1. International Conference on Computer-Aided Design San Jose, CA Nov. 2001ER UCLA UCLA 1 Congestion Reduction During Placement Based on Integer Programming 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 Conference on Computer-Aided Design San Jose, CA Nov. 2001ER UCLA UCLA 2OutlineOutline Introduction Previous Work on Congestion Integer Linear Programming(ILP) Formulation Approximation Algorithms Congestion Reduction based on ILP solution Experimental Results Conclusion Introduction Previous Work on Congestion Integer Linear Programming(ILP) Formulation Approximation Algorithms Congestion Reduction based on ILP solution Experimental Results Conclusion

3. International Conference on Computer-Aided Design San Jose, CA Nov. 2001ER UCLA UCLA 3IntroductionIntroduction Main Goals in Placement: Minimizing Chip Area (old) Routability and Timing (modern) Objectives/Cost for Routability Cut, Wirelength, Congestion Why congestion? Shorter Bounding Box  Better Routability Congestion models routability better Main Goals in Placement: Minimizing Chip Area (old) Routability and Timing (modern) Objectives/Cost for Routability Cut, Wirelength, Congestion Why congestion? Shorter Bounding Box  Better Routability Congestion models routability better

4. International Conference on Computer-Aided Design San Jose, CA Nov. 2001ER UCLA UCLA 4 Previous Work on Congestion Mayrhofer and Lauther, ICCAD’90. Partitioning based method Cheng, ICCAD’94 “RISA” model used in Simulated Annealing Parakh et. al., DAC’98 Quadratic Placement combined with Area Router Wang and Sarrafzadeh, ISPD’99, ISPD’00 Post-processing after global placement Congestion Estimation Yang et.al, Congestion Estimation at early placement based on Rent’s Rule Lou et. al, Congestion Estimation at late placement stages using probabilistic analysis Mayrhofer and Lauther, ICCAD’90. Partitioning based method Cheng, ICCAD’94 “RISA” model used in Simulated Annealing Parakh et. al., DAC’98 Quadratic Placement combined with Area Router Wang and Sarrafzadeh, ISPD’99, ISPD’00 Post-processing after global placement Congestion Estimation Yang et.al, Congestion Estimation at early placement based on Rent’s Rule Lou et. al, Congestion Estimation at late placement stages using probabilistic analysis

5. International Conference on Computer-Aided Design San Jose, CA Nov. 2001ER UCLA UCLA 5 Our Contribution Work Summary Post-processing step to reduce congestion Routing-estimation for congestion cost Reduce congestion in an enlarged area by moving cells Our Main Contribution Global Picture for Congestion Problem ILP based congested spot expansion to alleviate congestion Approximation algorithm for ILP Work Summary Post-processing step to reduce congestion Routing-estimation for congestion cost Reduce congestion in an enlarged area by moving cells Our Main Contribution Global Picture for Congestion Problem ILP based congested spot expansion to alleviate congestion Approximation algorithm for ILP

6. International Conference on Computer-Aided Design San Jose, CA Nov. 2001ER UCLA UCLA 6 Congestion Cost Routing Estimation --- Bounding Box Model k-termimal nets: Net weight q(k) k-termimal nets: Net weight q(k) k2345… q(k)1.001.081.151.22… Cheng ICCAD’94

7. International Conference on Computer-Aided Design San Jose, CA Nov. 2001ER UCLA UCLA 7 Congestion Cost Routing Estimation --- Bounding Box Model W H k-termimal nets: Net weight q(k) k-termimal nets: Net weight q(k) k2345… q(k)1.001.081.151.22… Cheng ICCAD’94

8. International Conference on Computer-Aided Design San Jose, CA Nov. 2001ER UCLA UCLA 8 Congestion Cost Congestion Cost Function Bin congestion degree

9. International Conference on Computer-Aided Design San Jose, CA Nov. 2001ER UCLA UCLA 9 Congested Spot Identify congested spots Alleviate congestion in the expanded area Identify congested spots Alleviate congestion in the expanded area

10. International Conference on Computer-Aided Design San Jose, CA Nov. 2001ER UCLA UCLA 10 Congestion Alleviation Conflict between expanded areas How big the expanded area should be? Conflict between expanded areas How big the expanded area should be?

