March 20, 2007 ISPD 2007 1 An Effective Clustering Algorithm for Mixed-size Placement Jianhua Li,...

March 20, 2007March 20, 2007 ISPD 2007ISPD 2007 11

An Effective Clustering An Effective Clustering Algorithm for Mixed-size Algorithm for Mixed-size

PlacementPlacement

Jianhua Li, Laleh Behjat, and Jie HuangJianhua Li, Laleh Behjat, and Jie Huang

SCHULICH School of EngineeringSCHULICH School of EngineeringUniversity of Calgary, Calgary, Canada University of Calgary, Calgary, Canada


OutlineOutline

IntroductionIntroduction Previous WorkPrevious Work Proposed Clustering AlgorithmProposed Clustering Algorithm Numerical ResultsNumerical Results Conclusions and Future WorksConclusions and Future Works


Introduction – What is Introduction – What is clustering?clustering?

Application AreasApplication Areas VLSI circuit partitioning and placementVLSI circuit partitioning and placement

ObjectiveObjective To identify and cluster the groups of To identify and cluster the groups of

cells that are highly interconnectedcells that are highly interconnected ConstraintsConstraints

Maximum cluster area/weightMaximum cluster area/weight Minimum clustering ratioMinimum clustering ratio


Introduction – Why Introduction – Why clustering?clustering?

Deal with today’s increasing design Deal with today’s increasing design complexitycomplexity Algorithm scalability, e.g., FM algorithm Algorithm scalability, e.g., FM algorithm

Speed up the runtime of design processSpeed up the runtime of design process Fine Granularity Clustering, best choice, etc. Fine Granularity Clustering, best choice, etc.

Improve the solution qualityImprove the solution quality Device utilization, layout area, power Device utilization, layout area, power

consumption, etc. in FPGA designconsumption, etc. in FPGA design


OutlineOutline



Existing Clustering Existing Clustering AlgorithmsAlgorithms

Scoreless Clustering AlgorithmsScoreless Clustering Algorithms No comparison between different potential No comparison between different potential

clusters: FirstChoiceclusters: FirstChoice Fast procedure, but random resultFast procedure, but random result

Score-based Clustering AlgorithmsScore-based Clustering Algorithms Score comparison between different potential Score comparison between different potential

clusters: Best choiceclusters: Best choice Relative slower procedure, but determined and Relative slower procedure, but determined and

better resultbetter result Better choice for placementBetter choice for placement


Clustering Application in Clustering Application in PlacementPlacement

Edge clustering algorithms are the Edge clustering algorithms are the most popular techniquesmost popular techniques FirstChoice and best choiceFirstChoice and best choice

Placers using FirstChoicePlacers using FirstChoice Indirectly: Capo10, FengShui5.1Indirectly: Capo10, FengShui5.1 Directly: NTUPlace3Directly: NTUPlace3

Placers using best choicePlacers using best choice Directly: mPL6, APlace3, hATPDirectly: mPL6, APlace3, hATP


Outline



Research MotivationsResearch Motivations

Analysis of edge clustering Analysis of edge clustering algorithms: pair wise operationalgorithms: pair wise operation Pros:Pros:

Fast Fast Cons: Cons:

Local view of netlist structureLocal view of netlist structure Non-consistent with the force-directed Non-consistent with the force-directed

model model


Cons of Edge Clustering Cons of Edge Clustering AlgorithmsAlgorithms

From the view of cell connectivityFrom the view of cell connectivity Considered: connections from seed cell Considered: connections from seed cell

to neighborsto neighbors Non-considered: connections among Non-considered: connections among

neighbors neighbors

3311

22

55

44 66

77


Cons of Edge Clustering Cons of Edge Clustering AlgorithmsAlgorithms

From the view of force-directed From the view of force-directed modelmodel Forces from all nets are applied Forces from all nets are applied togethertogether Not Not in a pair wise wayin a pair wise way

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22

55

44 66

77


Proposed Research Proposed Research ObjectivesObjectives

A new clustering algorithm A new clustering algorithm Connectivity modelConnectivity model

Consider the connectivity as a whole, not Consider the connectivity as a whole, not pair wise pair wise

Be consistent with the force-directed modelBe consistent with the force-directed model Net clustering operationNet clustering operation

Make clusters based on net clustering scoreMake clusters based on net clustering score Make clusters naturally, not pair wise.Make clusters naturally, not pair wise.


