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International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001ER UCLA UCLA 1 Wirelength Estimation based on Rent Exponents.

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Presentation on theme: "International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001ER UCLA UCLA 1 Wirelength Estimation based on Rent Exponents."— Presentation transcript:

1 International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001ER UCLA UCLA 1 Wirelength Estimation based on Rent Exponents 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

2 International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001ER UCLA UCLA 2OutlineOutline 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

3 International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001ER UCLA UCLA 3IntroductionIntroduction 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

4 International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001ER UCLA UCLA 4 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?

5 International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001ER UCLA UCLA 5 Partitioning Rent Exponent log P log B B – Number of cells P – Number of external nets

6 International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001ER UCLA UCLA 6 Partitioning Rent Exponent slope = r log P log B B – Number of cells P – Number of external nets

7 International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001ER UCLA UCLA 7 Placement Rent exponent log P log B slope = r’

8 International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001ER UCLA UCLA 8 Difference 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 r

9 International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001ER UCLA UCLA 9 Relation 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

10 International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001ER UCLA UCLA 10 Pure Partitioning Cut-size = C Cut-size = C

11 International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001ER UCLA UCLA 11 Terminal Propagation Cut-size = C’ > C Cut-size = C’ > C

12 International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001ER UCLA UCLA 12 Cut size increases cut-size : C  C’ cut-size : C  C’ P P P1 P1 P1 P1 P1 P1 P1 P1 P2 P2 P2 P2 P2 P2 P2 P2 CC B2 B2 B2 B2 B2 B2 B2 B2 B1 B1 B1 B1 B1 B1 B1 B1 u u P 1 +C = TB 1 r = P P 1 +C = TB 1 r = P P 1 +P 2 = T(B 1 +B 2 ) r P 1 +P 2 = T(B 1 +B 2 ) r P 1 = 2 r-1 P P 1 = 2 r-1 P  --- effect of external net

13 International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001ER UCLA UCLA 13RelationshipRelationship r --- Partitioning Rent exponent r’ --- Placement Rent exponent B --- number of cells  --- 0    1, effect of external net r --- Partitioning Rent exponent r’ --- Placement Rent exponent B --- number of cells  --- 0    1, effect of external net Limited Range Limited Range Rough Estimation from r to r’ Rough Estimation from r to r’ Limited Range Limited Range Rough Estimation from r to r’ Rough Estimation from r to r’

14 International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001ER UCLA UCLA 14 Experiment 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

15 International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001ER UCLA UCLA 15 Experimental Observation (1) Example: ibm11, 68k cells Partitioning r Placement r’ Estimated Placement r’ CapoCapo Feng Shui DragonDragon

16 International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001ER UCLA UCLA 16 Wirelength Estimation based on Rent’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)

17 International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001ER UCLA UCLA 17 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% Partitioning r = 0.600 Partitioning Actual WL Capo FS Dragon Actual WL Capo FS Dragon Placement Rent r’ Capo FS Dragon Placement Rent r’ Capo FS Dragon

18 International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001ER UCLA UCLA 18 Estimation based on r’ Recursively bipartitioning Derivation of Placement Rent exponent circuitcircuit Wirelength Estimation Estimated total wirelength Estimated r (partition r)r r’ r’ (place r)

19 International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001ER UCLA UCLA 19 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

20 International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001ER UCLA UCLA 20 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?

21 International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001ER UCLA UCLA 21 Experimental Observation Rent exponent Bounding box wirelength wirelength RoutedwirelengthRoutedwirelength Weak correlation: most shorter wirelengths Weak correlation: most shorter wirelengths correspond to lower Rent exponents correspond to lower Rent exponents Open question Open question Weak correlation: most shorter wirelengths Weak correlation: most shorter wirelengths correspond to lower Rent exponents correspond to lower Rent exponents Open question Open question

22 International Workshop on System-Level Interconnection Prediction, Sonoma County, CA March 2001ER UCLA UCLA 22ConclusionConclusion 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?

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