1 / 18

Maze Routing with Buffer Insertion and Wire sizing

Maze Routing with Buffer Insertion and Wire sizing. Minghorng Lai , D.F. Wong DAC 2000. Elmore delay model. Elmore delay model. R wire =1.2 C wire =2.4F. Elmore delay model. R wire =1.2 C wire =2.4F R buffer =0.2 C buffer =1F. t. s. Problem. Solution. Previously Proposed Methods

javier
Download Presentation

Maze Routing with Buffer Insertion and Wire sizing

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Maze Routing with Buffer Insertion and Wire sizing Minghorng Lai , D.F. Wong DAC 2000

  2. Elmore delay model

  3. Elmore delay model Rwire=1.2 Cwire=2.4F

  4. Elmore delay model Rwire=1.2 Cwire=2.4F Rbuffer=0.2 Cbuffer=1F

  5. t s Problem

  6. Solution • Previously Proposed Methods • Dynamic programming • Waste time and space • With wire sizing, the sizes of the sub-solution sets for dynamic programming increase significantly. • Proposed method • Shortest Path Formulation • Time :O(|V|2log(|V|)) • Space:O(|B|2|V|2)

  7. u t sb-1 tb-1 s Graph G={V,E} SP Graph BG ={VBG,EBG} x v Shortest Path Formulation

  8. Step 1.Compute shortest distance Step 2.Create new vertices and edges Step 3.Assign every edges’ weight Shortest Path Formulation Wire sizing Construct SP Graph Find the shortest path from source to sink

  9. Step 1.Compute shortest distance Step 2.Create new vertices and edges Step 3.Assign every edges’ weight Shortest Path Formulation • Construct SP Graph

  10. v u Shortest Path Formulation Step 2.Create new vertices & edges Buffer Library B={b0,b1} vb0 ub0 vb1 ub1

  11. u s t bo bo bo bo bo b1 b1 b1 b1 b1 x v Shortest Path Formulation Step 2.Create new vertices & edges t u s v x Graph G={V,E}

  12. sb-1 tb-1 Shortest Path Formulation Step 2.Create new vertices & edges • Add pseudo node sb-1 & tbi-1 SP Graph

  13. Step 1.Compute shortest distance Step 2.Create new vertices and edges Step 3.Assign every edges’ weight Step 4.Find the shortest path from source to sink Shortest Path Formulation

  14. h1 h2 bi bj h3 hn l1 l2 l3 ln Shortest Path Formulation Step 3.Assign every edges’ weight • C. Chu and D. F.Wong, “ A New Approach to Simultaneous Buffer Insertion and Wire Sizing," IEEE Trans. on CAD, 1997 • use (bi, bj, d(u, v)) as index to check look-up table d(u, v)

  15. Step 1.Compute shortest distance Step 2.Create new vertices and edges Step 3.Assign every edges’ weight Shortest Path Formulation Step 4.Find the shortest path from source to sink

  16. Shortest Path Formulation • Time Complexity • Shortest path O(|VGV|log|VGV|) • at most |B||V| new vertices are created in the BP-Graph • Space Complexity • O(|VBG|2)=>O(|B|2|V|2).

  17. DP-Routing SP-Routing Name Memory(Mb) Time(s) Memory(Mb) Time(s) Experimental Results SRL1 SRL2 SRL3 SRL4 SRL5 SRL6 SRL7 SRL8 SRL9 SRL10 2.88 2.71 2. 3.09 3.08 2.69 2.82 2.88 2.85 3.48 741 919 827 1044 1306 961 969 767 868 1243 0.524 0.318 0.355 0.740 0.672 0.572 0.767 0.384 0.479 0.869 35.3 18.2 19.5 51.0 60.2 38.1 46.1 25.5 22.6 71.0

  18. Conclusion • The lookup-table construction only needs to be done once and can be reused in multi-net maze routing. • congestion avoidance

More Related