Presentation is loading. Please wait.

Presentation is loading. Please wait.

"Fast estimation of the partitioning Rent characteristic" Fast estimation of the partitioning Rent characteristic using a recursive partitioning model.

Published byMadlyn Shelton Modified over 8 years ago

Similar presentations

Presentation on theme: ""Fast estimation of the partitioning Rent characteristic" Fast estimation of the partitioning Rent characteristic using a recursive partitioning model."— Presentation transcript:

1 "Fast estimation of the partitioning Rent characteristic" Fast estimation of the partitioning Rent characteristic using a recursive partitioning model J. Dambre, D. Stroobandt and J. Van Campenhout SLIP’03 - April 5-6, 2003

2 "Fast estimation of the partitioning Rent characteristic" Presentation outline Rent’s rule vs. the Rent characteristicRent’s rule vs. the Rent characteristic Recursive (bi-)partitioning equationsRecursive (bi-)partitioning equations Cut probability modelsCut probability models Validation and application for fast estimation of the Rent characteristicValidation and application for fast estimation of the Rent characteristic Conclusions & future workConclusions & future work

3 "Fast estimation of the partitioning Rent characteristic" N c connections between gates (internal nets)N c connections between gates (internal nets) T ext Connections to circuit’s exterior (external nets or pins)T ext Connections to circuit’s exterior (external nets or pins) The circuit graph Circuit netlist, consists of: G c gatesG c gates Only two-terminal connections considered !

4 "Fast estimation of the partitioning Rent characteristic" Donath-based prediction of placement wire lengths circuitarchitecture Perform recursive partitioning of circuit and architecture

5 "Fast estimation of the partitioning Rent characteristic" Donath-based prediction of placement wire lengths circuit At each level: calculate number of cut nets...

6 "Fast estimation of the partitioning Rent characteristic" Donath-based prediction of placement wire lengths architecture... and their length distribution from the architecture site functions

7 "Fast estimation of the partitioning Rent characteristic" Recursive circuit partitioning... modeled by Rent’s rule?? For a particular circuit netlist: p: Rent exponent t: Rent coefficient Region III Region II Region I Perform complete recursive circuit partitioningPerform complete recursive circuit partitioning Find average data points for T vs. G (=Rent characteristic)Find average data points for T vs. G (=Rent characteristic) Fit power law to region I:Fit power law to region I:

8 "Fast estimation of the partitioning Rent characteristic" Recursive circuit partitioning... modeled by Rent’s rule?? T = 51.58 G 0.45 ? T = 7.45 G 0.78 ? Which Rent parameters to use ??

9 "Fast estimation of the partitioning Rent characteristic" Rent’s rule vs. the Rent characteristic Rent’s rule is not a very accurate model, so....... use the Rent characteristic instead of Rent’s rule!

10 "Fast estimation of the partitioning Rent characteristic" Last year’s results... Prediction of average wire lengths, based on Donath’s technique, but... using the Rent characteristic instead of Rent’s rule Overestimation, but very good correlation !

11 "Fast estimation of the partitioning Rent characteristic"... becomes very inaccurate if too few levels... doesn’t help much if many levels 5 levels of partitioning Rent’s rule vs. the Rent characteristic Problem: full recursive partitioning takes a lot of time Solution I*: perform only limited number of partitioning levels and interpolate... * suggested in, e.g. Hagen et al., “On the intrinsic Rent parameter and spectra-based partitioning methodologies”, 1994

12 "Fast estimation of the partitioning Rent characteristic" Rent’s rule vs. the Rent characteristic Problem: recursive partitioning takes a lot of time Solution II: find a better model than Rent’s rule ??

