| Input: , |
| Output: |
| 1. Initialize , , ; |
| 2. for |
| 3. Store the nodes that belong to the lower level into a buffer ; |
| 4. Calculate according to and ; |
| 5. According to , find the nodes that are in and connected to |
| only one branch; |
| 6. Match the found nodes with the connected branches; |
| 7. Remove the matched nodes from and mark the matched |
| branches as occupied; |
| 8. Update and ; |
| 9. Sort the nodes in in decreasing order according to ; |
| 10. while |
| 11. Take out the first node in , say ; |
| 12. if there is a nonoccupied branch that has the minimum |
| weight and is connected with (breaking ties based on the |
| branch ID) |
| 13. Match with this branch; |
| 14. else if there is an augmenting path of which is an end |
| vertex, and the total weight of the augmenting path can be |
| reduced by matching |
| 15. Match with the branch in the augmenting path and |
| change the previous matched pairs; |
| 16. else |
| 17. Match with the branch that has minimum weight |
| (breaking ties based on the branch ID); |
| 18. end if |
| 19. mark the matched branch as occupied; |
| 20. update and ; |
| 21. remove from ; |
| 22. end while |
| 23. For any node in the lower level, it should select its connected |
| node that belongs to the matched branch and has the minimum |
| number of neighbors as its next hop. |
| 24. Update B, Q←; |
| 25. end for |