Proposed Algorithm Proposed Algorithm Procedure Procedure

Input: A flat netlistInput: A flat netlistOutput: A clustered netlistOutput: A clustered netlistPhase1: Potential Cluster Identification:Phase1: Potential Cluster Identification:For each netFor each net: :

Initial Cluster FormationInitial Cluster Formation Initial Cluster RefinementInitial Cluster Refinement Cluster Score CalculationCluster Score Calculation

Phase2: Final Cluster FormationPhase2: Final Cluster Formation Net Cluster FormationNet Cluster Formation


Initial Cluster FormationInitial Cluster Formation Visit each net as a seed netVisit each net as a seed net Group cells in the seed net and Group cells in the seed net and

neighbor cellsneighbor cells Net1: cells 1, 2, 3, and 4Net1: cells 1, 2, 3, and 4

n6n6

3311 22

5544 66

77

88n1n1

n2n2

n5n5

n4n4

n3n3

n7n7

n8n8

n9n9

n11n11

n10n10

Partition: Partition: ClusterCluster Partition: Partition:

NetlistNetlist


Initial Cluster RefinementInitial Cluster Refinement

FM algorithm based cell movement, untilFM algorithm based cell movement, until All cell gains in “All cell gains in “ClusterCluster” are non-positive” are non-positive All cell gains in “All cell gains in “NetlistNetlist” are negative” are negative

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5544 66

77

88-2-2 -5-5

ClusterCluster NetlistNetlist

-2-2

11 -3-311

-2-2

-2-2

-1-1-3-3 -1-1


Cluster Score CalculationCluster Score Calculation

1.1. Calculate the Calculate the clustercluster score score

areaclusterclusterinsidecells

clusterinsidenetsclusterScore

1

#

#_

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5544 66

77

8828.0

5

1

5

7)( 1 CSc



Cluster Score CalculationCluster Score Calculation

2.2. Update the incident Update the incident netnet scores scores ClusteredClustered nets:nets: CutCut nets: nets:

71,28.028.00)( jnSn j

3311 22

5544 66

77

88n1n1

n2n2

n5n5

n4n4

n3n3

n7n7

n6n6 n8n8

n9n9

n11n11

n10n10

)()()( CiScnSnnSn jj

)()()( CiScnSnnSn jj

28.028.00)( 8 nSn



Potential Cluster Potential Cluster IdentificationIdentification

Final scores for each net after phase 1Final scores for each net after phase 1

.119,05.1)(

,01.2)(

,76,12.3)(

,32.0)(

,41,4.1)(

8

5

jnSn

nSn

jnSn

nSn

jnSn

j

j

j

3311 22

5544 66

77

88n1n1

n2n2

n5n5

n4n4

n3n3

n7n7

n6n6 n8n8

n9n9

n11n11

n10n10


Final Cluster FormationFinal Cluster Formation

1.1. Order nets based on scoresOrder nets based on scores

2.2. Cluster and merge nets with score Cluster and merge nets with score > 0> 0

3311 22

5544 66

77

88n1n1

n2n2

n5n5

n4n4

n3n3

n7n7

n6n6 n8n8

n9n9

n11n11

n10n10

1,2,31,2,3 6,7,86,7,84,54,5


Analogy to Force-directed Analogy to Force-directed ModelModel

Initial Cluster FormationInitial Cluster Formation Equivalent: Equivalent: manuallymanually allocate cells in an allocate cells in an

initial clusterinitial cluster Initial Cluster RefinementInitial Cluster Refinement

Equivalent: Equivalent: naturallynaturally allocate cells based allocate cells based on overall forceson overall forces

Cluster Score CalculationCluster Score Calculation Equivalent: Equivalent: globallyglobally evaluate the net evaluate the net

quality quality


Algorithm SummaryAlgorithm SummaryCharacteristics:Characteristics: New connectivity computation New connectivity computation

Identify the natural clusters in a circuit, Identify the natural clusters in a circuit, despite the number of cells in clustersdespite the number of cells in clusters

Consistent with the force-directed modelConsistent with the force-directed model

Net score computation Net score computation Remove cluster overlapping Remove cluster overlapping Choose globally the best nets for clusteringChoose globally the best nets for clustering


Outline

IntroductionIntroduction Previous WorkPrevious Work Proposed Clustering AlgorithmProposed Clustering Algorithm Numerical ResultsNumerical Results Conclusions and future worksConclusions and future works


Numerical ResultsNumerical Results

Clustering Statistics ExperimentsClustering Statistics Experiments

Placement ExperimentsPlacement Experiments


Clustering Statistics Clustering Statistics ExperimentsExperiments

SetupSetup Predefined Predefined cell cell clustering ratio (clustering ratio (CCRCCR)) Compare Compare netnet clustering ratios ( clustering ratios (NCRNCR))

Why net clustering ratio comparison?Why net clustering ratio comparison? Kind of measurement of interconnect Kind of measurement of interconnect

complexity for placement and routingcomplexity for placement and routing Comparison algorithmsComparison algorithms

FirstChoice, best choice FirstChoice, best choice Benchmark circuitsBenchmark circuits

ICCAD04 Mixed-sizeICCAD04 Mixed-size


Out of 18 benchmark circuits, Ours Out of 18 benchmark circuits, Ours achievedachieved

17 smallest net clustering ratios17 smallest net clustering ratiosCCRCCR NCRNCR

OursOurs Best Best choicechoice

FirstChoicFirstChoicee

AverageAverage 0.6210.621 0.6950.695 0.7280.728 0.7480.748

Average Clustering Ratio Average Clustering Ratio Comparison on ICCAD04 Comparison on ICCAD04

