international workshop on system-level interconnection prediction, sonoma county, ca march 2001er...
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International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001
ERER UCLAUCLA
Wirelength Estimation based on Rent Wirelength Estimation based on Rent Exponents of Partitioning and PlacementExponents of Partitioning and Placement
Xiaojian Yang
Elaheh Bozorgzadeh
Majid Sarrafzadeh
Embedded and Reconfigurable System Lab
Computer Science Department, UCLA
Xiaojian Yang
Elaheh Bozorgzadeh
Majid Sarrafzadeh
Embedded and Reconfigurable System Lab
Computer Science Department, UCLA
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International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001
ERER UCLAUCLA
OutlineOutlineOutlineOutline
Introduction Motivation Rent Exponents of Partitioning and Placement Wirelength Estimation based on Rent’s rule Rent Exponent and Placement Quality Conclusion
Introduction Motivation Rent Exponents of Partitioning and Placement Wirelength Estimation based on Rent’s rule Rent Exponent and Placement Quality Conclusion
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International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001
ERER UCLAUCLA
IntroductionIntroductionIntroductionIntroduction
Rent’s rule and its application P = TB r
Introduced by Landman and Russo, 1971 Used for Wirelength estimation
Rent Exponent Key role in Rent’s rule applications Extracted from partitioning-based method “Intrinsic Rent exponent”, Hagen, et.al 1994
Rent’s rule and its application P = TB r
Introduced by Landman and Russo, 1971 Used for Wirelength estimation
Rent Exponent Key role in Rent’s rule applications Extracted from partitioning-based method “Intrinsic Rent exponent”, Hagen, et.al 1994
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International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001
ERER UCLAUCLA
Introduction (cont’d)Introduction (cont’d)Introduction (cont’d)Introduction (cont’d)
Two Rent Exponents Topological and Geometrical (Christie, SLIP2000) Partitioning and Placement
Questions: Same or different? Which one is appropriate for Rent’s rule applications? Relationship?
Two Rent Exponents Topological and Geometrical (Christie, SLIP2000) Partitioning and Placement
Questions: Same or different? Which one is appropriate for Rent’s rule applications? Relationship?
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International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001
ERER UCLAUCLA
Partitioning Rent ExponentPartitioning Rent ExponentPartitioning Rent ExponentPartitioning Rent Exponent
log P
log B B – Number of cells
P – Number of external nets
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International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001
ERER UCLAUCLA
Partitioning Rent ExponentPartitioning Rent ExponentPartitioning Rent ExponentPartitioning Rent Exponent
slope = r
log P
log B B – Number of cells
P – Number of external nets
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International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001
ERER UCLAUCLA
Placement Rent exponentPlacement Rent exponentPlacement Rent exponentPlacement Rent exponent
log P
log B
slope = r’
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International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001
ERER UCLAUCLA
Difference between two exponentsDifference between two exponentsDifference between two exponentsDifference between two exponents
Partitioning objective: Minimizing cut-size Embed partitions into two-dimensional plane Cut-size increases in placement compared to
partitioning
Partitioning objective: Minimizing cut-size Embed partitions into two-dimensional plane Cut-size increases in placement compared to
partitioning log P
log B
Placement
Partitioning
Placement r’ > Partitioning rPlacement r’ > Partitioning r
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International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001
ERER UCLAUCLA
Relation between two Rent exponentsRelation between two Rent exponentsRelation between two Rent exponentsRelation between two Rent exponents
Based on min-cut placement approaches (recursively bipartitioning)
Different partitioning instances Partitioning tree approach: Pure Partitioning Partitioning in Placement: terminal propagation
