1. A Min-area Solution to Performance and RLC Crosstalk Driven Global Routing Problem
Tong Jing, Ling Zhang, Jinghong Liang
Jingyu Xu, Xianlong Hong Jinjun Xiong, Lei He
CS&T Department EE Department
Tsinghua University UCLA
Beijing , China Los Angeles, CA, USA
Speaker: Jinghong Liang

2. ASP-DAC2005, Shanghai, China
Outline
1. Introduction
2. Preliminaries
3. Our Work (AT-PO-GR Algorithm)
4. Experimental Results & Discussions
5. Conclusions
November 27, 2018
ASP-DAC2005, Shanghai, China

3. Backgrounds
VLSI / ULSI
Coupling effects and crosstalk
System-On-a-Chip (SOC)
Clock frequency increases
New challenge to global routing
Global routing plays an important role in very/ultra large scale integrated circuits (VLSI/ULSI) physical design
The progress in VLSI/ULSI enables system-on-a-chip (SOC) integration instead of system-on-a-board (SOB) integration
Chip design is with greatly shrinking of geometries and giga-hertz clock frequencies
All these advances enable us to get high-performance chips
However, one of the great concerns is coupling effects and crosstalk
Crosstalk elimination has become a challenge to global routing
November 27, 2018
ASP-DAC2005, Shanghai, China

4. ASP-DAC2005, Shanghai, China
Previous Work (1)
The existing works can be divided into three categories
Noise modeling
[T. Sakurai, S. Kobayashi, and M. Node. ISCAS, 1991]
Derived expressions for a coupling capacitance and a crosstalk voltage height
[L. He and K. M. Lepak. ISPD, 2000]
Declared that on-chip inductance, especially mutual inductance, should be considered for high-performance interconnect design and presented the effective coupling model, called the Keff model
November 27, 2018
ASP-DAC2005, Shanghai, China

5. ASP-DAC2005, Shanghai, China
Previous Work (2)
Noise minimization
[T. X. Xue, E. S. Kuh. IEEE Trans on CAD, 1997]
Described a two-pass algorithm including region-based crosstalk risk estimation and crosstalk reduction
[H. Zhou and D. F. Wong. IEEE Trans on CAD, 1999 ]
Presented a cost function taking crosstalk into consideration, and is used during the phase of constructing the routing tree
[J. J. Xiong and L. He. IEEE Trans on CAD, 2004]
Proposed a three-phase algorithm based on crosstalk budgeting, simultaneous shield insertion and net ordering (SINO), and local refinement
November 27, 2018
ASP-DAC2005, Shanghai, China

6. ASP-DAC2005, Shanghai, China
Previous Work (3)
Simultaneous noise minimization and performance optimization
[L. Zhang, T. Jing, X. L. Hong, J. Y. Xu, J. J. Xiong, L.He. ASICON, 2003]----(PO-GR)
[J. Y. Xu, X. L. Hong, T. Jing, L. Zhang, J. Gu. ASP-DAC, 2004]
Both proposed performance optimization global routing algorithms considering crosstalk reduction. The former mainly focuses on coupling capacitance and uses spacing method. The latter considers coupling inductance and is based on shield insertion
[L. Zhang, T. Jing, X. L. Hong, J. Y. Xu, J. J. Xiong, L.He. ISCAS, 2004]----(T-PO-GR)
Presented an efficient RLC crosstalk reduction algorithm
November 27, 2018
ASP-DAC2005, Shanghai, China

7. ASP-DAC2005, Shanghai, China
Outline
1. Introduction
2. Preliminaries
3. Our Work (AT-PO-GR Algorithm)
4. Experimental Results & Discussions
5. Conclusions
November 27, 2018
ASP-DAC2005, Shanghai, China

8. Global Routing Problem
With the progress in multi-layer routing technology, routing area is a whole chip plane
A net can be specified as a set of nodes in global routing graph (GRG)
The problem of routing a net can be described as a rectilinear Steiner minimal tree (RSMT) problem of specified nodes in GRG.
November 27, 2018
ASP-DAC2005, Shanghai, China

9. Global Routing Graph (GRG)1
GRC
GRG e v 2 1 v
November 27, 2018
ASP-DAC2005, Shanghai, China

10. LSK Model for RLC Crosstalk Estimation1 K
f(i)
g(j) gl Ni Nj gr
Wire
order
Kij
Fast computation of Ki,j:
The total amount of inductive coupling induced on Nit:
For all net segments Njt that are sensitive to Nit
Different from earlier noise model Sakurai, the LSK model considers coupling inductance between adjacent and non-adjacent sensitive nets
November 27, 2018
ASP-DAC2005, Shanghai, China

