BTrees: A New Representation for NonSlicing Floorplans

1
B-Trees A New Representation forNon-Slicing
Floorplans

• Yun-Chih Chang, Yao-Wen Chang,
• Guang-Ming Wu, and Shu-Wei Wu

Department of Computer and Information
Science National Chiao Tung University Hsinchu,
Taiwan, ROC
2
Outline
Introduction
Our Contributions
Pre-placed Modules
Representations
Operations
Soft Modules
Algorithm
Rectilinear Modules
Experimental results
Conclusion
3
Introduction
Our Contributions
Pre-placed Modules
Representations
Operations
Soft Modules
Algorithm
Rectilinear Modules
Experimental results
Conclusion
4
Introduction

• Floorplanning becomes more critical due to
  hierarchical design and IP modules.
• Need an efficient, flexible, and effective
  representation for floorplans.
• Two types of floorplans slicing structure and
  non-slicing structure.

3
1
4
5
2
6
7
5
Floorplan Representations

• Slicing Floorplans
• Binary tree Otten, DAC82
• Normalized Polish expression Wong and Liu,
  DAC86
• Non-slicing Floorplans
• Sequence pair Murata et al., ICCAD95
• Bounding slicing grid Nakatake et al., ICCAD96
• O-tree Guo, Cheng, and Yoshimura, DAC99

6
Introduction
Our Contributions
Pre-placed Modules
Representations
Operations
Soft Modules
Algorithm
Rectilinear Modules
Experimental results
Conclusion
7
Contributions
Introduce the B-tree representation for
non-slicing floorplans.
8
Characteristics of B-trees

• Efficiency
• Is based on ordered binary tree, fast and easy
  for implementation.
• Needs no constraint graphs for area cost
  evaluation.
• Evaluates area cost incrementally.
• Only needs to transform from a B-tree to
  placement during processing, except for handling
  soft modules.
• Effectiveness
• Results in smaller silicon area.
• Flexibility
• Handles hard, pre-placed, soft and rectilinear
  modulesdirectly and efficiently.

9
Introduction
Our Contributions
Pre-placed Modules
Representations
Operations
Soft Modules
Algorithm
Rectilinear Modules
Experimental results
Conclusion
10
The O-tree Representation

• Compacts modules to left and bottom
• Represents by an arbitrary ordered tree
• Needs sequence encoding

b10
b5
b6
1
0
0
1
1
0
b3
n1
n0
n5
b1
b4
b2
0
1
0
1
0
1
0
1
1
1
0
0
n2
n9
n10
n8
n6
n7
1
0
1
b9
b0
0
n11
n3
b8
b11
0
1
b7
n4
(001001101011000011110011, b0 b7 b8 b11 b9 b10
b1 b2 b3 b4 b5 b6)
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Limitation of the O-tree

• Can insert only at external positions, due to the
  overhead in encoding sequence.
• May deviate from the optimal during solution
  perturbations.

n1
n5
n0
n6
n2
n9
n10
n7
n8
n11
n3
n4
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The B-tree Construction
n0
b10
b5
b6
b3
b1
n1
n7
b4
b2
n2
n5
n8
b0
b9
n3
n6
n9
n11
b8
b11
b7
n4
n10
1-1 correspondence
13
The B-tree Representation

• Apply the Depth-First Search (DFS) to construct
  the tree.
• left child gt adjacent, bottom-most module on
  the right
• right child gt module above and adjacent with
  the same x-coordinate.
• x-coordinates can be determinated by the tree
  structure.
• y-coordinates?

b1
x1x0
b0
b7
(x0,y0)
x7x0w0
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Contour Structure

• Reduce the complexity of computing a y-coordinate
  to O(1) time.
• First introduced in the O-tree.

horizontal contour
b10
vertical contour
b3
b1
b4
b0
b9
b8
b11
b7
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Introduction
Our Contributions
Pre-placed Modules
Representations
Operations
Soft Modules
Algorithm
Rectilinear Modules
Experimental results
Conclusion
16
Introduction
Our Contributions
Pre-placed Modules
Representations
Operations
Soft Modules
Algorithm
Rectilinear Modules
Experimental results
Conclusion
17
Pre-placed Modules
n0
n1
n1
n7
b2
n5
n2
n2
n5
n8
n3
n3
n6
n9
n11
n4
n10
D6 b1, b2
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Pre-placed Modules
n0
n1
n1
n7
b2
n5
n5
n8
n6
n3
n3
n9
n11
n2
n4
n10
D6 b1, b2
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Pre-placed Modules
n0
b2
b10
b5
b3
b1
b4
b6
b0
b9
b8
b11
b7
D6 b1, b2
20
Introduction
Our Contributions
Pre-placed Modules
Representations
Operations
Soft Modules
Algorithm
Rectilinear Modules
Experimental results
Conclusion
21
Soft Modules