Based on min-cut placement approaches (recursively bipartitioning)
Different partitioning instances Partitioning tree approach: Pure Partitioning Partitioning in Placement: terminal propagation
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International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001
ERER UCLAUCLA
Pure PartitioningPure PartitioningPure PartitioningPure Partitioning
Cut-size = CCut-size = C Cut-size = CCut-size = C
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International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001
ERER UCLAUCLA
Terminal PropagationTerminal PropagationTerminal PropagationTerminal Propagation
Cut-size = C’ > CCut-size = C’ > C Cut-size = C’ > CCut-size = C’ > C
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International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001
ERER UCLAUCLA
Cut size increasesCut size increasesCut size increasesCut size increases
cut-size : C cut-size : C C’ C’ cut-size : C cut-size : C C’ C’
PP PP
PP11 PP11 PP22 PP22
CCCC BB22 BB22
BB11 BB11
uu uu
PP11+C = TB+C = TB11r r = P= P PP11+C = TB+C = TB11r r = P= P
PP11+P+P22 = T(B = T(B11+B+B22))rr PP11+P+P22 = T(B = T(B11+B+B22))rr PP11= 2= 2r-1 r-1 PP PP11= 2= 2r-1 r-1 PP
--- effect of external net--- effect of external net --- effect of external net--- effect of external net
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International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001
ERER UCLAUCLA
RelationshipRelationshipRelationshipRelationship
Brr
r
log
)21log( 1
r --- Partitioning Rent exponentr --- Partitioning Rent exponentr’ --- Placement Rent exponentr’ --- Placement Rent exponentB --- number of cellsB --- number of cells --- 0 --- 0 1, effect of external 1, effect of external netnet
r --- Partitioning Rent exponentr --- Partitioning Rent exponentr’ --- Placement Rent exponentr’ --- Placement Rent exponentB --- number of cellsB --- number of cells --- 0 --- 0 1, effect of external 1, effect of external netnet
• Limited RangeLimited Range• Rough Estimation from r to r’Rough Estimation from r to r’• Limited RangeLimited Range• Rough Estimation from r to r’Rough Estimation from r to r’
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International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001
ERER UCLAUCLA
Experiment BackgroundExperiment BackgroundExperiment BackgroundExperiment Background
Benchmark: MCNC+IBM IBM: Derived from ISPD98 partitioning benchmark Size from 20k cells --- 220k cells
Partitioning: hMetis Placement: wirelength-driven
Capo, Feng Shui, Dragon Rent exponent extraction
Linear regression Each point corresponds to one level in partitioning or
placement
Benchmark: MCNC+IBM IBM: Derived from ISPD98 partitioning benchmark Size from 20k cells --- 220k cells
Partitioning: hMetis Placement: wirelength-driven
Capo, Feng Shui, Dragon Rent exponent extraction
Linear regression Each point corresponds to one level in partitioning or
placement
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International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001
ERER UCLAUCLA
Experimental Observation (1)Experimental Observation (1)Experimental Observation (1)Experimental Observation (1)
Example: ibm11, 68k cells Example: ibm11, 68k cells
0.608
0.6930.682
0.6670.680
0.56
0.58
0.6
0.62
0.64
0.66
0.68
0.7
Partitioning rPartitioning rPartitioning rPartitioning r Placement r’Placement r’Placement r’Placement r’ Estimated Placement r’Estimated Placement r’Estimated Placement r’Estimated Placement r’
CapoCapoCapoCapo Feng ShuiFeng ShuiFeng ShuiFeng Shui DragonDragonDragonDragon
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International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001
ERER UCLAUCLA
Wirelength Estimation based on Wirelength Estimation based on Rent’s ruleRent’s ruleWirelength Estimation based on Wirelength Estimation based on Rent’s ruleRent’s rule Classical problem
Donath 1979 Stroobandt et.al 1994 Davis et.al 1998
Needs geometrical (placement) Rent exponent Comparison
Estimated WL using Partitioning Rent exponent Estimated WL using Placement Rent exponent Total Wirelength after global routing (maze-based)
Classical problem Donath 1979 Stroobandt et.al 1994 Davis et.al 1998
Needs geometrical (placement) Rent exponent Comparison