11. International Conference on Computer-Aided Design San Jose, CA Nov. 2001ER UCLA UCLA 11ProblemProblem Two expansion areas for each congested spot Congestion degree after expanding Minimize the maximum congestion degree over the entire area Two expansion areas for each congested spot Congestion degree after expanding Minimize the maximum congestion degree over the entire area

12. International Conference on Computer-Aided Design San Jose, CA Nov. 2001ER UCLA UCLA 12 ILP Based Approach For congested spot k: x k =0 small expansion, x k =1 large expansion For bin (i, j), define incremental degree For congested spot k: x k =0 small expansion, x k =1 large expansion For bin (i, j), define incremental degree bin(i,j)

13. International Conference on Computer-Aided Design San Jose, CA Nov. 2001ER UCLA UCLA 13 ILP Based Approach MinimizeMinimize Subject to: bin(i,j)

14. International Conference on Computer-Aided Design San Jose, CA Nov. 2001ER UCLA UCLA 14 Approximation Algorithm Threshold Rounding Solve the LP Relaxation:Relaxation: Rounding:Rounding: 2-approximation algorithm

15. International Conference on Computer-Aided Design San Jose, CA Nov. 2001ER UCLA UCLA 15 α-Approximation Algorithm α-approximation algorithm Proof:Proof: α =1.5 at p=0.22

16. International Conference on Computer-Aided Design San Jose, CA Nov. 2001ER UCLA UCLA 16 Congestion Reduction Flow Wirelength Minimization Placement Routing Estimation & Congested Spot Identification Assign two expansion areas for each spot Formulating and solving ILP Local congestion reduction based on the expansion area Finalization to a new placement

17. International Conference on Computer-Aided Design San Jose, CA Nov. 2001ER UCLA UCLA 17 Experimental Setup Wirelength Minimization Congestion Reduction CircuitsCircuits Global Routing (Dragon)(Dragon) (Labyrinth)(Labyrinth) output1output1 output2output2 Compare:Compare:OverflowOverflow Bounding Box Wirelength Routed Wirelength Dragon produces comparable placement with commercial tools

18. International Conference on Computer-Aided Design San Jose, CA Nov. 2001ER UCLA UCLA 18 Experimental Results Congestion reduction in placement affects routing result Runtime: 11s—389s for circuit size 12,000 – 67,000 (Pentium 733MHz) Congestion reduction in placement affects routing result Runtime: 11s—389s for circuit size 12,000 – 67,000 (Pentium 733MHz)

19. International Conference on Computer-Aided Design San Jose, CA Nov. 2001ER UCLA UCLA 19 Bounding Box Wire Length Wirelength is no longer a good measurement of routability

20. International Conference on Computer-Aided Design San Jose, CA Nov. 2001ER UCLA UCLA 20 Routed Wire Length Congestion models routability better

21. International Conference on Computer-Aided Design San Jose, CA Nov. 2001ER UCLA UCLA 21 Experimental Results (cont’d) Comparison between single expansion and double expansion Comparison between single expansion and double expansion circuit: ibm02

22. International Conference on Computer-Aided Design San Jose, CA Nov. 2001ER UCLA UCLA 22SummarySummary Congestion reduction as a post-processing ILP based congestion reduction control Approximation algorithms with good bound Future Work Extend the approach using ILP instead of 0-1 ILP Web site: http://www.cs.ucla.edu/~xjyang/iccad Congestion reduction as a post-processing ILP based congestion reduction control Approximation algorithms with good bound Future Work Extend the approach using ILP instead of 0-1 ILP Web site: http://www.cs.ucla.edu/~xjyang/iccad