Iterative Improvement Technique

1. Maximum Matching in Bipartite
Graphs
Iterative Improvement Method
1
Dr. P. Subathra
Prof/ IT
KAMARAJ College of Engg. & Tech
Madurai

2. Ford Fulkerson’s Augmenting Path
Method
2

3. Ford Fulkerson’s Augmenting Path
Method
3

4. Ford Fulkerson’s Augmenting Path
Method
4

5. Ford Fulkerson’s Augmenting Path
Method
2,6,1,7
5

6. Ford Fulkerson’s Augmenting Path
Method
2,6,1,7
6

7. Ford Fulkerson’s Augmenting Path
Method
2,6,1,7
7

8. Ford Fulkerson’s Augmenting Path
Method
2,6,1,7
8

9. Ford Fulkerson’s Augmenting Path
Method
2,6,1,7
9

10. Ford Fulkerson’s Augmenting Path
Method
3,6,1  No path
10

11. Ford Fulkerson’s Augmenting Path
Method
3,6,1  No path
X
11

12. Ford Fulkerson’s Augmenting Path
Method
3,6,2  No path
12

13. Ford Fulkerson’s Augmenting Path
Method
3,8,4,9,5,10
13

14. Ford Fulkerson’s Augmenting Path
Method
3,8,4,9,5,10
14

15. Ford Fulkerson’s Augmenting Path
Method
3,8,4,9,5,10
15

16. Ford Fulkerson’s Augmenting Path
Method
3,8,4,9,5,10
16

17. Ford Fulkerson’s Augmenting Path
Method
3,8,4,9,5,10
17

18. Ford Fulkerson’s Augmenting Path
Method
3,8,4,9,5,10
18

19. Ford Fulkerson’s Augmenting Path
Method
3,8,4,9,5,10
19

20. Ford Fulkerson’s Augmenting Path
Method
3,8,4,9,5,10
20

21. Ford Fulkerson’s Augmenting Path
Method
21

22. Maximum Matching Theorem
22

23. Shortest Augmenting Path - BFS
23
Initial Matching Pairs = 2

24. Shortest Augmenting Path - BFS
24

25. Shortest Augmenting Path - BFS
1
25
6

26. Shortest Augmenting Path - BFS
26
Number of Matching Pairs = 3

27. Shortest Augmenting Path - BFS
27

28. Shortest Augmenting Path - BFS
2
28

29. Shortest Augmenting Path - BFS
2 3
29

30. Shortest Augmenting Path - BFS
6
30

31. Shortest Augmenting Path - BFS
8
31
6

32. Shortest Augmenting Path - BFS
7
1
32
6 8

33. Shortest Augmenting Path - BFS
7
1
33
6

34. Shortest Augmenting Path - BFS
7
1
34
6

35. Shortest Augmenting Path - BFS
7
1
35

36. Shortest Augmenting Path - BFS
7
1
36
Number of Matching Pairs = 4

37. Shortest Augmenting Path - BFS
37

38. Shortest Augmenting Path - BFS
38
3

39. Shortest Augmenting Path - BFS
39
6

40. Shortest Augmenting Path - BFS
40
6 8

41. Shortest Augmenting Path - BFS
41
6 8

42. Shortest Augmenting Path - BFS
42
10
6 8

43. Shortest Augmenting Path - BFS
43
10
6 8
Augmenting Path From Node 10 : 3-84-10
(Trace backward from 10 as 10-4-8-3)

44. Shortest Augmenting Path - BFS
44
10
6 8
Augmenting Path From Node 10 : 3-84-10
(Trace backward from 10 as 10-4-8-3)

45. Shortest Augmenting Path - BFS
45
10
6 8
Augmenting Path From Node 10 : 3-84-10
(Trace backward from 10 as 10-4-8-3)

46. Shortest Augmenting Path - BFS
46
10
Augmenting Path From Node 10 : 3-84-10
(Trace backward from 10 as 10-4-8-3)
8

47. Shortest Augmenting Path - BFS
47
10

48. Shortest Augmenting Path - BFS
48
10

49. Shortest Augmenting Path - BFS
49
10
Total Number of Matching Pairs = 5

50. Shortest Augmenting Path - BFS
50
10
Queue : Empty
Maximum Matching Achieved

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