1. International Symposium of Physical Design Sonoma County, CA April 2001ER UCLA UCLA 1 Congestion Estimation During Top-Down Placement Xiaojian Yang Ryan Kastner Majid Sarrafzadeh Embedded and Reconfigurable System Lab Computer Science Department, UCLA Xiaojian Yang Ryan Kastner Majid Sarrafzadeh Embedded and Reconfigurable System Lab Computer Science Department, UCLA

2. International Symposium of Physical Design Sonoma County, CA April 2001ER UCLA UCLA 2OutlineOutline Introduction Motivation Peak Congestion Prediction Regional Congestion Estimation Experimental Results Conclusion Introduction Motivation Peak Congestion Prediction Regional Congestion Estimation Experimental Results Conclusion

3. International Symposium of Physical Design Sonoma County, CA April 2001ER UCLA UCLA 3IntroductionIntroduction Place & Route Objectives: Routability and Timing Placement Minimizing Bounding Box Wirelength Shorter Bounding Box  Better Routability Congestion Routability problem Detours --- Timing problem Place & Route Objectives: Routability and Timing Placement Minimizing Bounding Box Wirelength Shorter Bounding Box  Better Routability Congestion Routability problem Detours --- Timing problem

4. International Symposium of Physical Design Sonoma County, CA April 2001ER UCLA UCLA 4 Motivation of Congestion Est. Early stages of Top-down Placement Logic design Congestion Relieving in Top-down Placement Early stages of Top-down Placement Logic design Congestion Relieving in Top-down Placement

5. International Symposium of Physical Design Sonoma County, CA April 2001ER UCLA UCLA 5 Motivation of Congestion Est. Congestion Relieving based on estimation White space re-allocation Moving cells out of congested area Congestion Relieving based on estimation White space re-allocation Moving cells out of congested area

6. International Symposium of Physical Design Sonoma County, CA April 2001ER UCLA UCLA 6 Basis of Estimation Rent’s Rule P = T B r P - Number of external terminals B – Number of cells T – Rent coefficient r – Rent exponent P - Number of external terminals B – Number of cells T – Rent coefficient r – Rent exponent

7. International Symposium of Physical Design Sonoma County, CA April 2001ER UCLA UCLA 7 Peak Congestion Estimation --- Worst Case C1C1 C2C2 C3C3 C1C1 C2C2 H: # levels

8. International Symposium of Physical Design Sonoma County, CA April 2001ER UCLA UCLA 8 Peak Congestion Estimation --- Uniform Distribution C1C1

9. International Symposium of Physical Design Sonoma County, CA April 2001ER UCLA UCLA 9 Peak Congestion Estimation Result CircuitReal max cong.Est. max cong. Ibm013130.3 Ibm026762.7 Ibm036247.8 Ibm045252.1 Ibm059089.1 Ibm066082.3 Ibm079086.8 Ibm08100111.9 Ibm097593.0 Ibm10112135.8 Ibm115053.9 Ibm127676.1 Ibm1310885.5 ibm14111117.6

10. International Symposium of Physical Design Sonoma County, CA April 2001ER UCLA UCLA 10 Peak Congestion Estimation Result

11. International Symposium of Physical Design Sonoma County, CA April 2001ER UCLA UCLA 11 Regional Congestion Est. Internal routing demand External routing demand Uniformly distributed routing supply

12. International Symposium of Physical Design Sonoma County, CA April 2001ER UCLA UCLA 12 Internal Routing Estimation Wirelength Estimation based on Rent’s rule P = TB Rent exponent r Locality of Rent’s rule Different subcircuits have different Rent Exponents Rent Exponent Extraction Dynamic extraction using partitioning tool Linear regression on data points Wirelength Estimation Model Donath’s (1979) and Davis’s (1998) Wirelength Estimation based on Rent’s rule P = TB Rent exponent r Locality of Rent’s rule Different subcircuits have different Rent Exponents Rent Exponent Extraction Dynamic extraction using partitioning tool Linear regression on data points Wirelength Estimation Model Donath’s (1979) and Davis’s (1998) rr

13. International Symposium of Physical Design Sonoma County, CA April 2001ER UCLA UCLA 13 External Routing Estimation 1.00.5 0.25 0.5 Routing demand caused by inter-block connection Probability-matrix within the Bounding box

14. International Symposium of Physical Design Sonoma County, CA April 2001ER UCLA UCLA 14 Regional Congestion Est. Routing demand (congestion) Of a region Routing demand (congestion) Of a region Internal Routing demand (wirelength estimation) Internal Routing demand (wirelength estimation) External Routing demand (routing estimation) External Routing demand (routing estimation) == ++

15. International Symposium of Physical Design Sonoma County, CA April 2001ER UCLA UCLA 15 Region Congestion Est. Experiments Maze Router Top-down Placement Congestion Estimator Compare after Normalization Normalization Compare after Normalization Normalization C1C1C1C1 C1C1C1C1 C2C2C2C2 C2C2C2C2 C3C3C3C3 C3C3C3C3 C4C4C4C4 C4C4C4C4 C1’C1’C1’C1’ C1’C1’C1’C1’ C2’C2’C2’C2’ C2’C2’C2’C2’ C3’C3’C3’C3’ C3’C3’C3’C3’ C4’C4’C4’C4’ C4’C4’C4’C4’ 64 x 64 or 128 x 128

16. International Symposium of Physical Design Sonoma County, CA April 2001ER UCLA UCLA 16 Estimation Result 8 benchmarks, 12k cells --- 147k cells 2 x 2 regions Wirelength Estimation only 9% Including External Routing demand 8% 4 x 4 regions Wirelength Estimation only 13% Including External Routing demand 9% Running time Partitioning speed 147k cells, 2 x 2, 860 seconds, Sun Ultra-10 Place / Route8000 seconds 8 benchmarks, 12k cells --- 147k cells 2 x 2 regions Wirelength Estimation only 9% Including External Routing demand 8% 4 x 4 regions Wirelength Estimation only 13% Including External Routing demand 9% Running time Partitioning speed 147k cells, 2 x 2, 860 seconds, Sun Ultra-10 Place / Route8000 seconds

17. International Symposium of Physical Design Sonoma County, CA April 2001ER UCLA UCLA 17 Conclusion & Future Work Possibility to estimate congestion by Rent’s rule Congestion can be estimated during Top-down placement Peak congestion after L-shape routing can be accurately estimated Regional congestion estimation is within 10% comparing with actual congestion by place/route Future work More accurate model for “hot spot” estimation Fast estimation by Rent parameter prediction Possibility to estimate congestion by Rent’s rule Congestion can be estimated during Top-down placement Peak congestion after L-shape routing can be accurately estimated Regional congestion estimation is within 10% comparing with actual congestion by place/route Future work More accurate model for “hot spot” estimation Fast estimation by Rent parameter prediction