Multi-Bend Bus-Driven Floorplanning

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Multi-Bend Bus-Driven Floorplanning

• Jill H.Y.Law Evangeline F.Y.Young
• The Chinese University of Hong Kong

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Outline

• Introduction
• Background
• Sequence Pair
• Methodology
• Shape Validation
• Bus Ordering
• Floorplan Realization
• Experimental Results
• Conclusion

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Introduction
4
Background

• Why is bus-driven floorplanning important?
• Previous work
• Hua Xiang, Xiaoping Tang and Martin D.F. Wong
  Bus-Driven Floorplanning ICCAD 2003
• 0-bend is not enough for buses going through many
  blocks

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Problem Formulation

• A set of n blocks B b0, b1, , bn-1
• A set of m buses U u0, u1, , um-1, where
  each bus is associated with a width ti
• Decide the position of blocks, such that
• Buses go through their blocks
• Chip area minimized
• Bus area minimized
• Buses can have at most 2-bends

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Problem Formulation

• What is meant by going through ?
• Assume block height gt bus width

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Problem Formulation
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Sequence Pair (SP)

• A pair of sequences of n elements
• (ab, ab), a is on the left of b
• (ab, ba), a is on top of b
• Example (acbde, daceb)

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Methodology
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Overview

• While Temp gt threshold
• Apply a move to obtain a new SP
• Evaluate the floorplan
• Shape Validation
• Bus Ordering
• Floorplan Realization
• Accept or reject according to Cost and Temp

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Steps

• Assumption
• 2 layers for bus routing
• Evaluation
• Shape Validation
• 0-bend
• 1-bend
• 2-bend
• Bus Ordering
• Floorplan Realization

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Shape Validation

• Check the bus one by one
• From the relative position of the blocks, check
  if a bus of at most 2 bends can go through all
  blocks

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Shape Validation 0 bend

• Step 1 Extract the related blocks from the
  sequence pair
• Example For a bus ABE
• Given a SP (ABCDE, ABCED) ? (ABE, ABE)
• Step 2 Check relative position between blocks
• Example For a bus ABC
• Horizontal bus (ABCDE, ADEBC) ? (ABC, ABC)
• Vertical bus (CDBEA , ABCDE) ? (CBA, ABC)

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Shape Validation 1 bend

• L-shape bus
• 1 horizontal component
• 1 vertical component
• How to recognize them?
• Step 1 Extract the related blocks (X, Y)
• Step 2 Find the Longest Common Subsequence (LCS)
  of (X, Y) ? Horizontal component

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Shape Validation 1 bend

• Step 3 Check if the remaining blocks in reverse
  order
• Example (ABCDEF, ABCFED)
• LCS?ABCD, remaining blocks (DEF, FED)
• Step 4 Check if T-shape
• T-shape also contains one horizontal component
  and one vertical component
• T-shape is kept for later 2-bend checking

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Shape Validation 1 bend

• When will a T-shape be formed?

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Shape Validation 1 bend

• Example (ABCDE, ADCBE)
• Horizontal Component ABE
• Vertical Component CD

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Shape Validation 2 bend

• C-Shapes, Z-Shapes, mirrored Z-Shapes
• HVH or VHV
• Assume HVH (VHV is similar)
• How to recognize them?
• Step 1 Extract the related blocks (X, Y)
• Step 2 Find the LCS of (X, YR) ? vertical
• Example (ABCDE, ADCBE)
• Find the LCS of (ABCDE, EBCDA) BCD

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Shape Validation 2 bend

• Step 3 Put the remaining blocks in different
  relationships with the vertical component

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Shape Validation 2 bend

• 8 possible relationships
• Step 4 Put the blocks into 2 horizontal
  components

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Shape Validation 2 bend

• Example (GHABCEFD, EFDCBGHA)
• (GHABCEFD, AHGBCDFE) ? vertical component
• Upper A, H, G, Lower D, E, F
• A C-shape can be formed

