A Network-Flow Based Algorithm For Power Density Mitigation at Post-Placement Stage

1. A Network-Flow Based Algorithm For Power Density Mitigation at Post-Placement Stage Sean Shih-Ying Liu, Ren-GuoLuo,Hung-Ming Chen DATE’13

2. Outline • Introduction • Problem formulation • Algorithm • Bin Clustering • Balance Regional Power Density • Cell Shifting and Relocation • Experimental result • Conclusion

3. Introduction • The uneven distribution of power density creates hot spots or regions with unusual high temperature. • These hot spots may induce undesirable effect Ex: Increase in interconnect delay.

4. Problem formulation The Post-Placement Temperature Mitigation Problem: Given a legalized design with known power density for each cell, minimize the maximum on chip temperature with minimal increase in total displacement.

5. Algorithm Flow

6. Temperature profile

7. Bin Clustering • Using maximum temperature bin as center, the cluster of bins progressively expands until the percentage in temperature difference between selected bin and maximum temperature bin is below r . • Tbin > r * Tmax • r is set from 75% to 90%.

8. Iterative Power Density Propagation

9. Iterative Power Density Propagation

10. Balance Regional Power Density

11. Balance Regional Power Density • Min-Cost Max-Flow :

12. Min-Cost Max-Flow solution

13. Ford-Fulkerson

14. Ford-Fulkerson

15. Cycle Canceling Algorithm • Bellman Ford Algorithm is applied to identify negative cost cycle and iteratively saturates every identified negative cost cycle until none can be found.

16. Cycle Canceling Algorithm

17. Min-Cost Max-Flow solution

18. Cell Shifting and Relocation

19. Experimental result

20. Experimental result

21. Conclusion • In this paper, network flow based power density mitigation technique is proposed • By modeling regional power density balancing problem as supply-demand problem, temperature profile can be effectively smoothed out with minimal increase to total displacement.