An Improved Two-Way Partitioning Algorithm with Stable Performance

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An Improved Two-Way Partitioning Algorithm with
Stable Performance

• Chung-Kuan Cheng
• Yen-Chuen A. Wei

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Motivation

• KL based Algorithms highly sensitive to initial
  conditions
• Can be solved by multiple runs of the Algorithm
• Probability of finding good initial conditions
  drop exponentially with circuit size

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Tools(1) Ratio Cut

• Two way partitioning Algorithm
• Finds partitioning with best ratio using RAB
  CAB / (A x B)
• Partitioning not necessarily even

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Tools(2) - FM

• Fiduccia-Mattheyses Partitioning
• Move node with best gain that satisfies the
  balance condition from one partition to the other
  until all are locked

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Step One - Divide

• Divide the design into two partitions using ratio
  cut
• Keep applying ratio cut to any partition larger
  than Nodes/g
• Authors suggest g 50

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Step Two Conquer

• Form Supernodes
• Partition Supernodes using FM number_of_reps
  times using size constraints
• Authors suggest 10 for number_of_reps
• Choose best results from FM

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Step Three Clean Up

• Expand the Supernodes back out
• Apply one more run of FM

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Experimental Results