a net reduction based clustering preprocessing algorithm
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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

  1. 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

  2. Outline • Introduction • Background and Motivation • Net Cluster Algorithm • Numerical Results • Conclusions and Future Work A net reduction-based clustering preprocessing algorithm - ISPD 2006

  3. Introduction Exponential growth in circuit sizes, Moore’s Law 1E+2 Product Function/chip 1E+1 Giga transistors 1E+0 1E-1 1E-2 1995 2000 2005 2010 2015 Year of Production - Source: ITRS report 2005 A net reduction-based clustering preprocessing algorithm - ISPD 2006

  4. Introduction Multi-level platforms have become the norm Original circuit Consist of three phases: Original circuit a) Clustering b) Initial partitioning placement or routing a) Refinement clustering refinement partitioning, placement or routing A net reduction-based clustering preprocessing algorithm - ISPD 2006

  5. • Introduction • Background and Motivation • Net Cluster Algorithm • Numerical Results • Conclusions and Future Work A net reduction-based clustering preprocessing algorithm - ISPD 2006

  6. Background - Clustering algorithms Numerous clustering algorithms: • Edge coarsening (EC) • First Choice (FC) • Edge Separability (ESC) • Fine Granularity (FG) • Best-Choice A net reduction-based clustering preprocessing algorithm - ISPD 2006

  7. 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 A net reduction-based clustering preprocessing algorithm - ISPD 2006

  8. Background - Example 4 and 5 can be put together based on local connectivity 4 5 A net reduction-based clustering preprocessing algorithm - ISPD 2006

  9. Background - Example 3 4 5 6 1 2 7 8 A net reduction-based clustering preprocessing algorithm - ISPD 2006

  10. Background - Example 3 4 5 6 1 2 7 8 Eliminating natural clusters in the circuit A net reduction-based clustering preprocessing algorithm - ISPD 2006

  11. 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 A net reduction-based clustering preprocessing algorithm - ISPD 2006

  12. • Introduction • Background and Motivation • Net Cluster Algorithm • Numerical Results • Conclusions and Future Work A net reduction-based clustering preprocessing algorithm - ISPD 2006

  13. 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 A net reduction-based clustering preprocessing algorithm - ISPD 2006

  14. Net Cluster - initial Cluster Identification • Visit each cell as a seed cell • Group seed cell with neighboring cells n4 n6 4 5 6 9 n5 n7 n9 n3 1 2 3 7 8 n1 n2 n8 Cell 1 initial cluster A net reduction-based clustering preprocessing algorithm - ISPD 2006

  15. Net Cluster - initial Cluster Identification n4 n6 4 5 6 9 n5 n7 n9 n3 1 2 3 7 8 n1 n2 n8 A net reduction-based clustering preprocessing algorithm - ISPD 2006

  16. Net Cluster - initial Cluster Identification n4 n6 4 5 6 9 n5 n7 n9 n3 1 2 3 7 8 n1 n2 n8 A net reduction-based clustering preprocessing algorithm - ISPD 2006

  17. Net Cluster - Cluster refinement Use one-way FM to remove any cell with more connection to outside n4 n6 4 5 6 9 n5 n7 n9 n3 1 2 3 7 8 n1 n2 n8 Cell 1 initial cluster A net reduction-based clustering preprocessing algorithm - ISPD 2006

  18. Net Cluster - Cluster refinement n4 n6 4 5 6 9 n5 n7 n9 n3 1 2 3 7 8 n1 n2 n8 A net reduction-based clustering preprocessing algorithm - ISPD 2006

  19. Net Cluster - Cluster refinement n4 n6 4 5 6 9 n5 n7 n9 n3 1 2 3 7 8 n1 n2 n8 Which clusters to choose? A net reduction-based clustering preprocessing algorithm - ISPD 2006

  20. Net Cluster - Cluster refinement n4 n6 4 5 6 9 n5 n7 n9 n3 1 2 3 7 8 n1 n2 n8 Let’s forget about the clusters A net reduction-based clustering preprocessing algorithm - ISPD 2006

  21. Net Cluster - Score Calculation Nets cut: n4 n3, n6, n7 n6 4 5 6 9 n5 n7 n9 n3 1 2 3 7 8 n1 n2 n8 A net reduction-based clustering preprocessing algorithm - ISPD 2006

  22. Net Cluster - Score Calculation Nets only clustered: n4 n4, n5 n6 4 5 6 9 n8,n9 n5 n1,n2 n7 n9 n3 1 2 3 7 8 n1 n2 n8 A net reduction-based clustering preprocessing algorithm - ISPD 2006

  23. Net Cluster - Score Calculation Net Score Calculations: # times clustered if not cut s n (n) = { 0 if cut n4 n6 4 5 6 9 n5 n7 n9 n3 1 2 3 7 8 n1 n2 n8 A net reduction-based clustering preprocessing algorithm - ISPD 2006

  24. Net Cluster - Cluster Formation Cluster nets based on their score till a clustering ratio is achieved 9 n4 n9 4 5 n6 7 8 n8 n5 4,5 6 7,8,9 n7 n3 1 2 3 n1 n2 A net reduction-based clustering preprocessing algorithm - ISPD 2006

  25. Net Cluster - Cluster Formation Final Clustered circuit n3 n6 n7 1,2,3 4,5 6 7,8,9 A net reduction-based clustering preprocessing algorithm - ISPD 2006

  26. 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 A net reduction-based clustering preprocessing algorithm - ISPD 2006

  27. • Introduction • Background and Motivation • Net Cluster Algorithm • Numerical Results • Conclusions and Future Work A net reduction-based clustering preprocessing algorithm - ISPD 2006

  28. Numerical Results Tested as a preprocessing step for multilevel partitioning. Why Partitioning: • Easy implementation • Less parameters affecting the results A net reduction-based clustering preprocessing algorithm - ISPD 2006

  29. Numerical Results Preprocessing: • The number of natural clusters decreases dramatically after first few levels n3 n6 n7 1,2,3 4,5 6 7,8,9 A net reduction-based clustering preprocessing algorithm - ISPD 2006

  30. Numerical Results - net cuts (1) Difference in Average net cut 100 80 compared to Net Cluster 60 hMethis 40 MLPart 20 0 -20 1 2 3 4 5 6 7 8 9 Benchmarks Net cut comparison for ISPD 98 benchmarks A net reduction-based clustering preprocessing algorithm - ISPD 2006

  31. Numerical Results - net cuts (2) Difference in Average net cut 350 300 compared to Net Cluster 250 200 150 hMethis 100 MLPart 50 0 -50 -100 -150 10 11 12 13 14 15 16 17 18 Benchmarks Net cut comparison for ISPD 98 benchmarks A net reduction-based clustering preprocessing algorithm - ISPD 2006

  32. Numerical Results - run times (1) Difference in Average run time 200 compared to Net Cluster 150 100 hMethis MLPart 50 0 -50 1 2 3 4 5 6 7 8 9 Benchmarks Net cut comparison for ISPD 98 benchmarks A net reduction-based clustering preprocessing algorithm - ISPD 2006

  33. Numerical Results - run times (2) Difference in Average run time 1500 1000 compared to Net Cluster 500 0 hMethis -500 MLPart -1000 -1500 -2000 -2500 10 11 12 13 14 15 16 17 18 Benchmarks Net cut comparison for ISPD 98 benchmarks A net reduction-based clustering preprocessing algorithm - ISPD 2006

  34. 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 A net reduction-based clustering preprocessing algorithm - ISPD 2006

  35. 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

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