1. Performance Optimization Global Routing with RLC Crosstalk Constraints
Ling Zhang, Tong Jing,
Xianlong Hong, Jingyu Xu Jinjun Xiong, Lei He
Dept. of CST, Tsinghua Univ Dept. of EE, UC, Los Angeles

2. Outline Introduction Previous Work Our Algorithm: CEE-Gr
Experimental Results & Discussions
Conclusions
2018年11月28日星期三
ASICON2003, Beijing

3. Introduction Device size shrinking and clock frequency increasing
Coupling capacitance and inductance could not be ignored
Longer delay and crosstalk caused by coupling effects
Global routing with performance optimization becomes more important.
2018年11月28日星期三
ASICON2003, Beijing

4. Outline Introduction Previous Work Our Algorithm: CEE-Gr
Experimental Results & Discussions
Conclusions
2018年11月28日星期三
ASICON2003, Beijing

5. Previous Work (1) Noise minimization Spacing in detailed routing
(K. Chaudhary, A. Onozawa et al, 1993)
Track permutation in detailed routing
(T. Gao, C. L. Liu, 1996)
Wire perturbation in detailed routing
(P. Saxena, C. L. Liu, 1999)
Crosstalk reduction after global routing
(T. X. Xue, E. S. Kuh, D. F. Wang, 1997)
(J. J. Xiong, J. Chen, J. Ma, L. He, 2002)
2018年11月28日星期三
ASICON2003, Beijing

6. Previous Work (2) Noise modeling Sakurai model
(T. Sakurai, C. Kobayashi, M. Node, 1993)
LSK model for calculating coupling inductance
(L. He, K. M. Lepak, 2000)
Model for calculating noise voltage
(K. M. Lepak, I. Luwandi, L. He, 2001)
2018年11月28日星期三
ASICON2003, Beijing

7. Outline Introduction Previous Work Our Algorithm: CEE-Gr
Experimental Results & Discussions
Conclusions
2018年11月28日星期三
ASICON2003, Beijing

8. Our Algorithm: CEE-Gr The major contribution of this work
We present a performance optimization global routing algorithm, named CEE-Gr, with RLC crosstalk constraints.
To our knowledge, it is the first to study RLC coupling noise, timing performance, and routability simultaneously at global routing level.
2018年11月28日星期三
ASICON2003, Beijing

9. Fig.1 Global Routing Graph(GRG)
Problem Formulation 1
GRC
GRG e v 2 1 v
Fig.1 Global Routing Graph(GRG)
2018年11月28日星期三
ASICON2003, Beijing

10. The CEE-Gr Algorithm (1)
Gr: Timing and congestion optimization
CEE: Crosstalk estimation and elimination
Gr firstly generates an initial routing solution considering congestion and timing optimization
Then, CEE eliminates the crosstalk from the solution by inserting shields and gets a mid-result
Finally, regard the mid-result as input and send it to Gr for iterations
2018年11月28日星期三
ASICON2003, Beijing

11. The CEE-Gr Algorithm (2)
generate initial routing solution considering congestion and timing optimization
eliminates the crosstalk from the solution by inserting shields and gets a mid-result
Gr (without crosstalk consideration)
CEE
Gr (subtract tracks used by shields)
do iterate again regarding the mid-result as input
Fig.2 CEE-Gr flow chart
2018年11月28日星期三
ASICON2003, Beijing

12. (1) Gr Congestion and timing optimization
Based on our previous methods
SSTT (search space traversing technology) and RINO (considering independent of net ordering)
(T. Jing, X. L. Hong, H. Y. Bao, Y. C. Cai, J. Y. Xu, 2001)
Critical-network-based technology
(T. Jing, X. L. Hong, H. Y. Bao, Y. C. Cai, J. Y. Xu et al, 2002)
2018年11月28日星期三
ASICON2003, Beijing

13. (2) CEE (1) Eliminate crosstalk in each GRG:
According to each , this step applies simulated annealing method in each region to insert shields, so that all region’s crosstalk is within bound value.
Local Refinement:
Check each net to eliminate possible remnant crosstalk and delete unnecessary shields to minimize the area.
2018年11月28日星期三
ASICON2003, Beijing

14. Insert shield with simulated annealing method
(2) CEE (2)
Flow chart:
partition the LSK bound at each sink of a net into the GRG edges belonging to the source-sink paths.
Get global routing solution from Gr and
Crosstalk bound budgeting
Eliminate crosstalk in each region
Local refinement
CEE
LSK
bound
Insert shield with simulated annealing method
Check each net to eliminate possible remnant crosstalk and delete unnecessary shields to minimize total area.
2018年11月28日星期三
ASICON2003, Beijing

