A Net-Reduction based Clustering Preprocessing Algorithm Jianhua Li, - - PowerPoint PPT Presentation

▶
a net reduction based clustering preprocessing algorithm
SMART_READER_LITE
LIVE PREVIEW

A Net-Reduction based Clustering Preprocessing Algorithm Jianhua Li, - - PowerPoint PPT Presentation

Oct 11, 2023 405 likes •777 views

A Net-Reduction based Clustering Preprocessing Algorithm Jianhua Li, Laleh Behjat University of Calgary, Calgary, Canada ISPD April 12, 2006 A net reduction-based clustering preprocessing algorithm - ISPD 2006 Outline Introduction

slide-1
SLIDE 1

A net reduction-based clustering preprocessing algorithm - ISPD 2006

A Net-Reduction based Clustering Preprocessing Algorithm

Jianhua Li, Laleh Behjat University of Calgary, Calgary, Canada ISPD April 12, 2006

slide-2
SLIDE 2

A net reduction-based clustering preprocessing algorithm - ISPD 2006

Outline

  • Introduction
  • Background and Motivation
  • Net Cluster Algorithm
  • Numerical Results
  • Conclusions and Future Work
slide-3
SLIDE 3

A net reduction-based clustering preprocessing algorithm - ISPD 2006

Introduction

Exponential growth in circuit sizes, Moore’s Law

1995 2000 2005 2010 2015 Year of Production - Source: ITRS report 2005 1E-2 1E+1 1E+0 1E-1 1E+2 Product Function/chip Giga transistors

slide-4
SLIDE 4

A net reduction-based clustering preprocessing algorithm - ISPD 2006

Introduction

Multi-level platforms have become the norm

Consist of three phases: a) Clustering b) Initial partitioning placement or routing a) Refinement partitioning, placement or routing refinement Original circuit clustering Original circuit

slide-5
SLIDE 5

A net reduction-based clustering preprocessing algorithm - ISPD 2006

  • Introduction
  • Background and Motivation
  • Net Cluster Algorithm
  • Numerical Results
  • Conclusions and Future Work
slide-6
SLIDE 6

A net reduction-based clustering preprocessing algorithm - ISPD 2006

Background - Clustering algorithms

Numerous clustering algorithms:

  • Edge coarsening (EC)
  • First Choice (FC)
  • Edge Separability (ESC)
  • Fine Granularity (FG)
  • Best-Choice
slide-7
SLIDE 7

A net reduction-based clustering preprocessing algorithm - ISPD 2006

Background - Clustering algorithms

General Drawbacks:

  • Lack of global view
  • Ignore natural cluster
  • Limitations on number of cells in a cluster
  • Edge based - need clique transformation
slide-8
SLIDE 8

A net reduction-based clustering preprocessing algorithm - ISPD 2006

Background - Example

4 and 5 can be put together based on local connectivity

4 5

slide-9
SLIDE 9

A net reduction-based clustering preprocessing algorithm - ISPD 2006

Background - Example

1 2 3 4 5 7 6 8

slide-10
SLIDE 10

A net reduction-based clustering preprocessing algorithm - ISPD 2006

Background - Example

1 2 3 4 5 7 6 8

Eliminating natural clusters in the circuit

slide-11
SLIDE 11

A net reduction-based clustering preprocessing algorithm - ISPD 2006

Background - motivations

  • Capture the natural clusters in a circuit
  • Focus on clustering nets versus cells
  • Avoid using a clique model
  • Remove hard limitations on the number of

cells in a cluster

slide-12
SLIDE 12

A net reduction-based clustering preprocessing algorithm - ISPD 2006

  • Introduction
  • Background and Motivation
  • Net Cluster Algorithm
  • Numerical Results
  • Conclusions and Future Work
slide-13
SLIDE 13

A net reduction-based clustering preprocessing algorithm - ISPD 2006

Net Cluster - Outline

Input: flat netlist Output: clustered netlist For all cells:

  • 1. Initial Cluster Identification
  • 2. Initial Cluster refinement
  • 3. Score Calculation

Form clusters based on score

slide-14
SLIDE 14

A net reduction-based clustering preprocessing algorithm - ISPD 2006

Net Cluster - initial Cluster Identification

  • Visit each cell as a seed cell
  • Group seed cell with neighboring cells

1 2 3 4 5 n1 n2 n3 n5 n4 n6 7 6 9 8 n7 n9 n8 Cell 1 initial cluster

slide-15
SLIDE 15

A net reduction-based clustering preprocessing algorithm - ISPD 2006

Net Cluster - initial Cluster Identification

1 2 3 4 5 7 6 9 8 n1 n2 n3 n5 n4 n6 n7 n9 n8

slide-16
SLIDE 16

A net reduction-based clustering preprocessing algorithm - ISPD 2006

Net Cluster - initial Cluster Identification

1 2 3 4 5 7 6 9 8 n1 n2 n3 n5 n4 n6 n7 n9 n8

slide-17
SLIDE 17

A net reduction-based clustering preprocessing algorithm - ISPD 2006

Net Cluster - Cluster refinement

Use one-way FM to remove any cell with more connection to outside

1 2 3 4 5 7 6 9 8 n1 n2 n3 n5 n4 n6 n7 n9 n8 Cell 1 initial cluster

slide-18
SLIDE 18

A net reduction-based clustering preprocessing algorithm - ISPD 2006

Net Cluster - Cluster refinement

1 2 3 4 5 7 6 9 8 n1 n2 n3 n5 n4 n6 n7 n9 n8

slide-19
SLIDE 19

A net reduction-based clustering preprocessing algorithm - ISPD 2006

Net Cluster - Cluster refinement

1 2 3 4 5 7 6 9 8 n1 n2 n3 n5 n4 n6 n7 n9 n8

Which clusters to choose?