13 "Fast estimation of the partitioning Rent characteristic" Presentation outline Rent’s rule vs. the Rent characteristicRent’s rule vs. the Rent characteristic Recursive (bi-)partitioning equationsRecursive (bi-)partitioning equations Cut probability modelsCut probability models Validation and application for fast estimation of the Rent characteristicValidation and application for fast estimation of the Rent characteristic Conclusions & future workConclusions & future work

14 "Fast estimation of the partitioning Rent characteristic" Verplaetse’s recursive (bi-)partitioning equations Level k-1 G k-1 = 16 T k-1 = 6 N k-1 = 30 Hierarchy levels k = 0...H, with: level 0 = entire circuit, level H = single gate

15 "Fast estimation of the partitioning Rent characteristic" Verplaetse’s recursive (bi-)partitioning equations Level k Partition in two equal parts (balanced)

16 "Fast estimation of the partitioning Rent characteristic" Define:  k-1 : fraction of N k-1 that is cut (=cut probability) Verplaetse’s recursive bipartitioning model Level k Recursive partitioning equations:

17 "Fast estimation of the partitioning Rent characteristic" Verplaetse’s recursive bipartitioning model Level k New problem: find expression for  k-1 instead of expression for T k-1 ?? Define:  k-1 : fraction of N k-1 that is cut (=cut probability)

18 "Fast estimation of the partitioning Rent characteristic" Presentation outline Rent’s rule vs. the Rent characteristicRent’s rule vs. the Rent characteristic Recursive (bi-)partitioning equationsRecursive (bi-)partitioning equations Cut probability modelsCut probability models Validation and application for fast estimation of the Rent characteristicValidation and application for fast estimation of the Rent characteristic Conclusions & future workConclusions & future work

19 "Fast estimation of the partitioning Rent characteristic" module 1 module 2 Cut probabilities for random partitioning Random bipartitioning of a two- terminal net = randomly assigning both connected gates to two modules P cut = (1/2) G k /(G k -1) =  k, rand 4 possible assignments, net is cut for two of them:

20 "Fast estimation of the partitioning Rent characteristic" Cut probabilities for random partitioning 0.5  k, rand = (1/2) G k /(G k -1)

21 "Fast estimation of the partitioning Rent characteristic" Cut probabilities for optimal circuit partitioning Measured values of  k ?? Must perform some manipulations on Rent characteristic because: circuit size not equal to 2 Hcircuit size not equal to 2 H partitionings not perfectly balancedpartitionings not perfectly balanced

22 "Fast estimation of the partitioning Rent characteristic" Cut probabilities for optimal circuit partitioning random ibm17 Always = 1 (boundary condition) Always = 1 (boundary condition)

23 "Fast estimation of the partitioning Rent characteristic" Cut probabilities for optimal circuit partitioning Verplaetse’s model for  k : With  and  parameters to be fitted

24 "Fast estimation of the partitioning Rent characteristic" Cut probabilities for optimal circuit partitioning random ibm17 Verplaetse

25 "Fast estimation of the partitioning Rent characteristic" Cut probabilities for optimal circuit partitioning New model for  k : based on observed relationship between  k and  k,rand +

26 "Fast estimation of the partitioning Rent characteristic" Cut probabilities for optimal circuit partitioning random ibm17 Verplaetse New model

27 "Fast estimation of the partitioning Rent characteristic" Cut probabilities for optimal circuit partitioning 1 10 100 1000 10000 1101001000100001000001E+06 Module size G k Module terminals  k ibm17 Verplaetse New model

28 "Fast estimation of the partitioning Rent characteristic" Presentation outline Rent’s rule vs. the Rent characteristicRent’s rule vs. the Rent characteristic Recursive (bi-)partitioning equationsRecursive (bi-)partitioning equations Cut probability modelsCut probability models Validation and application for fast estimation of the Rent characteristicValidation and application for fast estimation of the Rent characteristic Conclusions & future workConclusions & future work

29 "Fast estimation of the partitioning Rent characteristic" Cut probabilities for optimal circuit partitioning Both models have comparable fitting quality New model only has a single fitting parameter

