Placement Feedback: A Concept and Method for Better Min-Cut Placements

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Placement Feedback A Concept and Method for
Better Min-Cut Placements
Andrew B. Kahng
Sherief Reda
CSE ECE Departments University of CA, San
Diego La Jolla, CA 92093 abk_at_cs.ucsd.edu
CSE Department University of CA, San Diego La
Jolla, CA 92093 sreda_at_cs.ucsd.edu
VLSI CAD Laboratory at UCSD http//vlsicad.ucsd.ed
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Outline

• Min-cut Placement and Terminal Propagation
• Ambiguous Terminal Propagation
• Placement Feedback
• Iterated Controlled Feedback
• Accelerated Feedback
• Experimental Results
• Conclusions

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Min-Cut Placement Objective

• Min-cut Placement Objective Total wirelength
  minimization

• Steiner tree represents the minimum wirelength
  need to connect a number of cells
• Total wirelength is the sum of the length of
  Steiner trees
• Routed wirelength is the typically larger than
  total wirelength due to detours arising from
  contention on routing resources

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Min-Cut Placement Method

• Min-Cut Placement Method Sequential min-cut
  partitioning

Netlist (hyper-graph)
block
Input
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Terminal Propagation
A
B
C
D
Simple hypergraph
After first placement level

• Well-studied problem
• Terminal propagation (Dunlop/Kernighan85)
• Global objectives/cycling (HuangK97,
  Zheng/Dutt00, Yildiz/Madden01)

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Terminal Propagation Mechanism
B1
B2
u
v

• B1 has been partitioned B2 is to be partitioned
• u is propagated as a fixed vertex uf to the
  subblock that is closer
• uf biases the partitioner to move v upward

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Ambiguous Terminal Propagation
f2
f1
X
f3

• Ambiguous propagation occurs when terminals,
  e.g. Y4, are equally close to the two subblocks
  of a block under partitioning
• Traditional solution either propagate to both
  subblocks or not to propagate at all

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Effect of Ambiguous Terminal Propagations
L
R
Given an edge e with a set of cells I
Conclusion Ambiguous propagations lead to
indeterminism in propagation decisions ?
wirelength increase
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Min-Cut Placement Flow
Level m Partitioning
Terminal Propagation
Level 2 Partitioning
Level 1 Partitioning
Terminal Propagation
Terminal Propagation
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Outline

• Min-cut Placement and Terminal Propagation
• Ambiguous Terminal Propagation
• Placement Feedback
• Iterated Controlled Feedback
• Accelerated Feedback
• Experimental Results
• Conclusions

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Mitigating Ambiguous Terminal Propagation

• Two hyperedges A, B, C, X, A, B. B1 is
  partitioned before B2

B1
B2
A
X
C
B
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Placement Feedback
For each placement level - Undo all
partitioning/block bisecting results, but retain
the new cell locations for terminal
propagations - Use the new cell locations to
re-do the levels placement
Placement Flow with Feedback
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Placement Feedback Assessment

• Metrics
• Reduction in ambiguous terminal propagations
• Associated reduction in HPWL

• Experimental Setup
• We implement feedback in Capo (version 8.7)
• For each placement level
• Measure the number of ambiguous terminal
  propagations before and after feedback
• Measure the HPWL estimate before and after
  feedback (assuming all previous placements levels
  had feedback)

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Feedback Effects
Percentage reduction in ambiguous propagations
Placement Level

• Reductions in ambiguous terminals and HPWL per
  level are strongly correlated

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Outline

• Min-cut Placement and Terminal Propagation
• Ambiguous Terminal Propagation
• Placement Feedback
• Iterated Controlled Feedback
• Accelerated Feedback
• Experimental Results
• Conclusions

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Iterative Placement Feedback
Level 1 Partitioning
Terminal Propagation
Level 2 Partitioning
Terminal Propagation
Level m Partitioning
Terminal Propagation
Feedback Controller
Placement Flow with Feedback Controllers

• Since the feedback loop produces new outputs ?
  iterate over the feedback loop a number of times
• If the feedback response is not desirable ?
  insert a feedback controller to enhance the
  response.

Feedback controller should

• Evaluate and optimize some placement quality or
  objective
• Decide when to terminate feedback iterating

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Feedback Controller Objectives
B1

• Two possible objectives (placement qualities) to
  optimize

d1
c1

• Cut partitioning objective QP c1 c2
• HPWL objective QH c1 d1 c2 d2

B2
c2
d2

• QP and QH are not correlated!