slide-20
SLIDE 20

A net reduction-based clustering preprocessing algorithm - ISPD 2006

Net Cluster - Cluster refinement

1 2 3 4 5 7 6 9 8 n1 n2 n3 n5 n4 n6 n7 n9 n8

Let’s forget about the clusters

slide-21
SLIDE 21

A net reduction-based clustering preprocessing algorithm - ISPD 2006

Net Cluster - Score Calculation

Nets cut: n3, n6, n7

1 2 3 4 5 7 6 9 8 n1 n2 n3 n5 n4 n6 n7 n9 n8

slide-22
SLIDE 22

A net reduction-based clustering preprocessing algorithm - ISPD 2006

Net Cluster - Score Calculation

Nets only clustered: n4, n5 n8,n9 n1,n2

1 2 3 4 5 7 6 9 8 n1 n2 n3 n5 n4 n6 n7 n9 n8

slide-23
SLIDE 23

A net reduction-based clustering preprocessing algorithm - ISPD 2006

Net Cluster - Score Calculation

Net Score Calculations: sn(n) = { # times clustered if not cut if cut

1 2 3 4 5 7 6 9 8 n1 n2 n3 n5 n4 n6 n7 n9 n8

slide-24
SLIDE 24

A net reduction-based clustering preprocessing algorithm - ISPD 2006

Net Cluster - Cluster Formation

Cluster nets based on their score till a clustering ratio is achieved

1 2 3 6 n1 n2 n3 n6 n7 4,5 7,8,9 7 9 8 n9 n8 4 5 n4 n5

slide-25
SLIDE 25

A net reduction-based clustering preprocessing algorithm - ISPD 2006

Net Cluster - Cluster Formation

6 n3 n6 4,5 7,8,9 1,2,3 n7

Final Clustered circuit

slide-26
SLIDE 26

A net reduction-based clustering preprocessing algorithm - ISPD 2006

Net Cluster - Discussion

Characteristics:

  • Identify the natural clusters in a circuit
  • Uses a simplified FM to refine clusters
  • Assigns scores to nets
  • Clusters nets versus cell
slide-27
SLIDE 27

A net reduction-based clustering preprocessing algorithm - ISPD 2006

  • Introduction
  • Background and Motivation
  • Net Cluster Algorithm
  • Numerical Results
  • Conclusions and Future Work
slide-28
SLIDE 28

A net reduction-based clustering preprocessing algorithm - ISPD 2006

Numerical Results

Tested as a preprocessing step for multilevel partitioning. Why Partitioning:

  • Easy implementation
  • Less parameters affecting the results
slide-29
SLIDE 29

A net reduction-based clustering preprocessing algorithm - ISPD 2006

Numerical Results

Preprocessing:

  • The number of natural clusters decreases

dramatically after first few levels

6 n3 n6 4,5 7,8,9 1,2,3 n7

slide-30
SLIDE 30

A net reduction-based clustering preprocessing algorithm - ISPD 2006

Numerical Results - net cuts (1)

  • 20

20 40 60 80 100 1 2 3 4 5 6 7 8 9 hMethis MLPart

Net cut comparison for ISPD 98 benchmarks

Benchmarks Difference in Average net cut compared to Net Cluster

slide-31
SLIDE 31

A net reduction-based clustering preprocessing algorithm - ISPD 2006

Numerical Results - net cuts (2)

  • 150
  • 100
  • 50

50 100 150 200 250 300 350 10 11 12 13 14 15 16 17 18 hMethis MLPart

Net cut comparison for ISPD 98 benchmarks

Benchmarks Difference in Average net cut compared to Net Cluster

slide-32
SLIDE 32

A net reduction-based clustering preprocessing algorithm - ISPD 2006

Numerical Results - run times (1)

  • 50

50 100 150 200 1 2 3 4 5 6 7 8 9 hMethis MLPart

Net cut comparison for ISPD 98 benchmarks

Benchmarks Difference in Average run time compared to Net Cluster

slide-33
SLIDE 33

A net reduction-based clustering preprocessing algorithm - ISPD 2006

Numerical Results - run times (2)

  • 2500
  • 2000
  • 1500
  • 1000
  • 500

500 1000 1500 10 11 12 13 14 15 16 17 18 hMethis MLPart

Net cut comparison for ISPD 98 benchmarks

Benchmarks Difference in Average run time compared to Net Cluster

slide-34
SLIDE 34

A net reduction-based clustering preprocessing algorithm - ISPD 2006

Conclusions and Future Work

  • Developed a deterministic clustering algorithm
  • Is capable of finding the natural clusters
  • Focuses on clustering nets versus cells

Future Work

  • Techniques for developing initial clusters in the

lower levels

  • Application to placement
slide-35
SLIDE 35

A net reduction-based clustering preprocessing algorithm - ISPD 2006

A Net-Reduction based Clustering Preprocessing Algorithm

Jianhua Li, Laleh Behjat University of Calgary, Calgary, Canada ISPD April 12, 2006