11. ASP-DAC2005, Shanghai, China
Tabu Search
The basic idea of this technology is simple, which records and taboos the local minimum points that have been reached so as to avoid getting stuck at these points and finds out new search ways that could lead to the global minimum point eventually.
Select an initial solution xnow, and set Tabu list H = empty;
While not meet the stop conditions do
Generate a candidate list from the neighborhood of xnow that
does not conflict with H;
Select the best solution xnext from the candidate list;
xnow = xnext;
Update Tabu list H;
End While
There are 3 key factors in Tabu search:
tabu object, tabu length, and aspiration rule
November 27, 2018
ASP-DAC2005, Shanghai, China

12. ASP-DAC2005, Shanghai, China
Outline
1. Introduction
2. Preliminaries
3. Our Work (AT-PO-GR Algorithm)
4. Experimental Results & Discussions
5. Conclusions
November 27, 2018
ASP-DAC2005, Shanghai, China

13. Our Main Contributions
Goal: Reduce the final routing area by means of improving the gross algorithm based on holistic optimization
The main contribution of this paper is a min- area solution to performance and RLC crosstalk driven global routing problem
The proposed algorithm can achieve smaller routing area and fewer shields under the same design constraints, yet use less running time
November 27, 2018
ASP-DAC2005, Shanghai, China

14. ASP-DAC2005, Shanghai, China
Problem Formulation
Let
Then we have
Minimize
Subject to:
(1)
(2)
(3)
Formula(1) is the congestion constraint, which forbids the overflow on each GRG edge
Formula(2) guarantees the actual delay value from source i to sink j, T(i, j), is no more than the given timing constraint TD (i, j)
Formula(3) sets the upper bound of LSK, , for each source sink pair ij.
November 27, 2018
ASP-DAC2005, Shanghai, China

15. The Main Flow of AT-PO-GR
Use Grrandom() to get an initial solution X0
It considers congestion and timing issues
Use CtkEst() to budget and estimate crosstalk in X0
Iterate Grrandom(X0) to rip-up X0 so as to reduce its crosstalk, and get a good mid-solution Xtemp
Use Gr(Xtemp) to reduce wire length, congestion, and delay
Get a solution X1
Use CtkEli() to eliminate crosstalk in X1 by means of shield insertion and changing net orders
Get the final result X2
November 27, 2018
ASP-DAC2005, Shanghai, China

16. Use Grrandom() to get an initial solution X0
A new cost formula of GRG edge taking crosstalk into account is used as follows ,
(4)
where ct is the capacity of edge t, ft is the number of used tracks in edge t, δ is a small real number that validates formula (4) while ct is 0, is the actual congestion of edge t, K is a large integer used as the penalty factor, wt is the weighted cost of edge t, and nvt is the number of net segments in edge t that violate crosstalk constraint.
Considering possible shield may be inserted due to these net segments, we add nvt in such that these edges tend to become more congested. Then, nets crossing such edges will have higher cost and thus it will be avoided.
November 27, 2018
ASP-DAC2005, Shanghai, China

17. Use CtkEst() to budget and estimate crosstalk in X0
Firstly,
Where
is the crosstalk bound at sink pij for net Nj
len is the total length from the source pio to sink pij.
Secondly, having got , CtkEst() computes actual Kit with LSK model.
At last, we can obtain Kslack for each source-sink pair ij.
Kslack has the following definition.
November 27, 2018
ASP-DAC2005, Shanghai, China

18. Use Gr(Xtemp) to get a solution X1
Transition from a local minimum point
Gr() include 3 different strategies: stochastic optimization, deterministic optimization, and local enumeration optimization strategy.
Grrandom() only uses stochastic optimization strategy.
November 27, 2018
ASP-DAC2005, Shanghai, China

19. ASP-DAC2005, Shanghai, China
Use CtkEli() to eliminate crosstalk in X1 by means of shield insertion and changing net orders
Firstly, insert shields in each GRG region so that the crosstalk of most regions is within the given bound
Secondly, insert shield in those regions which have possible remnant crosstalk, so that crosstalk is completely eliminated
Finally, delete unnecessary shields so that the final area is minimized
November 27, 2018
ASP-DAC2005, Shanghai, China

20. Pseudo code of AT-PO-GR
November 27, 2018
ASP-DAC2005, Shanghai, China

21. ASP-DAC2005, Shanghai, China
Outline
1. Introduction
2. Preliminaries
3. Our Work (AT-PO-GR Algorithm)
4. Experimental Results & Discussions
5. Conclusions
November 27, 2018
ASP-DAC2005, Shanghai, China

