1. High-Performance Global Routing with Fast Overflow Reduction Huang-Yu Chen, Chin-Hsiung Hsu, and Yao-Wen Chang National Taiwan University Taiwan

2. 2 Outline  Introduction  Preliminary  Routing flow of NTUgr  Multiple forbidden-regions expansion  Critical nets rerouting selection  Look-ahead historical cost increment  Experimental results  Conclusions

3. 3 Outline  Introduction  Preliminary  Routing flow of NTUgr  Multiple forbidden-regions expansion  Critical nets rerouting selection  Look-ahead historical cost increment  Experimental results  Conclusions

4. 4 Global Routing Problem  Global routing  Global routing is the first stage to tackle modern VLSI routing challenges  Connect pins of each net in the global routing graph: global tile node  A global tile node represents a tile (global cell) global edge  A global edge models the relationship between adjacent tiles  Overflow of a global edge: the amount of routing demand that exceeds the given capacity Tile Tile boundary Global tile node Global edge

5. 5 Objectives of Global Routing  Major objectives:  minimize the total overflow  minimize the maximum overflow  Minor objectives:  minimize the total wirelength  minimize running time

6. 6 Outline  Introduction  Preliminary  Routing flow of NTUgr  Multiple forbidden-regions expansion  Critical nets rerouting selection  Look-ahead historical cost increment  Experimental results  Conclusions

7. 7 State-of-the-art Global Routers  Archer [ICCAD’07]  BoxRouter [ICCAD’07]  FastRoute [ICCAD’06, ASPDAC’07, TCAD’08]  FGR [ICCAD’07]  NTHU-Route [ASPDAC’08, ICCAD’08] INR  Those routers adopt INR (Iteratively Negotiation-based Rip-up/rerouting) to effectively reduce overflows

8. 8 INR (Iteratively Negotiation-based Rip-up/rerouting)  Proposed in PathFinder [McMurchie and Ebeling, FPGA’95]  Spreads the congested wires iteratively  At the (i)-th iteration, the cost of a global edge e:  b e : base cost of using e,  p e : # of nets passing e,  h e (i) : historical cost on e,  INR may get stuck as the number of iterations increases [Ozdal, ICCAD’07] [Gao et al., ASPDAC’08]

9. 9 Contributions  NTUgr  NTUgr --- a high-quality global router  The 2 nd place of ISPD 2008 Global Routing Contest 3D Benchmark 3D  2D capacity mapping Enhanced 2D routing 2D  3D layer assignment 3D routing result Prerouting Initial Routing Iterative Forbidden-region Rip-up/rerouting (IFR)

10. 10 Outline  Introduction  Preliminary  Routing flow of NTUgr  Multiple forbidden-regions expansion  Critical nets rerouting selection  Look-ahead historical cost increment  Experimental results  Conclusions

11. 11 The Routing Flow 3D Benchmark 3D  2D capacity mapping Enhanced 2D routing 2D  3D layer assignment 3D routing result PreroutingPrerouting Initial Routing Iterative Forbidden-region Rip-up/rerouting (IFR)

12. 12 Prerouting 1.Congestion-hotspot historical cost pre-increment  Identify the high-pin-density tiles (#pin exceeds total tile capacity)  Increase the historical cost lying around these tiles by 10 To avoid other nets passing through these congested tiles 2.Small bounding-box area routing  Route the less-flexibility nets with smaller bounding-box area Prerouting of newblue3 (49.22% routed nets, 74374 overflows)

13. 13 The Routing Flow 3D Benchmark 3D  2D capacity mapping Enhanced 2D routing 2D  3D layer assignment 3D routing result Prerouting Initial Routing Iterative Forbidden-region Rip-up/rerouting (IFR)

14. 14 Initial Routing  The first stage completing all nets in the whole chip iterative monotonic routing  Apply iterative monotonic routing until the overflow improvement is less than 5%, cf. the previous iteration Initial routing of newblue3 (100% routed nets, 306082 overflows)

15. 15 The Routing Flow 3D Benchmark 3D  2D capacity mapping Enhanced 2D routing 2D  3D layer assignment 3D routing result Prerouting Initial Routing Iterative Forbidden-region Rip-up/rerouting (IFR)

16. 16  An enhanced flow over the traditional INR  Perform iteratively until no overflow or timeout Iterative Forbidden-region Rip-up/rerouting (IFR) Critical nets rerouting selection Look-ahead historical cost increment Multiple forbidden regions expansion No overflow or timeout No overflow or timeout N Y IFR:

