Final maximum matching in bipartite graphs
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The document discusses Ford Fulkerson's augmenting path method for finding maximum matchings in bipartite graphs. It explains how the algorithm works by finding augmenting paths between unmatched node pairs and incrementally increasing the size of the matching. The document also provides an example applying the shortest augmenting path algorithm using breadth-first search to find a maximum matching in a sample bipartite graph.
Final maximum matching in bipartite graphs
- 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
- 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 : 3-84-10 (Trace backward from 10 as 10-4-8-3)
- 44. Shortest Augmenting Path - BFS 44 10 6 8 Augmenting Path From Node 10 : 3-84-10 (Trace backward from 10 as 10-4-8-3)
- 45. Shortest Augmenting Path - BFS 45 10 6 8 Augmenting Path From Node 10 : 3-84-10 (Trace backward from 10 as 10-4-8-3)
- 46. Shortest Augmenting Path - BFS 46 10 Augmenting Path From Node 10 : 3-84-10 (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
- 51. 51