Estimated WL using Partitioning Rent exponent Estimated WL using Placement Rent exponent Total Wirelength after global routing (maze-based)
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International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001
ERER UCLAUCLA
Experimental Observation (2)Experimental Observation (2)Experimental Observation (2)Experimental Observation (2)
Example: ibm13, 81k cells
Overall: Estimation based on Partitioning Rent exponent under-estimate total wirelength 19% --- 32%
Example: ibm13, 81k cells
Overall: Estimation based on Partitioning Rent exponent under-estimate total wirelength 19% --- 32%
PartitioningPartitioningr = 0.600r = 0.600PartitioningPartitioningr = 0.600r = 0.600
Actual WLActual WLCapo FS DragonCapo FS Dragon
Actual WLActual WLCapo FS DragonCapo FS Dragon
Placement Rent r’Placement Rent r’Capo FS DragonCapo FS DragonPlacement Rent r’Placement Rent r’Capo FS DragonCapo FS Dragon
500
0
676716
605
0
675
627586
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International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001
ERER UCLAUCLA
Estimation based on r’Estimation based on r’Estimation based on r’Estimation based on r’
Recursively bipartitioning
Derivation of Placement Rent exponentcircuitcircuitcircuitcircuit
Wirelength Estimation
Estimated Estimated total wirelengthtotal wirelength
Estimated Estimated total wirelengthtotal wirelength
r r (partition r)
r r (partition r)
r’ r’ (place r)r’ r’ (place r)
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International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001
ERER UCLAUCLA
Estimation based on r’Estimation based on r’Estimation based on r’Estimation based on r’
Estimation results: -12% --- +14%
Total wirelength estimation is hard Rent exponent Placement approach Routing approach Congestion --- unevenly distributed wires
Estimation results: -12% --- +14%
Total wirelength estimation is hard Rent exponent Placement approach Routing approach Congestion --- unevenly distributed wires
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International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001
ERER UCLAUCLA
Rent exponent, a placement metric?Rent exponent, a placement metric?Rent exponent, a placement metric?Rent exponent, a placement metric?
Hagen et.al Rent exponent is a measurement of partitioning
approach Ratio-cut gives the smallest Rent exponent
Similar case in Placement? Ordinary placement measurement
Total bounding box wirelength or routed wirelength Correlation between wirelength and Rent exponent?
Hagen et.al Rent exponent is a measurement of partitioning
approach Ratio-cut gives the smallest Rent exponent
Similar case in Placement? Ordinary placement measurement
Total bounding box wirelength or routed wirelength Correlation between wirelength and Rent exponent?
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International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001
ERER UCLAUCLA
Experimental ObservationExperimental ObservationExperimental ObservationExperimental Observation
Rent exponentRent exponentRent exponentRent exponent Bounding box Bounding box wirelengthwirelength
Bounding box Bounding box wirelengthwirelength
Routed Routed wirelengthwirelengthRouted Routed
wirelengthwirelength
• Weak correlation: most shorter wirelengths Weak correlation: most shorter wirelengths correspond to lower Rent exponents correspond to lower Rent exponents • Open questionOpen question
• Weak correlation: most shorter wirelengths Weak correlation: most shorter wirelengths correspond to lower Rent exponents correspond to lower Rent exponents • Open questionOpen question
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International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001
ERER UCLAUCLA
ConclusionConclusionConclusionConclusion
Topological (partitioning) Rent exponent and Geometrical (placement) Rent exponent are different.
Relationship between two Rent exponents. Wirelength Estimation should use Geometrical
Rent exponent. Open question: Is Rent exponent a metric of
placement quality?
Topological (partitioning) Rent exponent and Geometrical (placement) Rent exponent are different.
Relationship between two Rent exponents. Wirelength Estimation should use Geometrical
Rent exponent. Open question: Is Rent exponent a metric of
placement quality?