex-cover
problem
30.
Contd… The vertex-cover
problem
31.
Contd… The vertex-cover
problem
32.
Traveling salesman problem
33.
34.
35.
Algorithm Traveling salesman
problem
36.
Example Fig: 3
Traveling salesman problem 2 2 3 9 8 7 4 1 3 9 9 9 9 7 7 5 5 7 7 4 Solution for TSP
37.
The set cover
problem
38.
39.
Algorithm The set
cover problem
40.
41.
The set cover
problem Fig: 4 1 2 5 4 3 SET COVER SET COVER
42.
Genetic Algorithm
43.
44.
45.
46.
The Pictorial representation
of the Working Principle of a Simple Genetic Algorithm Fig: 5
47.
48.
49.
50.
51.
52.
53.
Two commonly adopted
fitness mappings is presented below: 1. 2. Genetic Algorithm
54.
55.
56.
57.
58.
One site crossover
operation Fig: 7 Genetic Algorithm
59.
60.
61.
62.
Solving TSP using
GA
63.
64.
65.
Fig 9: Flow
chart of TSP using GA
66.
67.
Fig: 10 Solving
TSP using GA
68.
69.
Fig: 11 Solving
TSP using GA
70.
71.
72.
73.
74.
75.
76.
77.
78.
79.
The resultant tour
will be, A->B-> C->D-> E->A=15 Solving TSP using GA
80.
Analysis of TSP
Algorithms
81.
82.
83.
Result
84.
Result Based on
Length Comparison Result 9906 4302 2295 Genetic Algorithm 10402 4478 2330 Greedy 500 100 30 Algorithm City Size
85.
Result Based on
Time Comparison Result 27 6 2 Genetic Algorithm 34 8 6 Greedy 500 100 30 Algorithm City Size
86.
Conclusion
87.
88.
89.