17. 17 Outline  Introduction  Preliminary  Routing flow of NTUgr  Multiple forbidden-regions expansion  Critical nets rerouting selection  Look-ahead historical cost increment  Experimental results  Conclusions

18. 18 forbidden regions  At each iteration of IFR, new forbidden regions are constructed from the most congested regions  Initially contains two adjacent tiles w.r.t. the most congested edge  Expand the region until the average congestion of each boundary is smaller than a threshold (overlap is allowed)  Apply a special cost metric for nets in forbidden regions  Introducing new overflows within these regions is almost forbidden by incurring a large penalty Multiple Forbidden-Regions Construction Forbidden-region routing of adaptec5

19. 19 Cost Considering Forbidden Regions  The cost function of a global edge e: (penalized base cost of e)

20. 20 Region Propagation Leveling  Applied when # of overflows stops decreasing (get stuck at the local optima)  Stop creating new forbidden regions  Expand all forbidden regions at the previous iteration simultaneously Forbidden-region routing of bigblue3 (i)-th iteration(i+1)-th iteration(i+2)-th iterationfinal iteration

21. 21 Final Expansion of Forbidden Regions  Applied when # of overflows < 0.5% of initial overflow  Expand the forbidden region to the whole routing graph to quickly reduce the remaining overflows IFR w/ final expansion IFR w/o final expansion Traditional INR Overflow reduction of adaptec5

22. 22 Comparisons of Congested Regions BoxRouterNTHU-Route 1.0NTUgr (Ours) TerminologyBoxCongested regionForbidden region ShapeRectangular Rectilinear # of regionsSingle boxSingle regionMultiple regions Objective Performing progressive ILP Selecting rerouting nets Performing different cost functions Simultaneous expansion No Yes

23. 23 Outline  Introduction  Preliminary  Routing flow of NTUgr  Multiple forbidden-regions expansion  Critical nets rerouting selection  Look-ahead historical cost increment  Experimental results  Conclusions

24. 24 Critical Nets Rerouting Selection  To speed up the rip-up/rerouting process critical nets  Only rip-up/reroute the critical nets in each iteration  The critical nets are those nets with overflows or small remaining capacity:

25. 25 Outline  Introduction  Preliminary  Routing flow of NTUgr  Multiple forbidden-regions expansion  Critical nets rerouting selection  Look-ahead historical cost increment  Experimental results  Conclusions

26. 26 near-overflow global edges  For the near-overflow global edges (those edges would have overflow if more N demands are added), increase their historical cost in advance  Setting N = 1 in NTUgr results in better quality and with about 2x runtime speedup Look-Ahead Historical Cost Increment

27. 27 Outline  Introduction  Preliminary  Routing flow of NTUgr  Multiple forbidden-regions expansion  Critical nets rerouting selection  Look-ahead historical cost increment  Experimental results  Conclusions

28. 28 Results on ISPD’08 Benchmarks  Compared with the winners of ISPD’08 global routing contest  Runtime is averagely the same with NTHU-Route 2.0 (for the ten overflow-free cases for the three routers)  Overflow is better than FastRoute 3.0 The best solution in the literature!

29. 29 Effects of Look-Ahead Historical Cost Increment  Achieved 1.94x speed up and better overflow reduction with similar total wirelength

30. 30 Outline  Introduction  Preliminary  Routing flow of NTUgr  Multiple forbidden-regions expansion  Critical nets rerouting selection  Look-ahead historical cost increment  Experimental results  Conclusions

31. 31 Conclusions  NTUgr--- a high-quality global router for overflow reduction 1.Prerouting  Congestion-hotspot historical cost pre-increment  Small bounding-box area routing 2.Initial iterative monotonic routing 3.Iterative forbidden-region rip-up/rerouting (IFR)  Multiple forbidden-regions expansion  Look-ahead historical cost increment  Critical nets rerouting selection  Have achieved good results in terms of both overflow and runtime for the new ISPD’08 benchmarks

32. 32 Conclusions and Future Work  A dummy fill algorithm considering both gradient minimization and coupling constraints  Achieve more balanced metal density distribution with fewer dummy features and an acceptable timing overhead  Future work: integration of gradient minimization and coupling constraints  Simultaneously minimize the gradient and the coupling capacitance Thank You! Huang-Yu Chen yellowfish@eda.ee.ntu.edu.tw