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02/23/14
Safina kanwal
13-NTU-4013
MScs
Topics
Push relable method
edmonds-karP algorithm

02/23/14
TERMS TO KNOW
1.
2.
3.
4.

02/23/14

Residual graph
Augmented path
Exes flow/ net flow
Active vertex
Push Relable method
• One of the most efficient algorithms Used for
maximum flow problems
• By Dr. Andrew Goldberg and Rob...
Preflow Basics

02/23/14
Example
0

2

2
3

5
2

1
3

s
3

2

4
0

3
1
02/23/14

2

2

t
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 conse...
algorithm

9
Time complexity

• Generally it has O(V2E)
• It depends on its method of implementation

02/23/14
Edmond Karp Algorithm

02/23/14
Overview
• An algorithm of ford Fulkerson used for
finding the shortest augmenting path
• Uses breadth first search
• Cons...
Calculating Residual graph

02/23/14
02/23/14
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
...
Time complexity

• Runs in time O(V E2).

02/23/14
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  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

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