A Semi-Persistent Clustering Technique for VLSI Circuit Placement

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A Semi-Persistent Clustering Technique for VLSI
Circuit Placement
Charles J. Alpert1, Andrew Kahng2, Gi-Joon Nam1,
Sherief Reda2 and Paul G. Villarrubia1 1IBM
Corp. 2Department of CSE, UCSD
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bigblue4 design from ISPD2005 Suite
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Implications in Placement

• Scalability
• Tractability
• Runtime vs. quality trade-off
• SoC (System-on-Chip) designs
• Mixed-size objects
• White space

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Problem Statement

• What is the most effective and efficient
  clustering strategy for analytic placement?
• Quality of solution
• CPU time

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Clustering Concept
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Clustering Literature

• Tremendous amounts of research here
• Edge-Coarsening (EC)
• First-Choice (FC)
• Edge-Separability (ESC)
• Peak-Clustering
• Etc
• General drawbacks
• Clique transformation
• Edge weight discrepancy
• Pass-based iteration
• Lack of global clustering view

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Best-Choice Clustering

• Avoid clique transformation
• Avoid pass-based iterations
• More global view of clustering sequence
• Priority-queue management
• Lazy-update speed-up technique
• Area-controlled balanced clustering

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Best-Choice Clustering

• Initialize the priority-queue PQ
• - For each cell u calculate its clustering
  score c with its closest neighbor v.
• - Insert the pair (u, v) into PQ based on
  their cost c.
• Until the target cell number is reached
• - Pick the top of the heap (m, n)
• - Cluster (m, n) into a new object mn update
  the netlist
• - Calculate mn closest neighbor k insert
  (mn, k) into PQ
• - Recalculate the clustering cost of all the
  neighbors to m and n

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Best-Choice Example

• Assume
• N-pin net weight 1 / (n-1)
• Each object size 1
• Timing criticality is 1 for all nets

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Best-Choice Example
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Best-Choice Example
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Best-Choice Example
ABCDEF
EF1/3
ABCD1/3
? clustering_score 2.875
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Best-Choice Clustering Summary

• Globally optimal clustering sequence via
  priority-queue data structure
• Produce better quality of results
• Clustering framework
• Arbitrary clustering score function can be
  plugged in

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Best-Choice Clustering

• Clustering score distribution
• First-choice (FC) ? clustering_score 5612.83
• Best-choice (BC) ? clustering_score 6671.53

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Lazy Update Speed-up Technique
Priority Queue PQ
Top of the PQ
Node A

• Observations
• Node A might be updated a number of times before
  making it to the top of the PQ (if ever), but the
  last update is what determines its final position
  in PQ
• Statistics indicate than in 96 of our updating
  steps, updating node A score pushes A down in PQ

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Lazy Update Speed-up Technique
Main Idea Wait until A gets to the top of the
priority-queue and then update its score if
necessary
Until the target cell number is reached -
Pick the top of the heap (m, n) - If (m, n)
is invalid then - recalculate m closest
neighbor n and insert (m, n) in the heap
else - Cluster (m, n) into a new object
mn update the netlist - Calculate mn
closest neighbor k insert (mn, k) in the heap
- Mark all neighbors of m and n invalid
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Lazy Update Runtime Charateristic
Note Practically no impact to solution quality
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Experiments

• IBM CPLACE
• Analytic placement algorithm
• Semi-persistent clustering paradigm
• Up-front clustering
• Selective unclustering during main global
  placement
• Full unclustering before detailed placement
• Order-of-magnitude reduction by clustering
• Industrial ASIC designs
• Size ranges from 56K to 880K placeable objects

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Placement Results w/ Clustering

• Average 4.3 WL improvement over EC
• BC is x8.76 slower than EC

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No Clustering vs. BCLazy Clustering
WL() CPU CL-CPU
AL(270K) 2.09 0.40 1.17
BL(276K) -4.28 0.52 1.35
CL(351K) 3.27 0.51 1.14
DL(426K) 0.87 0.45 1.35
EL(456K) 1.59 0.33 1.10
FL(880K) 1.41 0.46 1.68
AD(389K) 8.23 0.50 0.98
BD(285K) -0.34 0.47 0.94
CD(56K) -0.36 0.69 0.51
Avg. 1.39 0.48 1.14
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Conclusions

• Globally optimal clustering sequence framework
• Independent of clustering scoring function
• Better clustering sequence
• Allow significant placement speed-up
• Almost no loss of quality of solution
• Size control via clustering scoring function
• Effective for dense design

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Future Work

• Handling fixed blocks during clustering
• Ignoring nets connected to fixed objects
• Ignoring pins connected to fixed objects
• Including fixed blocks during clustering
• Etc.
• No visible improvement at the moment

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Cluster Size Control Results
Standard k 1 Automatic k ?size(u)
size(v) / ?? where ?
expected avg. size
Standard Standard Standard Automatic Automatic Automatic
Max Avg WL Max Avg WL
AD 14823 171.4 0.00 1140 160.4 -0.88
BD 28600 150.0 0.00 1140 114.6 3.71
CD 9060 113.5 0.00 610 109.8 30.05