ECE260B - CSE241A VLSI Digital Circuits

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ECE260B CSE241A Winter 2005Placement
Website http//vlsicad.ucsd.edu/courses/ece260b
-w05
Slides courtesy of Prof. Andrew B. Kahng
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VLSI Design Flow and Physical Design Stage
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Placement Problem

• Input
• A set of cells and their complete information (a
  cell library).
• Connectivity information between cells (netlist
  information).
• Output
• A set of locations on the chip one location for
  each cell.
• Goal
• The cells are placed to produce a routable chip
  that meets timing
• and other constraints (e.g., low-power, noise,
  etc.)
• Challenge
• The number of cells in a design is very large (gt
  1 million).
• The timing constraints are very tight.

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Optimal Relative Order
A
B
C
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To spread ...
A
B
C
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.. or not to spread
A
B
C
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Place to the left
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or to the right
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Optimal Relative Order
A
B
C
Without free space, the placement problem is
dominated by order
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Placement Problem
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Global and Detailed Placement
In global placement, we decide the approximate
locations for cells by placing cells in global
bins. In detailed placement, we make some
local adjustment to obtain the final
non-overlapping placement.
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• Placement Footprints

Standard Cell
Data Path
IP - Floorplanning
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Placement Footprints
Reserved areas
Mixed Data Path sea of gates
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Placement Footprints
Perimeter IO
Area IO
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Placement objectives are subject to user
constraints / design style

• Hierarchical Design Constraints
• pin location
• power rail
• reserved layers
• Flat Design with Floorplan Constraints
• Fixed Circuits
• I/O Connections

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Standard Cells
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Standard Cells

• Power connected by abutment, placed in
  sea-of-rows
• Rarely rotated
• DRC clean in any combination
• Circuit clean (I.e. no naked T-gates, no huge
  input capacitances)
• 8,9,10 tracks in height
• Metal 1 only used (hopefully)
• Multi-height stdcells possible
• Buffers sizes, intrinsic delay steps, optimal
  repeater selection
• Special clock buffers gates (balanced PN)
• Special metastability hardened flops
• Cap cells (metal1 used?)
• Gap fillers (metal1 used?)
• Tie-high, tie-low

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Unconstrained Placement
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Floor planned Placement
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Placement Cube (4D)

• Cost Function(s) to be used
• Cut, wirelength, congestion, crossing, ...
• Algorithm(s) to be used
• FM, Quadratic, annealing, .
• Granularity of the netlist
• Coarseness of the layout domain
• 2x2, 4x4, .
• An effective methodology picks the right mix from
  the above and knows when to switch from one to
  next.
• Most methods today are ad-hoc

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Advantages of Hierarchy

• Design is carved into smaller pieces that can be
  worked on in parallel (improved throughput)
• A known floor plan provides the logic design team
  with a large degree of placement control.
• A known floor plan provided early knowledge of
  long wires
• Timing closure problems can be addressed by
  tools, logic design, and hierarchy manipulation
• Late design changes can be done with minimal
  turmoil to the entire design

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Disadvantages of Hierarchy

• Results depend on the quality of the hierarchy.
  The logic hierarchy must be designed with
  Physical Design taken into account.
• Additional methodology requirements must be met
  to enable hierarchy. Ex. Pin assignment, Macro
  abstract management, area budgeting, floor
  planning, timing budgets, etc
• Late design changes may affect multiple
  components.
• Hierarchy allows divergent methodologies
• Hierarchy hinders Design Automation algorithms.
  They can no longer perform global optimizations.

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Traditional Placement Algorithms

• Quadratic Placement
• Simulated Annealing
• Bi-Partitioning / Quadrisection
• Force Directed Placement
• Hybrid

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Quadratic Placement
Min (x1-x3)2 (x1-x2)2 (x2-x4)2 F

• Analytical Technique

x3
x1
dF/dx1 0 dF/dx2 0
Ax B
x2
x4
2 -1 -1 2
A
x3 x4
x1 x2
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Analytical Placement

• Get a solution with lots of overlap
• What do we do with the overlap?

