1. Lecture 21 Primal-Dual in Algorithms

2. Primal Type
At each iteration, a feasible solution is updated to approach the optimal.

3. Dual Type
At each iteration, a non-feasible “solution” is modified to approach to the feasibility.
E.g., Kruskal Algorithm and Prim Algorithm for minimum spanning tree.

4. Primal-Type Algorithm for Minimum Spanning Tree

5. Example 35 10 30 15 25 40 20 17 8 11 21 1 2 3 4 5 6 7 2 4 6 1 3 5 7

6. Find a Cycle 35 10 30 15 25 40 20 17 8 11 21 1 2 3 4 5 6 7 2 4 6 1 3 5 7

7. Delete the longest edge35 10 30 15 25 40 20 17 8 11 21 1 2 3 4 5 6 7 2 4 6 1 3 5 7

8. Find a cycle 35 10 30 15 25 40 20 17 8 11 21 1 2 3 4 5 6 7 2 4 6 1 3 5 7

9. Delete a longest edge 35 10 30 15 25 40 20 17 8 11 21 1 2 3 4 5 6 7 2 4 6 1 3 5 7

10. Find a cycle 35 10 30 15 25 40 20 17 8 11 21 1 2 3 4 5 6 7 2 4 6 1 3 5 7

11. Delete a longest edge 35 10 30 15 25 40 20 17 8 11 21 1 2 3 4 5 6 7 2 4 6 1 3 5 7

12. Find a cycle 35 10 30 15 25 40 20 17 8 11 21 1 2 3 4 5 6 7 2 4 6 1 3 5 7

13. Delete a longest edge 35 10 30 15 25 40 20 17 8 11 21 1 2 3 4 5 6 7 2 4 6 1 3 5 7

14. Find a cycle 35 10 30 15 25 40 20 17 8 11 21 1 2 3 4 5 6 7 2 4 6 1 3 5 7

15. Delete a longest edge 35 10 30 15 25 40 20 17 8 11 21 1 2 3 4 5 6 7 2 4 6 1 3 5 7

16. Find a cycle 35 10 30 15 25 40 20 17 8 11 21 1 2 3 4 5 6 7 2 4 6 1 3 5 7

17. Delete a longest edge 35 10 30 15 25 40 20 17 8 11 21 1 2 3 4 5 6 7 2 4 6 1 3 5 7

18. Maximum Flow Primal-type Ford-Fulkerson algorithm
Hopcroft–Karp algorithm
Dual-type
Push-relabel algorithm
Goldberg-Tarjan algorithm

21. Transportation Problem

22. Primal-Type Algorithm for Chinese Postman Problem

23. Primal-Dual Method for LP

24. Primal-Dual Type