1. FAR: Fixed Points Addition & Relaxation Based Placement
Bo Hu and Malgorzata Marek-Sadowska
University of California,
Santa Barbara

2. Outline Introduction Previous works
Fixed points Addition & Relaxation(FAR)
Experimental results
Conclusion

3. Placement Methodology
Introduction
Placement Methodology
Simulated Annealing
Quadratic
Partitioning
Partitioning
Constant force
AR model
FAR

4. Incremental Placement
Introduction cont.
Placement Category
Global Placement
Detailed Placement
Incremental Placement
FAR

5. Previous Works Constant Force Attractor-Repeller Model
“Generic Global Placement and Floorplanning”, Hans Eisenmann and Frank M. Johannes, DAC98.
Attractor-Repeller Model
“Attractor-Repeller Approach for Global Placement”, Hussein Etawil, Shawki Areibi, and Anthony Vannelli, ICCAD-99.

6. Constant Force (EQ1) (EQ2) (EQ3) (EQ4)
Vector e is constant force based on density.

7. Fixed Point
A fixed point p(x, y) is a dimensionless pseudo cell positioned at (x,y) on the chip plane.
Fixed point can be anywhere, not necessarily within the chip boundary.
Connectivity between fixed points and real cells can be dynamically modified.
(EQ5)

8. Category-I: controlling fixed points
Controlling fixed points are used to maintain force equilibrium state.
Controlling Fixed point

9. Category-II: Perturbing fixed points
Perturbing fixed points are used to transform the placement
Perturbing fixed point
Perturbing fixed point
Perturbing fixed point

10. Category-III: Constraining fixed points
Constraining fixed points are used to restrict the movement of cells.
constraining fixed point
constraining fixed point
constraining fixed point

11. Apply FAR in global placement – one transformCF
initial
FAR

12. FAR based incremental placement
Buffer Site Generation(BSG)

13. Apply FAR in BSG Controlling Fixed point Perturbing fixed point
Constraining fixed point

14. Experimental results for global placement – wire length

15. Experimental results for global placement – CPU time for one transformation

16. Experimental results for BSG – test cases

17. Experimental results for BSG – CF vs. FAR

18. Experimental results for BSG

19. Conclusion
FAR based placement approach can be applied in both global placement( overlapping elimination ) and incremental placement (Buffer Site Generation) contexts.
FAR is quadratic-solver friendly approach.