1. Closing the Smoothness and Uniformity Gap in Area Fill Synthesis
Supported by Cadence Design Systems, Inc.,
NSF, the Packard Foundation, and
State of Georgia’s Yamacraw Initiative
Closing the Smoothness and Uniformity Gap in Area Fill Synthesis
Y. Chen, A. B. Kahng, G. Robins, A. Zelikovsky
(UCLA, UCSD, UVA and GSU)
Thank you .…
Today, I will present our work on “Closing the Smoothness and Uniformity Gap in Area Fill Synthesis".
(20 sec)

2. fixed dissection window
The Smoothness Gap
Large gap between fixed-dissection and floating window density analysis
Gap!
fixed dissection window
with maximum density
floating window
with maximum density
The motivation of our work is a “smoothness gap” in the fill literature.
The very first paper on fill has pointed out that there is potentially large difference between fixed-dissection and
floating window density analysis.
For example, this is the fixed-dissection window with the maximum density on the given layout. However, by shifting the window up-right, we
can find a floating window with a larger density. Clearly, these two features contribute to the smoothness gap.
The consequence of the gap is that the fill result will not satisfy the given bounds.
However, despite this gap observation in 1998, all existing filling methods fail to consider the potential smoothness gap
(50 sec)
Fill result will not satisfy the given bounds
Despite this gap observation in1998, all existing filling methods fail to consider the potential smoothness gap

3. Accurate Layout Density Analysis
Optimal extremal-density analysis with complexity
intractable
Multi-level density analysis algorithm
shrunk on-grid windows are contained by arbitrary windows
any arbitrary window is contained by a bloated on-grid window
gap between bloated window and on-grid window accuracy
fixed dissection window
Prof. Kahng has proposed optimal extremal-density analysis algorithms. However, the algorithm with complexity K square becomes intractable
for layout with a large number of fill features.
Another method overcoming the intractability is the multi-level density analysis algorithm. It is based on the following facts:
Shrunk on-grid windows are contained by arbitrary windows
And any arbitrary window is contained by bloated on-grid windows
We use the gap between the bloated window and on-grid window as the accuracy of the algorithm
(45 sec)
arbitrary window W
shrunk fixed
dissection window
bloated fixed
dissection window
tile

4. Local Density Variation
Type I: max density variation of every r neighboring windows in each row of the fixed-dissection
Type II: max density variation of every cluster of windows which cover one tile
Type III: max density variation of every cluster of windows which cover tiles
We also suggest new methods to measure local uniformity of the layout based on the Lipschitz conditions. We proposed three kind of
Local density variations.
(click) Type One: the maximum density variation of every r neighboring windows in each row of the fixed-dissection
(click) Type Two: the maximum density variation of every cluster of windows which cover one tile
(click) Type Three: the maximum density variation of every cluster of windows which cover r/2 x r/2 tiles.
(45 sec)

5. Computational Experience
Testcase  LP
Greedy MC
IGreedy
IMC
Testcase
OrgDen FD
Multi-Level
T/W/r
MaxD
MinD
DenV
Denv
L1/16/4
.2572
.0516
.0639
.2653
.0855
.0621
.2706
.0783
.2679
.0756
.084
.0727
L1/16/16
.2643
.0417
.0896
.0915
.0705
.2696
.0773
.2676
.0758
.0755
.0753
The window density variation and violation of the maximum window density in fixed-dissection filling are underestimated
case
Min-Var LP
LipI LP
LipII LP
Comb LP
T/W/r
Den V
Lip1
Lip2
Lip3
L1/16/4
.0855
.0832
.0837
.0713
.1725
.0553
.167
.1268
.1265
.0649
.0663
.0434
.1143
.0574
.0619
.0409
L1/16/8
.0814
.0734
.0777
.067
.1972
.0938
.1932
.1428
.1702
.1016
.1027
.0756
.1707
.0937
.1005
.0766
L2/28/4
.1012
.0414
.0989
.0841
.0724
.0251
.072
.0693
.0888
.0467
.0871
.0836
.0825
.0242
.0809
.0758
L2/28/8
.0666
.034
.0658
.0654
.0264
.0744
.07
.0331
.0697
.0661
.0747
.0255
.0708
.0656
For the smoothness gap, our experiments show that the window density variation and violation of the maximum
window density in fixed-dissection filling are underestimated
For the local density variations, our experiments show that the solution with the Min-Var objective value do not always have the best
Value in terms of the local smoothness, and the LP with combined objective achieves the best comprehensive solutions.
(60 sec)
The solutions with the best Min-Var objective value do not always have the best value in terms of local smoothness
LP with combined objective achieves the best comprehensive solutions

6. Thank you!
Thank you for your attention.