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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
“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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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
“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 = p1*C + p2*D
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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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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
Two-terminal Net:
Multi-terminal Net:
1
V I
8
1
I
J
V
8 8
8 8
V I
J
V I
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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
How to select from the larger partition ? If > threshold
Random select If < 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