1. Approximation Algorithms Presented By Ahlam Ansari

4. Approximation Algorithm

8. Performance ratios of Approximation Algorithm

12. Examples of Approximation Algorithm

14. The vertex-cover problem

17. Example Fig: 1 The vertex-cover problem Optimal Size=3 Near Optimal size=6

24. Contd… Fig: 2 The vertex-cover problem

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

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

39. Algorithm The set cover problem

41. The set cover problem Fig: 4 1 2 5 4 3 SET COVER SET COVER

42. Genetic Algorithm

46. The Pictorial representation of the Working Principle of a Simple Genetic Algorithm Fig: 5

53. Two commonly adopted fitness mappings is presented below: 1. 2. Genetic Algorithm

58. One site crossover operation Fig: 7 Genetic Algorithm

62. Solving TSP using GA

65. Fig 9: Flow chart of TSP using GA

67. Fig: 10 Solving TSP using GA

69. Fig: 11 Solving TSP using GA

79. The resultant tour will be, A->B-> C->D-> E->A=15 Solving TSP using GA

80. Analysis of TSP Algorithms

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