15. Crosstalk Bound Budgeting (1)
CBUD (uniform distributed crosstalk budgeting) strategy
(1)
The crosstalk bound at sink pij for net Ni
Crosstalk sub-bound assigned to each GRG region t
len
The total length from the source pio to sink pij
2018年11月28日星期三
ASICON2003, Beijing

16. Crosstalk Bound Budgeting (2)
CBLP (linear programmed crosstalk budgeting) strategy
Consider different congestion situation in different GRG region in partitioning. Thus, introduce a linear programming problem.
The objective is to minimize the number of used tracks in most congested GRG region.
2018年11月28日星期三
ASICON2003, Beijing

17. Fig.4 One dimensional GRG
CBLP (1)
One dimensional GRG--horizontal wires routing in one row: …… R1 R2 Rt
Fig.4 One dimensional GRG
2018年11月28日星期三
ASICON2003, Beijing

18. CBLP (2) Minimize Subject to
(3)
(4)
ht: Number of tracks used by nets, shields or obstacles in region Rt
Gt: Number of nets in region Rt
Ot: Number of obstacles in region Rt
: Estimated number of shields in region Rt
2018年11月28日星期三
ASICON2003, Beijing

19. Fig.5 Two dimensionsal GRG
CBLP (3)
Two dimensional GRG: ……
CLMSET
ROWSET
Fig.5 Two dimensionsal GRG
2018年11月28日星期三
ASICON2003, Beijing

20. CBLP (4) Minimize Subject to (5) (6) (7) (8) 2018年11月28日星期三
ASICON2003, Beijing

21. Outline Introduction Previous Work Our Algorithm: CEE-Gr
Experimental Results & Discussions
Conclusions
2018年11月28日星期三
ASICON2003, Beijing

22. Experimental Results (1)
Circuits
Number of nets
Grids C2
745
9  11 C5
1764
16  18 C7
2356
Technology: 0.2um
Sensitivity rate: 0.5 for all nets and sensitivity matrix is random.
LSK bound:1000 at each sink
2018年11月28日星期三
ASICON2003, Beijing

23. Experimental Results (2)
Circuits C2 C5 C7
W mode
(Gr) Wire length (um)
459786
(CEE-Gr) Wire length (um)
473588
Increase in wire length
3.00%
2.95%
1.23%
Overflow edge number 1
T mode
466288
468836
0.55%
2.19%
0.16%
(Gr) Min-R
(CEE-Gr) Min-R
COMPARISON BETWEEN Gr AND CEE-Gr WITH CBUD
2018年11月28日星期三
ASICON2003, Beijing

24. Experimental Results (3)
Circuits C2 C5 C7
Wire length of Gr in W mode (um)
459786
Sink number that violates the crosstalk bound
583
1570
1845
CEE-Gr (CBUD)
Shield number
158
483
595
Area
154  200
273  298
346  380
Wire length (um)
473588
Increase in wire length
3.00%
2.95%
1.23%
Overflow edge number
CEE-Gr
(CBLP)
422
1315
1769
150  229
267  343
344  448
478240
4.01%
2.55%
2.30% 3 2
COMPARISON BETWEEN CBUD AND CBLP IN CEE-Gr
2018年11月28日星期三
ASICON2003, Beijing

25. Discussions
CEE-Gr can eliminate all crosstalk by adding shields, while the initial solution has serious crosstalk.
The increase in wire length of CEE-Gr is quite small compared to Gr.
The minimum redundancy of delay (requiredDelay-currentDelay) is almost unaffected.
CBUD strategy consumes less shields and small area than CBLP strategy.
CBLP reduces the maximal used tracks in GRG, which is helpful for optimization with other constraints and low power design.
Simulated annealing method increases the running time of CEE-Gr.(40 mins for C2)
2018年11月28日星期三
ASICON2003, Beijing

26. Outline Introduction Previous Work Our Algorithm: CEE-Gr
Experimental Results & Discussions
Conclusions
2018年11月28日星期三
ASICON2003, Beijing

27. Conclusions
Tackle coupling noise, timing performance and routability simultaneously
Take coupling inductance into consideration
Obtain good routing results
Efficiently eliminate crosstalk throughout the global routing phase by inserting shields and has little influence on wire length and timing performance.
2018年11月28日星期三
ASICON2003, Beijing

28. Dept. of CST, Tsinghua Univ
THANK YOU
Ling Zhang
Dept. of CST, Tsinghua Univ
2018年11月28日星期三
ASICON2003, Beijing