• Example
• Assume d1 6 and d2 8
• c1 c2 100 ? QP 200 and QH 1400
• c1 85, c2 112 ? QP 197 and QH 1406

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Feedback Controller Stopping Criteria
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Feedback Controller Stopping Criteria
B. Best Improvement Criterion Iterate per
placement level a fixed number of times but pass
the best results seen QP (or QH)
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Feedback Controller Stopping Criteria
C. Unconstrained Criterion Iterate per placement
level a fixed number of times and pass the last
results
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Controller Type Comparison
3 Stopping Criteria 2 Objectives
Monotonic Improvement Total Cut (QP)
Monotonic Improvement HPWL Estimate (QH)
Best Improvement Total Cut (QP)
Best Improvement HPWL Estimate (QH)
Unconstrained -

• Combinations of the 3 stopping criteria and 2
  objectives yield 5 controllers
• We study the aggregate impact of the different
  controllers on the final HPWL

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Effect of Controller on Final Wirelength
Final HPWL versus number of iterations for
different controllers
Monotonic QH
Best QH
Monotonic QP
Best QP
Unconstrained
Iteration

• QP (based on partitioning) controllers dominate
  QH (based on HPWL) controllers
• Best Improvement controllers outperform
  monotonic improvement controllers
• Best Improvement QP controller slightly
  outperforms the unconstrained controller

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Asymptotic Controller Behavior
Final HPWL versus number of iterations for
different controllers
Best QP
Iteration

• Results are average of 6 seeds for up to 12
  iterations using the best improvement QP
  controller
• Final value slightly oscillates around a fixed
  value with a 8-9 improvement in HPWL in
  comparison to traditional placement flow

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Accelerated Feedback
Coarsening
Uncoarsening
V Cycle

• Feedback runtime a number of feedback iterations

• Typically, placers call the multilevel
  partitioner a number of times and utilize the
  best cluster-tree partitioning results
• In iterated feedback, only the last feedback
  iteration determines the partitioning results
  other loops determine accurate terminal
  propagation.

To speedup our feedback implementation ?
Call the multi-level partitioner once (1 V-Cycle)
for each feedback loop ? Restore to default
placer settings (2 V-Cycles) for the last
feedback iteration
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Outline

• Min-cut Placement and Terminal Propagation
• Ambiguous Terminal Propagation
• Placement Feedback
• Iterated Controlled Feedback
• Accelerated Feedback
• Experimental Results
• Conclusions

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Experimental Setup

• We test our methodology in Capo version 8.7

• Cadences WarpRoute is used for routed
  wirelength evaluation

• Placement results are average of 6 seeds

• Code implementation took 130 lines of C code

• All experiments conducted on 2.4 GHz Xeon Linux
  workstation, 2 GB RAM

• We evaluate feedback on the IBM version 1,
  version 2, and PEKO benchmarks

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HPWL Results (IBM Version 1)

• We use 3 feedback iterations with the best
  improvement Qp feedback controller

AFB
FB
Percentage improvement in HPWL (Half-Perimeter
Wirelength) in comparison to Capo
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HPWL Results (IBM Version 1)

• Accelerated Feedback Max improvement 13.43 and
  average improvement 4.70 with 2.43x the original
  Capo runtime

• Feedback Max improvement 13.73 and average
  improvement 5.43 with 4.10x the original in Capo
  runtime

• PEKO benchmarks Max improvement 10 and average
  improvement 5 for feedback at the expense of
  2-3x increase in Capo runtime

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Routed Wirelength Results (IBM Version 2 - Hard)

benchmark Violations Violations
benchmark Capo FeedBack
Ibm01 601 103
Ibm02 0 0
Ibm07 450 0
Ibm08 59 0
Percentage improvement in routed wirelength in
comparison to Capo
Number of routing violations
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Routed Wirelength Results (IBM Version 2 - Easy)

benchmark Violations Violations
benchmark Capo FeedBack
Ibm01 1238 0
Ibm02 0 0
Ibm07 0 0
Ibm08 0 0
Percentage improvement in routed wirelength in
comparison to Capo.
Number of routing violations
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Conclusions

• New understanding of how ambiguous terminal
  propagation leads to indeterminism in propagation
  results and degraded placer performance
• Idea reduce indeterminism by undoing placement
  results, but still using them to guide future
  partitioning.
• Flavors of this approach proposed before, but
  for different contexts
• Our approach is captured as feedback, which we
  tune using controllers
• Detailed study of variant objectives that can be
  optimized by the controllers, as well as
  iterating criteria
• Accelerated feedback efficient implementations
  to reduce runtime impact
• IBMv1 HPWL results up to 14 (best) and 6
  (avg) improvement over Capo
• IBMv2 routed WL results up to 10 improvement
  over Capo, with improved routability and reduced
  via count
• Accelerated feedback is now the default mode in
  Capo

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Acknowledgments
We thank Igor Markov (University of Michigan) for
helpful discussions.
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Thank You
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Block Ordering

• Regular ordering
• Random ordering
• Alternate ordering

Results are inconclusive!