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Pros and Cons of QP

• Pros
• Very Fast Analytical Solution
• Can Handle Large Design Sizes
• Can be Used as an Initial Seed Placement Engine
• Cons
• Can Generate Overlapped Solutions Postprocessing
  Needed
• Not Suitable for Timing Driven Placement
• Not Suitable for Simultaneous Optimization of
  Other Aspects of Physical Design (clocks,
  crosstalk)
• Gives Trivial Solutions without Pads (and close
  to trivial with pads)

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Simulated Annealing Placement

• Initial Placement Improved through
• Swaps and Moves
• Accept a Swap/Move if it improves cost
• Accept a Swap/Move that degrades cost
• under some probability conditions

Cost
Time
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Pros and Cons of SA

• Pros
• Can Reach Globally Optimal Solution (given
  enough time)
• Open Cost Function.
• Can Optimize Simultaneously all Aspects of
  Physical Design
• Can be Used for End Case Placement
• Cons
• Extremely Slow Process of Reaching a Good Solution

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Bi-Partitioning/Quadrisection
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Pros and Cons of Partitioning Based Placement

• Pros
• More Suitable to Timing Driven Placement since it
  is Move Based
• New Innovation (hMetis) in Partitioning
  Algorithms have made this Extremely Fast
• Open Cost Function
• Move Based means Simultaneous Optimization of all
  Design Aspects Possible
• Cons
• Not Well Understood
• Lots of indifferent moves
• May not work well with some cost functions.

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Hypergraphs in VLSI CAD

• Circuit netlist represented by hypergraph

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Hypergraph Partitioning in VLSI

• Variants
• directed/undirected hypergraphs
• weighted/unweighted vertices, edges
• constraints, objectives,
• Human-designed instances
• Benchmarks
• up to 4,000,000 vertices
• sparse (vertex degree 4, hyperedge size 4)
• small number of very large hyperedges
• Efficiency, flexibility KL-FM style preferred

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Context Top-Down VLSI Placement
etc
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Context Top-Down Placement

• Speed
• 6,000 cells/minute to final detailed placement
• partitioning used only in top-down global
  placement
• implied partitioning runtime 1 second for
  25,000 cells, lt 30 seconds for 750,000 cells
• Structure
• tight balance constraint on total cell areas in
  partitions
• widely varying cell areas
• fixed terminals (pads, terminal propagation, etc.)

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Fiduccia-Mattheyses (FM) Approach

• Pass
• start with all vertices free to move (unlocked)
• label each possible move with immediate change in
  cost that it causes (gain)
• iteratively select and execute a move with
  highest gain, lock the moving vertex (i.e.,
  cannot move again during the pass), and update
  affected gains
• best solution seen during the pass is adopted as
  starting solution for next pass
• FM
• start with some initial solution
• perform passes until a pass fails to improve
  solution quality

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Cut During One Pass (Bipartitioning)
Cut
Moves
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Multilevel Partitioning
Refinement
Clustering
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Force Directed Placement

• Cells are dragged by forces.
• Forces are generated by nets connecting cells.
  Longer nets generate bigger forces.
• Placement is obtained by either a constructive or
  an iterative method.

Fij
i
i
j
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Pros and Cons of Force Directed Placement

• Pros
• Very Fast Analytical Solution
• Can Handle Large Design Sizes
• Can be Used as an Initial Seed Placement Engine
• The Force
• Cons
• Not sensitive to the non-overlapping constraints
• Gives Trivial Solutions without Pads
• Not Suitable for Timing Driven Placement

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Hybrid Placement

• Mix-matching different placement algorithms
• Effective algorithms are always hybrid

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GORDIAN (quadratic partitioning)
InitialPlacement
Partitionand Replace
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Congestion Minimization

• Traditional placement problem is to minimize
  interconnection length (wirelength)
• A valid placement has to be routable
• Congestion is important because it represents
  routability (lower congestion implies better
  routability)
• There is not yet enough research work on the
  congestion minimization problem

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Definition of Congestion
Routing demand 3 Assume routing supply is
1, overflow 3 - 1 2 on this edge.
Overflow on each edge
Routing Demand - Routing Supply (if Routing
Demand gt Routing Supply) 0 (otherwise)
Overflow overflow
S
all edges
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Correlation between Wirelength and Congestion
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Wirelength ? Congestion
A wirelength minimized placement
A congestion minimized placement
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Congestion Map of a Wirelength Minimized Placement
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Congestion MAP
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Congestion Reduction Postprocessing
Reduce congestion globally by minimizing the
traditional wirelength
Post process the wirelength optimized placement
using the congestion objective
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Congestion Reduction Postprocessing

• Among a variety of cost functions and methods for
  congestion minimization, wirelength alone
  followed by a post processing congestion
  minimization works the best and is one of the
  fastest.
• Cost functions such as a hybrid length plus
  congestion do not work very well.

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Cost Functions for Placement

• The final goal of placement is to achieve
  routability and meet timing constraints
• Constraints are very hard to use in optimization,
  thus we use cost functions (e.g., Wirelength) to
  predict our goals.
• We will show what happens when you try
  constraints directly
• The main challenge is a technical understanding
  of various cost functions and their interaction.