CircuitsCircuits


Placement ExperimentsPlacement Experiments

Setup Setup Cluster a netlist using the proposed algorithmCluster a netlist using the proposed algorithm Run other placers on the clustered netlistRun other placers on the clustered netlist Map the placement result and Run Capo10.1 to Map the placement result and Run Capo10.1 to

legalize and refine the resultlegalize and refine the result Comparison placersComparison placers

mPL6, NTUPlace3-LE, Capo10.1, and FengShui5.1mPL6, NTUPlace3-LE, Capo10.1, and FengShui5.1 Benchmark circuitsBenchmark circuits

ICCAD04 Mixed-size, and ISPD05 Placement ICCAD04 Mixed-size, and ISPD05 Placement ContestContest


Placement Results on ICCAD04 Placement Results on ICCAD04 Benchmarks Benchmarks

Capo10.1: Capo10.1: 1515 out of 18 improved HPWL out of 18 improved HPWL FengShui5.1: FengShui5.1: 1414 out of 18 improved HPWL out of 18 improved HPWL mPL6: mPL6: 1515 out of 18 improved HPWL out of 18 improved HPWL NTUPlace3-LE: NTUPlace3-LE: 1818 out of 18 improved HPWL out of 18 improved HPWL

PlacerPlacer HPWL (10^6)HPWL (10^6) Runtime (in Runtime (in seconds)seconds)

OriginalOriginal ClustereClusteredd


Capo10.1Capo10.1 1.0001.000 0.9720.972 1.0001.000 0.8740.874

FengShui5.1FengShui5.1 1.0001.000 0.9810.981 1.0001.000 1.0121.012

mPL6mPL6 1.0001.000 0.9780.978 1.0001.000 1.0051.005

NTUPlace3-NTUPlace3-LELE

1.0001.000 0.9490.949 1.0001.000 0.9200.920


Placement Results on ISPD05 Placement Results on ISPD05 Benchmarks Benchmarks

Capo10.1: Capo10.1: 00 out of 8 improved HPWL out of 8 improved HPWL mPL6: mPL6: 55 out of 8 improved HPWL out of 8 improved HPWL NTUPlace3-LE: NTUPlace3-LE: 77 out of 8 improved HPWL out of 8 improved HPWL

PlacerPlacer HPWL (10^6)HPWL (10^6) Runtime (in Runtime (in seconds)seconds)



Capo10.1Capo10.1 1.0001.000 1.0271.027 1.0001.000 0.8600.860

mPL6mPL6 1.0001.000 0.9960.996 1.0001.000 1.1741.174

NTUPlace3-NTUPlace3-LELE

1.0001.000 0.9850.985 1.0001.000 1.1011.101


Experimental SummaryExperimental Summary

Effective for ICCAD04 benchmark Effective for ICCAD04 benchmark circuitscircuits

Less effective for ISPD05 benchmark Less effective for ISPD05 benchmark circuitscircuits


Conclusions and Future Conclusions and Future WorksWorks

ConclusionsConclusions A new clustering algorithm for placement A new clustering algorithm for placement

A new connectivity model A new connectivity model Promising experimental results Promising experimental results

Future Work:Future Work: Improve the algorithm efficiencyImprove the algorithm efficiency

Runtime Runtime Improve the algorithm scalabilityImprove the algorithm scalability

ISPD05 benchmark circuits ISPD05 benchmark circuits Integrate into placersIntegrate into placers


Thank you!Thank you!


AppendixAppendix


Why not just group the Why not just group the clusters?clusters?

Directly cluster nets Directly cluster nets directly directly optimize the placement objectiveoptimize the placement objective

To deal with the cluster cell To deal with the cluster cell overlapping problemoverlapping problem

Net is a “finer” unit for clusteringNet is a “finer” unit for clustering


Runtime comparisonRuntime comparison

Generally our clustering algorithm is Generally our clustering algorithm is slower than both FirstChoice and slower than both FirstChoice and best choice, by 3 to 8 timesbest choice, by 3 to 8 times


Results on ISPD05Results on ISPD05

Probably due to the difference of the Probably due to the difference of the circuitcircuit

structure structure ICCAD04, short nets majorityICCAD04, short nets majority

Max net degree: from 17(ibm05) to Max net degree: from 17(ibm05) to 134(ibm02)134(ibm02)

ISPD05, large number of long netsISPD05, large number of long nets Max net degree: 1935(adaptec2) to Max net degree: 1935(adaptec2) to

11869(bigblue2)11869(bigblue2)


NTUPlace3-LENTUPlace3-LE Based on the Lp-norm wire modelBased on the Lp-norm wire model

NTUPlace3NTUPlace3

NTUplace3 is based on the log-sum-exp NTUplace3 is based on the log-sum-exp wire modelwire model

State-of-the-art: better performance State-of-the-art: better performance than NTUPlace3-LEthan NTUPlace3-LE

NTUPlace3-LE and NTUPlace3-LE and NTUPlace3NTUPlace3

March 20, 2007 ISPD 2007 1 An Effective Clustering Algorithm for Mixed-size Placement Jianhua Li,...

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