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Shape Validation 2 bend

• Example (AEBCDF, EDCBFA)
• (AEBCDF, AFBCDE) ? vertical component
• Upper A, Lower D, LowerLeft E,
  LowerRight F
• No valid 2-bend shape can be formed

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Shape Validation

• Extract the related blocks
• Check if 0-bend
• Check if 1-bend
• Assume HVH
• Check if 2-bend
• Assume VHV
• Check if 2-bend
• Mark it invalid if all no

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Steps

• Evaluation
• Shape Validation
• Bus Ordering
• Floorplan Realization

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Determine Bus Ordering
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Bus Ordering

• Step 1 Split all the buses into 0-bend bus
  components
• Step 2 Build vertical graph and horizontal graph
  by looking at each pair of bus components
• Use a node to represent each bus component
• If bus component a has to be on top of bus
  component b, add an edge from node a to node b
• If there is cycle, at least one bus component in
  the cycle has to be removed
• Horizontal graph can be built in a similar fashion

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Bus Ordering

• Step 3 If there are cycles, remove nodes (bus
  components) to make the graph acyclic
• Aim at removing the least number of nodes
• NP-complete
• Maximum degree heuristic
• Step 4 Remove the corresponding bus components
  in the other graph as well

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Steps

• Evaluation
• Shape Validation
• Bus Ordering
• Floorplan Realization

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Floorplan Realization

• Realization obtaining the positions of the
  blocks and buses
• This step is the same as that in Xiangs work

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Simulated Annealing

• Simulated Annealing Framework
• Moves
• Swap
• Rotation
• Cost Function
• Cost ??A ??B ??I
• A chip area, B total bus area, I number of
  invalid bus
• Can consider other aspects by adding more terms
  in the cost function
• Total wire length
• Routing congestion

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Summary

• While Temp gt threshold
• Apply a move to obtain a new floorplan
• Evaluate the floorplan
• Shape Validation
• Bus Ordering
• Floorplan Realization
• Accept or reject according to Cost and Temp

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Experimental Results
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Platform

• Language
• Implemented using C
• Machine
• Intel Xeon (2.2 GHz) with 1 G memory
• MCNC benchmarks

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Experimental Results

• The data set used in Xiangs work
• calculated by (y1 y0) / y0100

Xiangs Work Xiangs Work Our Work Our Work Comparison Comparison
Time (s) Dead space Time (s) Dead space Time Dead space
apte 15 0.72 30 0.48 100.00 -33.33
xerox 15 0.95 35 0.42 133.33 -55.79
hp 33 0.62 51 0.29 54.55 -53.23
ami33-1 11 0.94 93 1.00 745.55 6.38
ami33-2 92 1.27 144 1.19 56.62 -6.30
ami49-1 16 0.85 71 0.56 343.75 -34.12
ami49-2 302 0.84 713 0.58 136.09 -30.95
ami49-3 285 1.09 865 0.60 203.51 -44.95
Average 221.65 -31.54
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Experimental Results

• In this data set, each bus has to go through 10
  15 blocks
• calculated by (y1 y0) / y0100

Xiangs Work Xiangs Work Our Work Our Work Comparison Comparison
Time (s) Dead space Time (s) Dead space Time Dead space
ami33-3 86 1.81 32 1.01 -62.79 -44.20
ami33-4 gt1000 NA 92 1.90 NA NA
ami33-5 gt 1000 NA 95 3.80 NA NA
ami49-4 73 19.34 88 0.63 20.55 -96.74
ami49-5 gt 1000 NA 261 1.17 NA NA
ami49-6 gt 1000 NA 140 2.19 NA NA
Average 118 1.78
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Experimental Results

• ami49 2

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Experimental Results

• ami49 3

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Experimental Results

• ami49 6

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Conclusion

• Solve the bus-driven floorplanning problem for
  0-bend, 1-bend, 2-bend buses
• The presence of 1-bend and 2-bend buses is
  important, especially when the number of blocks
  that a bus goes through is large