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Prediction

• What is prediction ?
• every system has some critical cost functions
  Area, wirelength, congestion, timing etc.
• Prediction aims at estimating values of these
  cost functions without having to go through the
  time-consuming process of full construction.
• Allows quick space exploration, localizes the
  search
• For example
• statistical wire-load models
• Wirelength in placement

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Paradigms of Prediction

• Two fundamental paradigms
• statistical prediction
• of two-terminal nets in all designs
• of two-terminal nets with length greater than 10
  in all designs
• constructive prediction
• of two-terminal nets with length greater than 10
  in this design
• and everything in between, e.g.,
• of critical two-terminal nets in a design based
  on statistical data and a quick inspection of the
  design in hand.
• Absolute truth or I need it to make progress
• SLIP (System Level Interconnect Prediction)
  community.

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Cost Functions for Placement

• Net-cut
• Linear wirelength
• Quadratic wirelength
• Congestion
• Timing
• Coupling
• Other performance related cost functions
• Undiscovered crossing

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Net-cut Cost for Global Placement

• The net-cut cost is defined as the number of
  external nets between different global bins
• Minimizing net-cut in global placement tends to
  put highly connected cells close to each other.

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Linear Wirelength Cost
The linear length of a net between cell 1 and
cell 2 is l12 x1-x2 y1-y2 The linear
wirelength cost is the summation of the linear
length of all nets.
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Quadratic Wirelength Cost
The quadratic length of a net between cell 1 and
cell 2 is l12 (x1-x2)2 (y1-y2)2 The
quadratic wirelength cost is the summation of the
quadratic length of all nets.
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Congestion Cost
Routing demand 3 Assume routing supply is
1, overflow 3 - 1 2 on this edge.
Overflow on each edge
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Cost Functions for Placement

• Various cost functions (and a mix of them) have
  been used in practice to model/estimate
  routability and timing
• We have a good feel for what each cost function
  is capable of doing
• We need to understand the interaction among cost
  functions

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Congestion Minimization and Congestion vs
Wirelength

• Congestion is important because it closely
  represents routability (especially at
  lower-levels of granularity)
• Congestion is not well understood
• Ad-hoc techniques have been kind-of working since
  congestion has never been severe
• It has been observed that length minimization
  tends to reduce congestion.
• Goal Reduce congestion in placement (willing to
  sacrifice wirelength a little bit).

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Correlation between Wirelength and Congestion
Total Wirelength Total Routing Demand
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Wirelength ? Congestion
A wirelength minimized placement
A congestion minimized placement
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Congestion Map of a Wirelength Minimized Placement
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Different Routing Models for modeling congestion

• Bounding box router fast but inaccurate.
• Real router accurate but slow.
• A bounding box router can be used in placement if
  it produces correlated routing results with the
  real router.
• Note For different cost functions, answer might
  be different (e.g., for coupling, only a detailed
  router can answer).

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Different Routing Models
A MSTshortest_path routing model
A bounding box routing model
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Objective Functions Used in Congestion
Minimization

• WL Standard total wirelength objective.
• Ovrflw Total overflow in a placement (a direct
  congestion cost).
• Hybrid (1- a)WL a Ovrflw
• QL A quadratic plus linear objective.
• LQ A linear plus quadratic objective.
• LkAhd A modified overflow cost.
• (1- aT)WL aT Ovrflw A time changing hybrid
  objective which let the cost function gradually
  change from wirelength to overflow as
  optimization proceeds.

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Post Processing to Reduce Congestion
Reduce congestion globally by minimizing the
traditional wirelength
Post process the wirelength optimized placement
using the congestion objective
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Post Processing Heuristics

• Greedy cell-centric algorithm Greedily move
  cells around and greedily accept moves.
• Flow-based cell-centric algorithm Use a
  flow-based approach to move cells.
• Net-centric algorithm Move nets with bigger
  contributions to the congestion first.

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Greedy Cell-centric Heuristic
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Flow-based Cell-centric Heuristic
Bin Nodes
Cell Nodes
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Net-centric Heuristic
2
2
2
1
1
1
2
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From Global Placement to Detailed Placement
Global Placement Assuming all the cells are
placed at the centers of global bins.
Detailed Placement Cells are placed without
overlapping.
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Correlation Between Global and Detailed Placement
Conclusion Congestion at detailed placement
level is correlated with congestion at global
placement level. Thus reducing congestion in
global placement helps reduce congestion in final
detailed placement.

• WLg Wirelength optimized global placement.
• CONg Wirelength optimized detailed placement.
• WLd Congestion optimized global placement.
• CONd Congestion optimized detailed placement.

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Congestion

• Wirelength minimization can minimize congestion
  globally. A post processing congestion
  minimization following wirelength minimization
  works the best to reduce congestion in placement.
• A number of congestion-related cost functions
  were tested, including a hybrid length plus
  congestion (commonly believed to be very
  effective). Experiments prove that they do not
  work very well.
• