Fast estimation of the partitioning Rent characteristic using a recursive partitioning model

1
Fast estimation of the partitioning Rent
characteristic using a recursive partitioning
model

• J. Dambre, D. Stroobandt and J. Van Campenhout
• SLIP03 - April 5-6, 2003

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Presentation outline

• Rents rule vs. the Rent characteristic
• Recursive (bi-)partitioning equations
• Cut probability models
• Validation and application for fast estimation of
  the Rent characteristic
• Conclusions future work

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The circuit graph

• Circuit netlist, consists of

Only two-terminal connections considered !
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Donath-based prediction of placement wire lengths
circuit
architecture
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Donath-based prediction of placement wire lengths
At each level calculate number of cut nets ...
circuit
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Donath-based prediction of placement wire lengths
... and their length distribution from the
architecture site functions
architecture
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Recursive circuit partitioning ...modeled by
Rents rule??

• For a particular circuit netlist

• Perform complete recursive circuit partitioning
• Find average data points for T vs. G (Rent
  characteristic)
• Fit power law to region I

p Rent exponent t Rent coefficient
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Recursive circuit partitioning ...modeled by
Rents rule??
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Rents rule vs. the Rent characteristic
Rents rule is not a very accurate model, so ...
.... use the Rent characteristic instead of
Rents rule!
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Last years results ...
Prediction of average wire lengths, based on
Donaths technique, but ... using the Rent
characteristic instead of Rents rule
Overestimation, but very good correlation !
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Rents rule vs. the Rent characteristic
Problem full recursive partitioning takes a lot
of time
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Rents rule vs. the Rent characteristic
Problem recursive partitioning takes a lot of
time
Solution II find a better model than Rents rule
??
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Presentation outline

• Rents rule vs. the Rent characteristic
• Recursive (bi-)partitioning equations
• Cut probability models
• Validation and application for fast estimation of
  the Rent characteristic
• Conclusions future work

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Verplaetses recursive (bi-)partitioning equations
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Verplaetses recursive (bi-)partitioning equations
Partition in two equal parts (balanced)
Level k
Level k
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Verplaetses recursive bipartitioning model
Definea k-1 fraction of Nk-1 that is cut
(cut probability)
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Verplaetses recursive bipartitioning model
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Presentation outline

• Rents rule vs. the Rent characteristic
• Recursive (bi-)partitioning equations
• Cut probability models
• Validation and application for fast estimation of
  the Rent characteristic
• Conclusions future work

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Cut probabilities for random partitioning
Random bipartitioning of a two-terminal net
randomly assigning both connected gates to two
modules
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Cut probabilities for random partitioning
0.5
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Cut probabilities for optimal circuit partitioning
Measured values of ak ??

• Must perform some manipulations on Rent
  characteristic because
• circuit size not equal to 2H
• partitionings not perfectly balanced

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Cut probabilities for optimal circuit partitioning
random
ibm17
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Cut probabilities for optimal circuit partitioning
Verplaetses model for ak
With t and e parameters to be fitted
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Cut probabilities for optimal circuit partitioning
random
Verplaetse
ibm17
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Cut probabilities for optimal circuit partitioning
New model for ak based on observed relationship
between ak and ak,rand
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Cut probabilities for optimal circuit partitioning
random
Verplaetse
New model
ibm17
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Cut probabilities for optimal circuit partitioning
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Presentation outline

• Rents rule vs. the Rent characteristic
• Recursive (bi-)partitioning equations
• Cut probability models
• Validation and application for fast estimation of
  the Rent characteristic
• Conclusions future work

29
Cut probabilities for optimal circuit partitioning
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Update of last years results ...
Prediction of average wire lengths, based on
Donaths technique, but ... using the new
partitioning model instead of the Rent
characteristic (Rc)

• Correlation coefficients
• Verplaetse vs. Rc 0.988
• New model vs. Rc 0.995

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Fast estimation of the Rent characteristic
Can models for ak be applied to obtain accurate
estimations of the entire Rent characteristic
based on a few partitioning levels only??
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Fast estimation of the Rent characteristic
all levels
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Update of last years results ...
Prediction of average wire lengths, based on
Donaths technique, but ... using the new
partitioning model, fit for 3 levels of
partitioning

• Correlation coefficients
• Verplaetse vs. Rc 0.902
• New model vs. Rc 0.824

34
Presentation outline

• Rents rule vs. the Rent characteristic
• Recursive (bi-)partitioning equations
• Cut probability models
• Validation and application for fast estimation of
  the Rent characteristic
• Conclusions future work

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Conclusions

• Adaptation of Verplaetses recursive partitioning
  equations and cut probability model
• Application of this model for fast estimation of
  entire partitioning Rent characteristic

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Future work

• Extension to multi-terminal nets
• Try to find theoretical foundations for cut
  probability model
• Is it possible to estimate cut probabilities from
  circuit graph without performing partitioning??