• Step1 Change the shape of the inserted soft
  module
• Step2 Change the shapes of other soft modules

surplus space
b10
b5
b6
b3
b1
b4
b2
b0
b0
b9
b8
b11
b7
22
Soft Modules

• Step1 Change the shape of the inserted soft
  module
• Step2 Change the shape of other soft modules

b10
b0
b9
b8
b11
b7
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Soft Modules

• Step1 Change the shape of the inserted soft
  module
• Step2 Change the shapes of other soft modules

b5
b10
b6
b3
b1
surplus space
b4
b2
b2
b0
b9
b8
b11
b7
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Soft Modules

• Step1 Change the shape of the inserted soft
  module
• Step2 Change the shape of other soft modules

b5
b10
b6
b3
b1
b2
b4
b0
b9
b8
b11
b7
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Introduction
Our Contributions
Pre-placed Modules
Representations
Operations
Soft Modules
Algorithm
Rectilinear Modules
Experimental results
Conclusion
26
Rectilinear Modules

• A rectilinear module can be partitioned into
  rectangular sub-modules.

b5
b4
b6
b3
b2
b7
b1
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Orientations of L-Shaped Module

• An L-shaped module has four orientationsafter
  rotation.

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Location Constraint

• Location Constraint Keep b2 as b1s left child
  in the B-tree.

0
b2
1
2
b1
b1
b3
1
b3
b2
b4
b4
0
2
Location Constraint
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Fixing Mis-aligned Sub-Modules

• Mis-aligned sub-modules do not conform to the
  shape of their original module.

b2
1
b3
b4
0
2
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Fixing Mis-aligned Sub-Modules

• Mis-aligned sub-modules do not conform to the
  shape of their original module.

b2
1
b3
b4
0
2
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Introduction
Our Contributions
Pre-placed Modules
Representations
Operations
Soft Modules
Algorithm
Rectilinear Modules
Experimental results
Conclusion
32
Algorithm

• Based on the simulated annealing method.
• Flow

Initialize a B-tree
Perturb the B-tree
no
Meet termination conditions?
yes
Stop!
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Perturbations

• Four types of perturbations
• --Op1 Rotates a module.
• --Op2 Moves a module to another place.
• --Op3 Swaps two modules.
• --Op4 Removes a soft module and inserts it into
  the best internal or external
  positions.
• Needs deletion and insertion for Op2 Op4.

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Deletion

• Three cases for deletion
• -- Case1 A leaf node.

O(1)
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Deletion (contd)

• Case2 A node with one child.

O(1)
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Deletion (contd)

• Case3 A node with two children.

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Deletion (contd)

• Case3 A node with two children.

h
O(h)
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Insertion

• Three types of positions
• -- Inseparable position Between two nodes
  associated with two sub-modules of a rectilinear
  module.
• -- Internal position Between two nodes in a
  B-tree, but is not an inseparable one.
• -- External position Pointed by a NULL pointer.

0
Rectilinear module
1
2
5
3
6
4
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Introduction
Our Contributions
Pre-placed Modules
Representations
Operations
Soft Modules
Algorithm
Rectilinear Modules
Experimental results
Conclusion
40
Experimental Results

• Implemented two algorithms
• Iterative, deterministic algorithm to compare
  with O-tree.
• Simulated annealing algorithmto further improve
  the results.

• Consumes 60 less memory, runs 4.5 times faster,
  uses 1.4 less area.

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Resulting Placement for Ami49
49 rectangles dead space 3.6
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Experimental Results on Rectilinear Modules

• Achieves near optimum areas.

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Resulting Placement for Test5
10 rectangular, 10 L-shaped, and 10 T-shaped
modules dead space 5
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Introduction
Our Contributions
Pre-placed Modules
Representations
Operations
Soft Modules
Algorithm
Rectilinear Modules
Experimental results
Conclusion
45
Conclusion

• Have introduced the binary-tree based B-tree
  representation for non-slicing floorplans.
• Have shown the efficiency, flexibility, and
  effectiveness of the B-tree.
• Minimizes the gap between the representations for
  slicing and non-slicing floorplans.
• Applies to interconnect-driven floorplanning.

46
Acknowledgements

• Thank Prof. Chunk-Kuan Cheng and Dr. Pei-Ning Guo
  for providing us with the O-tree package and the
  benchmark circuits.

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Thank you for your attention
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Question1

• How do you handle timing?

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Question2

• Whats the difference between the O-tree and the
  B-tree?

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Question3

• The Location constraint for rectilinear modules
  is only a necessary condition. Is it possible to
  make it a necessary and sufficient condition?