Circuit%20Partitioning

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Circuit Partitioning

• Presented by Jill

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Outline

• Introduction
• Cut-size driven circuit partitioning
• Multi-objective circuit partitioning
• Our approach Network flow based
• Methodology
• Difficulties

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Introduction

• What is circuit partitioning ?
• Circuit partitioning is vital
• Complexity increases
• Number of transistors involved increases
• Chip size decreases
• Partitioning objective
• Cut-size
• Delay

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Cut-Size Driven Approach
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Cut-Size Driven Approach

• Multilevel Hypergraph Partitioning Application
  in VLSI Domain
• G.Karypis, R.Aggarwal, V.Kumar, S.Shekhar. DAC
  1997
• Multilevel hypergraph partitioning algorithm
  hMetis

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Cut-Size Driven Approach

• Three phases
• Coarsening Phase
• Partitioning Phase
• Uncoarsening and Refinement Phase

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Overview of hMetis
Uncoarsening and refinement
Coarsening
Partitioning
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Coarsening
Edge Coarsening
Hyperedge Coarsening
Modified Hyperedge Coarsening
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Uncoarsening and Refinement

• Successively projecting the partitioning to the
  next level
• Refinement
• Early-exit FM
• Max. number of pass 2
• In each pass, if no improvement after k move,
  exit
• Hyperedge Refinement
• Remove an entire hyperedge from the cut

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Multi - Objective Approach
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Multi-Objective Approach

• Multi-objective Circuit Partitioning for Cutsize
  and Path-Based Delay Minimization C.Ababei,
  N.Selvakkumaran, K.Bazargan, G.Karypis ICCAD 2002
• Multi-objective circuit partitioning based on
  hMetis
• Minimize cut-size
• Minimize delay

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Multi-Objective Approach

• Good solution
• Allow fine-tuned control of the objectives
• Provide way to handle objectives of different
  natures
• Two main differences
• Objective function
• Soln p1C p2D

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Multi-Objective Approach

• Delay
• Delay of the critical path
• of cut along each critical path
• Edge weight of all edges that lie on the critical
  path

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K-Most Critical Paths

• Partitioning without updating the K-most critical
  paths
• Update the list of the K-most critical paths
  during each move
• How to choose K?
• Small ? no improvement
• Large ? run time increase, solution space decrease

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Improvement Over hMetis

• Delay ? 14 decrease
• Cut-size ? 10 increase
• Run-time ? 2.4x

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Network Flow Based Approach
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Network Flow Based Approach

• Originated by Eric Wong, Prof. Young
• Delay driven K-way partitioning
• Three phase
• Net modelling
• Partitioning phase
• Refinement phase

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Net Modelling

• As network flow technique is used, circuits
  should be modelled as graph
• Acyclic partitioning for the following paths
• PI ? PO
• PI ? FF
• FF ? FF
• FF ? PO

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Net modelling

• Combinational net

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Net Modelling

• Sequential Net

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Partitioning Phase

• Max-Flow Min-Cut
• Guarantee min-cut
• Not necessarily balanced
• Efficient Network Flow Based Min-Cut Balanced
  Partitioning
• Honghua Yang, D.F. Wong ICCAD 1994

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Partitioning Phase
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Partitioning Phase

• How to select from the larger partition ?
• If gt threshold
• Random select
• If lt threshold
• Try all possible choices
• Follow acyclic constraint
• Apply the partitioning phase recursively to
  obtain k-way partitioning

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Refinement Phase

• FM post-processing step
• Apply FM to every pair of partition
• Different from original FM
• If delay increased, reject
• May yield cyclic result

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Experimental results

• 1to2.xls
• 1to5.xls

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Difficuties

• Possible reason
• Ratio increased ? decreased
• Method of bipartitioning
• Acyclic restriction
• Future Direction
• Cyclic ? Acyclic ?