Ke-Ren Dai, Wen- Hao Liu, and Yih -Lang Li, Member, IEEE

1. NCTU-GR : Efficient Simulated Evolution-Based Rerouting and Congestion-Relaxed Layer Assignment on 3-D Global Routing Ke-Ren Dai, Wen-Hao Liu, and Yih-Lang Li, Member, IEEE TVLSI 2012 NO.3

2. Outline • Introduction • Problem Formulation • 2-D Global Routing • Layer Assignment • Experiment Result

3. Introduction • The increasing complexity of interconnection designs has enhanced the importance of research into global routing. • The ideal approach for interconnection optimization is to undertake a simultaneous placement and global routing [12] or take interconnection delay into account in early stage.

4. Introduction • A routing using a short wire consumes less routing resource than using a long wire and more routing resource is thus reserved for subsequent routing. • Adopting too many detours in early routing stage should be well controlled to evade lowering the routability and overflow-free rate of subsequent routings due to overusing routing resources in early routing stage. • Thus control over the increase of wirelength is very important in global routing.

5. Problem Formulation Given a set of nets, a grid graph, and the capacityof every grid edges, the global routing is to find the paths to connect all the pins for every net such that the number of overflows is minimized.

6. 2D Global Routing Design flow of the proposed router.

7. 2D Global Routing • Net Decomposition and Initial Route • This study decomposes each net into two-pin nets via MST. • Then, FLUTE is employed to yield RSMT as the initial routing solution. • Circular Fixed-Ordering Monotonic Routing (CFOMR) • improve the overflow-removing efficiency of applying fixed net-ordering routing. • The CFOMR repeatedly rips up and reroutes all nets (one net at a time) in a decreasing order of wirelength using monotonic routing k times.

8. 2D Global Routing • Circular Fixed-Ordering Monotonic Routing (CFOMR) Example of CFOMR with routing order A B C D

9. 2D Global Routing • Simulated Evolution-Based Rip-Up and Rerouting • SILK[20]: • SILK scores each net in a generation by its routing violation and path quality as follows: A net is considered to have good quality if it comprises less vias and shorter wirelength. All scores are then normalized to 0.1–0.9. SILK generates a random number between 0.0 and 1.0 for each net.

10. 2D Global Routing • Simulated Evolution-Based Rip-Up and Rerouting

11. 2D Global Routing • Two-Stage Cost Function • Review : History-Base Routing cost function[16] is the base cost of node n; is the history cost of node n represents the penalty cost of node n.

12. 2D Global Routing • Two-Stage Cost Function • The cost function of maze routing is given by h(x) is the estimation from the current position to the target. g(x) Is the cost from the source to x. McMurchie’s function is given by g(x) Rapidly remove most overflows for ISPD benchmarks.

13. 2D Global Routing • Two-Stage Cost Function • If the rip-up and rerouting scheme cannot reduce the minimum number of overflows within several iterations, the rip-up and rerouting scheme enters its second stage to solve the remaining incomplete nets by using the following cost function: • In the second stage, routability is more important than wirelength and historical cost has more impact on the cost function than in the first stage.

14. LAYER Assignment

15. LAYER Assignment • Net Decomposition and Ordering

16. LAYER Assignment • Net Decomposition and Ordering

17. LAYER Assignment • Net Decomposition and Ordering

18. LAYER Assignment • Heuristic Algorithm to Preassign a Subnet Initially, the tree structure of asubnet is constructed and then each edge in the tree from bottom(leaf) to top (root) issequentially assigned to the layer withleastassignment cost.

19. LAYER Assignment • Heuristic Algorithm to Preassign a Subnet

20. LAYER Assignment • Heuristic Algorithm to Preassign a Subnet

21. LAYER Assignment • Heuristic Algorithm to Preassign a Subnet

22. LAYER Assignment • Dynamic Programming-Based Layer Assignment With • Layer Shifting (DPLALS)

23. LAYER Assignment • Dynamic Programming-Based Layer Assignment With • Layer Shifting (DPLALS)

25. LAYER Assignment • Dynamic Programming-Based Layer Assignment With • Layer Shifting (DPLALS)

26. EXPERIMENTAL RESULTS ISPD’07 Benchmarks

27. EXPERIMENTAL RESULTS ISPD’08 Benchmarks

28. EXPERIMENTAL RESULTS ISPD’08 Benchmarks

29. conclusion • This work proposes a high-performance congestion-driven 3-D global router. • This study also presents two routing methods for 2-D global routing—circular fixed-ordering monotonic routing and simulated evolution-based rip-up and rerouting using a two-stage cost function. • a congestion-relaxed dynamic programming-based layer assignment by using a layer shifting algorithm followed by layer rip-up and reassigning to further reduce the number of vias. • Experimental results demonstrate that our router achieves performance similar to the first two winning routers in ISPD 2008 Routing Contest in terms of both routability and wirelength at a 1.05x and 18.47x faster routing speed.