22. Experimental Environments
Platform
Hardware: sun V880 fire workstation
Software: gcc2.9.1, solaris5.8
Benchmark Data
Circuits
Number of nets
GRG grids C2
745
9*11 C5
1764
16*18 C7
2356
avq
21581
65*67
Parameters Setting
LSK bound at each sink is set to be 1000
Na=350, Nb=20, Nc=10, and Tabu length=3
November 27, 2018
ASP-DAC2005, Shanghai, China

23. In Comparison with Typical Algorithms
(1) PO-GR [L. Zhang, T. Jing, X. L. Hong, 2003] is the first algorithm to study inductance coupling noise, timing performance and routability simultaneously at global routing level. It uses SA algorithm in its crosstalk elimination.
(2) T-PO-GR [L. Zhang, T. Jing, X. L. Hong, 2004] runs much faster than PO-GR with the similar routing results. But the routing area and shield number in T-PO-GR are comparably larger than those in PO-GR
We will compare our AT-PO-GR with the above algorithms focusing on area, running time, etc.
November 27, 2018
ASP-DAC2005, Shanghai, China

24. The comparison of wire length, running time, and routing area between AT-PO-GR and PO-GR
Circuit C2 C5 C7
avq
AT-PO-GR
Vionum (X0)
654
1600
1960
9885
Vionum (Xtmp)
608
1485
1902
9690
Decrease
5.66%
7.19%
2.96%
1.97%
Vionum (X1)
622
1522
Wire length (X0)
477516
Wire length (X1)
450730
Running time (s)
84.33
245.55
336.94
6277.5
Area
150187
269304
337378
1206×986
PO-GR
Wire length
471840 --
160190
269309
364366
The decrease of AT-PO-GR running time compared
with PO-GR running time
3.43%
4.28%
3.37%
The decrease of AT-PO-GR wire length compared
with PO-GR wire length
4.47%
4.66%
4.75%
The decrease of AT-PO-GR area compared with
PO-GR area
7.73%
1.62%
4.38%
November 27, 2018
ASP-DAC2005, Shanghai, China

25. The comparison of wire length, running time, and routing area between AT-PO-GR and T-PO-GR
Circuit C2 C5 C7
avq
AT-PO-GR
Running time (s)
84.33
245.55
336.94
6277.5
Area
150187
269304
337378
1206×986
Shield numbers
166
484
665
4131
Wire length
450730
T-PO-GR --
160190
269309
364366
204
527
684
471840
The decrease of AT-PO-GR running time / T-PO-GR running time
50.12%
42.25%
46.58%
The decrease of AT-PO-GR wire length compared
with T-PO-GR wire length
2.10%
3.25%
5.29%
The decrease of AT-PO-GR area compared with
T-PO-GR area
21.34%
12.74%
6.67%
The decrease of AT-PO-GR shield numbers compared with T-PO-GR shield numbers
18.63%
8.16%
2.78%
November 27, 2018
ASP-DAC2005, Shanghai, China

26. ASP-DAC2005, Shanghai, China
Discussions
Grrandom() can reduce crosstalk violation number（2%-7% ）
The runtime of AT-PO-GR is no more than 5% of that of PO-GR
AT-PO-GR can reduce wire length by more than 4% compared with PO-GR
Running time of AT-PO-GR is about half of that of T-PO-GR
The wire length of AT-PO-GR is shorter than that of T-PO-GR
AT-PO-GR also gets improvements in area and shield number compared with T-PO-GR
November 27, 2018
ASP-DAC2005, Shanghai, China

27. ASP-DAC2005, Shanghai, China
Outline
1. Introduction
2. Preliminaries
3. Our Work (AT-PO-GR Algorithm)
4. Experimental Results & Discussions
5. Conclusions
November 27, 2018
ASP-DAC2005, Shanghai, China

28. ASP-DAC2005, Shanghai, China
Conclusions
A min-area solution to performance and RLC crosstalk driven global routing problem has been presented in this paper
The experimental results have shown that this algorithm is able to:
(i) obtain routing solutions with less routing area compared with typical existing works
(ii) preserve good routing results and greatly decrease running time compared with typical existing works
November 27, 2018
ASP-DAC2005, Shanghai, China

29. ASP-DAC2005, Shanghai, China
Future Work
As our future work, we plan to find more specific methods to construct the Steiner tree set for crosstalk minimization, and better strategies for crosstalk budgeting
November 27, 2018
ASP-DAC2005, Shanghai, China

30. ASP-DAC2005, Shanghai, China
Thank you!
Jinghong Liang(梁敬弘)
Dept . of CST, Tsinghua Univ.
Beijing , P. R. China
Tel.:
Fax:
November 27, 2018
ASP-DAC2005, Shanghai, China