30 "Fast estimation of the partitioning Rent characteristic" Correlation coefficients: Verplaetse vs. Rc: 0.988Verplaetse vs. Rc: 0.988 New model vs. Rc: 0.995New model vs. Rc: 0.995 Update of last year’s results... Prediction of average wire lengths, based on Donath’s technique, but... using the new partitioning model instead of the Rent characteristic (Rc)

31 "Fast estimation of the partitioning Rent characteristic" Can models for  k be applied to obtain accurate estimations of the entire Rent characteristic based on a few partitioning levels only?? Fast estimation of the Rent characteristic

32 "Fast estimation of the partitioning Rent characteristic" Fast estimation of the Rent characteristic all levels New model converges faster: for most benchmarks, two levels is enough use 3 or 4 levels to be sure

33 "Fast estimation of the partitioning Rent characteristic" Update of last year’s results... Prediction of average wire lengths, based on Donath’s technique, but... using the new partitioning model, fit for 3 levels of partitioning Correlation coefficients: Verplaetse vs. Rc: 0.902Verplaetse vs. Rc: 0.902 New model vs. Rc: 0.824New model vs. Rc: 0.824

34 "Fast estimation of the partitioning Rent characteristic" Presentation outline Rent’s rule vs. the Rent characteristicRent’s rule vs. the Rent characteristic Recursive (bi-)partitioning equationsRecursive (bi-)partitioning equations Cut probability modelsCut probability models Validation and application for fast estimation of the Rent characteristicValidation and application for fast estimation of the Rent characteristic Conclusions & future workConclusions & future work

35 "Fast estimation of the partitioning Rent characteristic" Conclusions Adaptation of Verplaetse’s recursive partitioning equations and cut probability modelAdaptation of Verplaetse’s recursive partitioning equations and cut probability model Application of this model for fast estimation of entire partitioning Rent characteristicApplication of this model for fast estimation of entire partitioning Rent characteristic

36 "Fast estimation of the partitioning Rent characteristic" Future work Extension to multi-terminal netsExtension to multi-terminal nets Try to find theoretical foundations for cut probability modelTry to find theoretical foundations for cut probability model Is it possible to estimate cut probabilities from circuit graph without performing partitioning??Is it possible to estimate cut probabilities from circuit graph without performing partitioning??

Download ppt ""Fast estimation of the partitioning Rent characteristic" Fast estimation of the partitioning Rent characteristic using a recursive partitioning model."

Similar presentations

Chapter 16 Inferential Statistics

Chapter 16 Inferential Statistics
Cadence Design Systems, Inc. Why Interconnect Prediction Doesn’t Work.

Cadence Design Systems, Inc. Why Interconnect Prediction Doesn’t Work.
Correlation and regression

Correlation and regression
4/22/2015 1 Clock Network Synthesis Prof. Shiyan Hu Office: EREC 731.

4/22/ Clock Network Synthesis Prof. Shiyan Hu Office: EREC 731.
Hoofdstuk 6 Het voorspellen van prestaties Prof. dr. ir. Dirk Stroobandt Academiejaar 2004-2005.

Hoofdstuk 6 Het voorspellen van prestaties Prof. dr. ir. Dirk Stroobandt Academiejaar
Interconnect Complexity-Aware FPGA Placement Using Rent’s Rule G. Parthasarathy Malgorzata Marek-Sadowska Arindam Mukherjee Amit Singh University of California,

Interconnect Complexity-Aware FPGA Placement Using Rent’s Rule G. Parthasarathy Malgorzata Marek-Sadowska Arindam Mukherjee Amit Singh University of California,
BSPlace: A BLE Swapping technique for placement 04.09.2014 Minsik Hong George Hwang Hemayamini Kurra Minjun Seo 1.

BSPlace: A BLE Swapping technique for placement Minsik Hong George Hwang Hemayamini Kurra Minjun Seo 1.
Tanuj Jindal ∗, Charles J. Alpert‡, Jiang Hu ∗, Zhuo Li‡, Gi-Joon Nam‡, Charles B. Winn‡‡ ∗ Department of ECE, Texas A&M University, College Station, Texas.

