Maximum matching in bipartite graphs iterative improvement method
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The document discusses two approaches for finding the maximum matching in bipartite graphs - Ford Fulkerson's augmenting path method and the shortest augmenting path method using breadth-first search (BFS). It provides examples of applying both methods to a sample graph, finding augmenting paths and increasing the number of matching pairs at each step until reaching the maximum matching.
Maximum matching in bipartite graphs iterative improvement method
- 1. Maximum Matching in Bipartite Graphs Iterative Improvement Method Dr. P. Subathra Prof/ IT KAMARAJ College of Engg. & Tech (AUTONOMOUS) Madurai Tamil Nadu India
- 2. Maximum Matching in Bipartite Graphs • The Maximum Matching in the Bipartite Graph can be done through Iterative Improvement methodology • Two different approaches are available: 1. Ford Fulkerson’s Method 2. Shortest Augmenting Path Method Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India 2
- 3. 1. Ford Fulkerson’s Augmenting Path Method 3 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 4. Ford Fulkerson’s Augmenting Path Method 4 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 5. Ford Fulkerson’s Augmenting Path Method 5 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 6. Ford Fulkerson’s Augmenting Path Method 2,6,1,7 6 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 7. Ford Fulkerson’s Augmenting Path Method 2,6,1,7 7 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 8. Ford Fulkerson’s Augmenting Path Method 2,6,1,7 8 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 9. Ford Fulkerson’s Augmenting Path Method 2,6,1,7 9 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 10. Ford Fulkerson’s Augmenting Path Method 2,6,1,7 10 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 11. Ford Fulkerson’s Augmenting Path Method 3,6,1 No path 11 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 12. Ford Fulkerson’s Augmenting Path Method 3,6,1 No path X 12 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 13. Ford Fulkerson’s Augmenting Path Method 3,6,2 No path 13 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 14. Ford Fulkerson’s Augmenting Path Method 3,8,4,9,5,10 14 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 15. Ford Fulkerson’s Augmenting Path Method 3,8,4,9,5,10 15 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 16. Ford Fulkerson’s Augmenting Path Method 3,8,4,9,5,10 16 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 17. Ford Fulkerson’s Augmenting Path Method 3,8,4,9,5,10 17 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 18. Ford Fulkerson’s Augmenting Path Method 3,8,4,9,5,10 18 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 19. Ford Fulkerson’s Augmenting Path Method 3,8,4,9,5,10 19 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 20. Ford Fulkerson’s Augmenting Path Method 3,8,4,9,5,10 20 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 21. Ford Fulkerson’s Augmenting Path Method 3,8,4,9,5,10 21 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 22. Ford Fulkerson’s Augmenting Path Method 22 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 23. Maximum Matching Theorem 23 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 24. 2. Shortest Augmenting Path - BFS 24 Initial Matching Pairs = 2 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 25. Shortest Augmenting Path - BFS 25 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 26. Shortest Augmenting Path - BFS 1 26 6 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 27. Shortest Augmenting Path - BFS 27 Number of Matching Pairs = 3 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 28. Shortest Augmenting Path - BFS 28 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 29. Shortest Augmenting Path - BFS 2 29 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 30. Shortest Augmenting Path - BFS 2 3 30 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 31. Shortest Augmenting Path - BFS 6 31 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 32. Shortest Augmenting Path - BFS 8 32 6 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 33. Shortest Augmenting Path - BFS 7 1 33 6 8 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 34. Shortest Augmenting Path - BFS 7 1 34 6 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 35. Shortest Augmenting Path - BFS 7 1 35 6 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 36. Shortest Augmenting Path - BFS 7 1 36 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 37. Shortest Augmenting Path - BFS 7 1 37 Number of Matching Pairs = 4 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 38. Shortest Augmenting Path - BFS 38 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 39. Shortest Augmenting Path - BFS 39 3 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 40. Shortest Augmenting Path - BFS 40 6 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 41. Shortest Augmenting Path - BFS 41 6 8 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 42. Shortest Augmenting Path - BFS 42 6 8 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 43. Shortest Augmenting Path - BFS 43 10 6 8 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 44. Shortest Augmenting Path - BFS 44 10 6 8 Augmenting Path From Node 10 : 3-84-10 (Trace backward from 10 as 10-4-8-3) Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 45. Shortest Augmenting Path - BFS 45 10 6 8 Augmenting Path From Node 10 : 3-84-10 (Trace backward from 10 as 10-4-8-3) Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 46. Shortest Augmenting Path - BFS 46 10 6 8 Augmenting Path From Node 10 : 3-84-10 (Trace backward from 10 as 10-4-8-3) Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 47. Shortest Augmenting Path - BFS 47 10 Augmenting Path From Node 10 : 3-84-10 (Trace backward from 10 as 10-4-8-3) 8 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 48. Shortest Augmenting Path - BFS 48 10 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 49. Shortest Augmenting Path - BFS 49 10 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 50. Shortest Augmenting Path - BFS 50 10 Total Number of Matching Pairs = 5 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 51. Shortest Augmenting Path - BFS 51 10 Queue : Empty Maximum Matching Achieved Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India
- 52. 52 Dr. P. Subathra, KAMARAJ College of Engg & Tech (AUTONOMOUS), Madurai, Tamil Nadu, India