NTUplace: A Partitioning Based Placement Algorithm for LargeScale Designs

1
NTUplace A Partitioning Based Placement
Algorithm for Large-Scale Designs

• Tung-Chieh Chen1, Tien-Chang Hsu1, Zhe-Wei
  Jiang1, and Yao-Wen Chang1,2
• Graduate Institute of Electronics Engineering1
• Department of Electrical Engineering2
• National Taiwan University
• Taipei, Taiwan
• April 6, 2005

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Outline

• Introduction
• Global placement
• HPWL modeling with min-cut
• Whitespace management
• Look-ahead partitioning
• Legalization
• Detailed placement
• Matching based detailed placement
• Results

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Introduction

• NTUplace is based on the min-cut partitioning
  technique.
• Algorithm

Wirelength modeling with
min-cut Whitespace management Look-ahead
partitioning
Global Placement
Legalization
Detailed Placement
Matching based detailed placement
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HPWL Modeling with Min-Cut

• The HPWL (half-perimeter wirelength) is exactly
  modeled with the min-cut objective.
• Finding the min-cut is equivalent to finding the
  minimum HPWL.
• The idea is similar to the Bounding Box aware
  Terminal Propagation (BBTP) in the TheTo placer
• Selvakkumaran and Karypis, Technical Report
  04-040, Univ. of Minnesota. Oct. 2004.
• They use 7 cases to discuss the HPWL modeling.
• We derive a unified method for the modeling.
• Our method can be applied to the diagonal-bin
  repartitioning.
• TheTo might need to consider tens of cases.

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Net-Weight Assignment (1/2)

• For each net, we compute three HPWL values.
• Consider the case for a net with 2 fixed pins and
  2 movable cells, and the x-range of the 2 pins is
  within that of the 2 cells and the center of the
  left partition is closer to the x-range
• w1 the wirelength when the 2 cells are at the
  left side
• w2 the wirelength when the 2 cells are at the
  right side,
• w12 the wirelength when the 2 cells are at
  different sides.
• Here, w12 gt w2 gt w1

X-range
2 cells are at the right side.
2 cells are at different side.
2 cells are at the left side.
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Net-Weight Assignment (2/2)

• Introduce a partitioning graph (hypergraph) and
  two fixed nodes to represent the two sides.
• Add two hyperedges into the graph.
• Since w2 gt w1, assign the weight of the hyperedge
  e1 between the cells and the left fixed node be
  (w2-w1).
• Assign the weight of the hyperedge e2 between the
  two cells be (w12-w2).
• Partition the resulting hypergraph to decide the
  cell/node partition.

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Three Possible Partitioning Results
Movable node
weight(e1) (w2-w1)
weight(e2) (w12-w2)
Left fixed node
Right fixed node
Movable node
1
3
2
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Relationship Between HPWL and Cutsize
1
2
3
ncut weight(e1) weight(e2) (w12-w2)
(w2-w1) (w12-w1)
ncut weight(e1) (w2-w1)
ncut 0
HPWL w1 w1 ncut
HPWL w12 w1 ncut
HPWL w2 w1 ncut
All three cases HPWL w1 ncut
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Relationship Between HPWL and Cutsize

• Theorem HPWL w1 ncut.
• Then, we have
• Finding the minimum HPWL is equivalent to
  finding the min-cut.

(Constant)
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Whitespace Management (1/2)

• Traditional min-cut placers uniformly distribute
  whitespace and tend to produce excessive
  wirelength when the whitespace is large.
• Adya, Markov, Villarrubia use filler (dummy)
  cells to control the whitespace allocation
  ICCAD-03.
• Add dummy cells to increase the utilization.
  Whitespace is distributed according to the dummy
  cell locations.
• However, their method tend to increase the number
  of cells, leading to longer running time and
  larger memory usage.

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Whitespace Management (2/2)

• We directly control the balance criteria during
  partitioning using the available free space.
• Relaxing the balance criteria leads to smaller
  cutsize and thus smaller wirelength.
• The balance criterion satisfies that the
  utilization of each partition is less than or
  equal to 1.
• The criterion is fed into the partitioner to
  allocate whitespace.

Uniform whitespace distribution
Left partition Utilization 1.0
Right partition Utilization 1.0
Block Area
Block Area
Left util. 1, right util. lt 1
Both util. lt 1
Left util. lt 1, right util. 1
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Look-Ahead Partitioning

• Simplify the idea in Cong et al., Fast
  floorplanning by look-ahead enabled recursive
  bipartitioning, ASPDAC-2005.
• Use the first-fit bin-packing heuristic to check
  if the subpartition can be legalized.
• Increase the chance of legalizing macro blocks.
• If the subpartition cannot be legalized, we move
  the cutline and redo the partitioning.

Re-partition
Legalization Fails
Legalization Succeeds
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Legalization

• Place all cells in the rows to obtain a feasible
  solution.
• Place cells into their nearest rows.
• Sort all standard cells according to their sizes,
  from the largest to the smallest.
• Assign the x-coordinates for all cells according
  to the sorted order. If overlap occurs, we will
  find a nearest empty slot to place the cell.

2
3
4
1
5
Place cells into nearest rows
Place cells one-by-one
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Detailed Placement

• Is based on cell location assignment (matching).
• Each cell has different costs atdifferent
  locations.
• Minimize total cost O(n3) time for n cells
• Is better than O(n!) time for a branch bound
  (BB) detailed placer
• Can use a much larger window (gt 64 cells)

1
2
3
A
B
C
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Old Results

• Old results in the ISPD-05 proceedings.

On a Pentium 4 3.2GHz PC
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New Results from the Enhanced Methods

• Enhance our placer with matching based detailed
  placement and other schemes (e.g.,
  repartitioning).
• Improve the published HPWL by 10.

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• Thank you for your attention!