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# foldfuckerson

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### foldfuckerson

1. 1. 02/23/14
2. 2. Safina kanwal 13-NTU-4013 MScs
3. 3. Topics Push relable method edmonds-karP algorithm 02/23/14
4. 4. TERMS TO KNOW 1. 2. 3. 4. 02/23/14 Residual graph Augmented path Exes flow/ net flow Active vertex
5. 5. Push Relable method • One of the most efficient algorithms Used for maximum flow problems • By Dr. Andrew Goldberg and Robert E Tarjan • Fastest maximum flow algorithm 02/23/14
6. 6. Preflow Basics 02/23/14
7. 7. Example 0 2 2 3 5 2 1 3 s 3 2 4 0 3 1 02/23/14 2 2 t
8. 8. Conditions • Three conditions 1. F(u, v) should be less or equal c(u, v) 2. Skew symmetry F(u, v) = -F(v, u) 3. Flow conservation 02/23/14
9. 9. algorithm 9
10. 10. Time complexity • Generally it has O(V2E) • It depends on its method of implementation 02/23/14
11. 11. Edmond Karp Algorithm 02/23/14
12. 12. Overview • An algorithm of ford Fulkerson used for finding the shortest augmenting path • Uses breadth first search • Considering each edge has a unit weight 02/23/14
13. 13. Calculating Residual graph 02/23/14
14. 14. 02/23/14
15. 15. Algorithm set f to 0 and Gf to 0 While Gf contains source to sink path P do 1. P is path with min no of edges from s to t 2. Augment f using P 3. Update Gf End while Return f 02/23/14
16. 16. Time complexity • Runs in time O(V E2). 02/23/14
17. 17. Make Presentation much more fun