Tanuj Jindal ∗, Charles J. Alpert‡, Jiang Hu ∗, Zhuo Li‡, Gi-Joon Nam‡, Charles B. Winn‡‡ ∗ Department of ECE, Texas A&M University, College Station, Texas.
Early Days of Circuit Placement Martin D. F. Wong Department of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

Early Days of Circuit Placement Martin D. F. Wong Department of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.
Farnoush Banaei-Kashani and Cyrus Shahabi Criticality-based Analysis and Design of Unstructured P2P Networks as “ Complex Systems ” Mohammad Al-Rifai.

Farnoush Banaei-Kashani and Cyrus Shahabi Criticality-based Analysis and Design of Unstructured P2P Networks as “ Complex Systems ” Mohammad Al-Rifai.
Iowa State University Department of Computer Science Artificial Intelligence Research Laboratory Research supported in part by grants from the National.

Iowa State University Department of Computer Science Artificial Intelligence Research Laboratory Research supported in part by grants from the National.
Balancing Interconnect and Computation in a Reconfigurable Array Dr. André DeHon BRASS Project University of California at Berkeley Why you don’t really.

Balancing Interconnect and Computation in a Reconfigurable Array Dr. André DeHon BRASS Project University of California at Berkeley Why you don’t really.
Toward Better Wireload Models in the Presence of Obstacles* Chung-Kuan Cheng, Andrew B. Kahng, Bao Liu and Dirk Stroobandt† UC San Diego CSE Dept. †Ghent.

Toward Better Wireload Models in the Presence of Obstacles* Chung-Kuan Cheng, Andrew B. Kahng, Bao Liu and Dirk Stroobandt† UC San Diego CSE Dept. †Ghent.
Intrinsic Shortest Path Length: A New, Accurate A Priori Wirelength Estimator Andrew B. KahngSherief Reda VLSI CAD Laboratory.

Intrinsic Shortest Path Length: A New, Accurate A Priori Wirelength Estimator Andrew B. KahngSherief Reda VLSI CAD Laboratory.
Problem 1 Defining Netlist Snarl Factor. Some Background A B C D F G EH A B C D F G EH Congested area PlacementRouting A B C D F G E H Netlist == Graph.

Problem 1 Defining Netlist Snarl Factor. Some Background A B C D F G EH A B C D F G EH Congested area PlacementRouting A B C D F G E H Netlist == Graph.
Penn ESE680-002 Spring2007 -- DeHon 1 ESE680-002 (ESE534): Computer Organization Day 15: March 12, 2007 Interconnect 3: Richness.

Penn ESE Spring DeHon 1 ESE (ESE534): Computer Organization Day 15: March 12, 2007 Interconnect 3: Richness.
Predictive Automatic Relevance Determination by Expectation Propagation Yuan (Alan) Qi Thomas P. Minka Rosalind W. Picard Zoubin Ghahramani.

Predictive Automatic Relevance Determination by Expectation Propagation Yuan (Alan) Qi Thomas P. Minka Rosalind W. Picard Zoubin Ghahramani.
International Symposium of Physical Design Sonoma County, CA April 2001ER UCLA UCLA 1 Congestion Estimation During Top-Down Placement Xiaojian Yang Ryan.

International Symposium of Physical Design Sonoma County, CA April 2001ER UCLA UCLA 1 Congestion Estimation During Top-Down Placement Xiaojian Yang Ryan.
On Modeling and Sensitivity of Via Count in SOC Physical Implementation Kwangok Jeong Andrew B. Kahng.

On Modeling and Sensitivity of Via Count in SOC Physical Implementation Kwangok Jeong Andrew B. Kahng.
Petter Mostad mostad@chalmers.se Linear regression Petter Mostad mostad@chalmers.se.

Petter Mostad Linear regression Petter Mostad

Similar presentations

Ads by Google