High-Performance Global Routing with Fast Overflow Reduction

1. High-Performance Global Routing withFast Overflow Reduction Huang-Yu Chen, Chin-HsiungHsu, and Yao-Wen Chang Department of EE, NTU, Taipei, Taiwan

2. Outline • Introduction • Problem formulation • Routing methodology • Prerouting • Initial iterative monotonic routing • Iterative Forbidden-region Rip-up/Rerouting (IFR) • Experimental result

3. Introduction • Global routing is the first stage to tackle the stringent routing challenges. • A good global router can systematically guide a detailed router to avoid congestion and achieve high routability, thus speeding up the time-consuming detailed routing process.

4. Introduction • Iterative negotiation-based rip-up/rerouting (INR) has revealed its great ability to spread out congestion as well as to reduce the overflow. • In this paper, we develop a new global router, NTUgr, that contains three major steps: prerouting, initial routing, and enhanced INR.

5. Problem formulation • For global routing, the routing region is partitioned into tilesand edgesmodels the routing region, where the global tile node represents a tile, and the global edge models the relationship between adjacent tiles.

6. Problem formulation • Each global edge is associated with a capacity.

7. Problem formulation • The main objective of global routing is to minimize the total overflow, which is calculated by the total amount of routing demand that exceeds the capacity for all edges.

8. Routing methodology • Prerouting • Initial iterative monotonic routing • Iterative Forbidden-region Rip-up/Rerouting (IFR)

9. Flow of NTUgr

10. Prerouting • Prerouting identifies the potential congestion hotspots to help guide the subsequent routing stages. • Congestion-hotspot Historical Cost Pre-increment • Mainly for difficult routing instances • Small Bounding-box Area Routing

11. Congestion-hotspot Historical Cost Pre-increment • Pre-increasethe historical cost for the global edges lying around the high-pin-density tiles before going into the iterative negotiation-based rip-up/reroute procedures.

12. Cost function of this paper • Where g(x) is the Manhattan distance from s to x, h(x) is the Manhattan distance from xto t, and e ∈ path(s, x) represents a global edge on the path from sto x, path(s, x). h(x) t e3 g(x) x e1 e2 + + s

13. Cost function of this paper(cont.) • The costRe(e) denotes the routing cost for a path passing e, whose value would depend on the congestion status of both eand the region Rewhere elies: = If Reis in a forbidden region and e is congested, otherwise

14. Cost function of this paper(cont.) • present-congestion cost • where Pndenotes an overflow penalty constant. • historical-congestion cost • where herepresents the historical cost of e, and the base cost peis usually set aspe=de/cefor ewith the capacity ceand the demand de. = If Reis in a forbidden region and e is congested, otherwise

15. Cost function of this paper(cont.) • Overflows between iterations would decline faster if enlarge the gap between the overflow-free global edges and the over-congestion ones. Therefore, we apply the modifies pein IFR as follows: ζ = 3.0

16. Small Bounding-box Area Routing • Route the subnets with smaller bounding box areas (smaller than a threshold α) • Since these subnets have less routing flexibility than the ones with larger bounding-box areas and thus have higher probability to become congestion hotspots.

17. Initial routing • Initial iterative monotonic routing • Increase the historical cost heonly once at the last iteration

18. Iterative Forbidden-Region Rip-up/Rerouting

19. Iterative Forbidden-Region Rip-up/Rerouting • At each iteration of IFR, some rectilinear regions, called the forbidden regions, are constructed and expanded from the congested regions.

20. Iterative Forbidden-Region Rip-up/Rerouting • Multiple Forbidden-Regions Expansion • apply the present-congestion cost function to reroute the subnets with overflow and lying in forbidden regions. • There are three phases for the multiple forbidden regions construction in IFR.

21. Iterative Forbidden-Region Rip-up/Rerouting • Multiple Forbidden-Regions Expansion • First phase. • Each forbidden region expands only from the most congested boundary of that region until an expansionstopping criterion is satisfied. Rebuild forbidden region at every iteration

22. Iterative Forbidden-Region Rip-up/Rerouting • Multiple Forbidden-Regions Expansion The multiple forbidden-regions expansion shown in the congestion map of adaptec5.

23. Iterative Forbidden-Region Rip-up/Rerouting • Multiple Forbidden-Regions Expansion • expansionstopping criterion • average congestion

24. Iterative Forbidden-Region Rip-up/Rerouting • Multiple Forbidden-Regions Expansion • Second phase. • Region propagation leveling (RPL)

25. Iterative Forbidden-Region Rip-up/Rerouting • Multiple Forbidden-Regions Expansion • Third phase.(Final expansion) • expands the forbidden region to the whole routing graph to quickly reduce the remaining overflows.

26. Iterative Forbidden-Region Rip-up/Rerouting • Critical Subnets Rerouting Selection • In IFR, we rip up only critical subnets and then reroute them, instead of ripping up all subnets. • A subnet n is critical if it satisfies the following criterion: where Sis a constant, and eis a global edge passed by n

27. Iterative Forbidden-Region Rip-up/Rerouting • Look-ahead Historical Cost Increment

28. Iterative Forbidden-Region Rip-up/Rerouting

29. Experimental result

30. Experimental result

31. Experimental result

32. CONCLUSION • In this paper, we have developed a high-performance global router NTUgrfor fast overflow reduction. • Iterative forbidden-region rip-up/rerouting (IFR), improves the traditional iterative negotiation-based rip-up/rerouting (INR).

33. Thank you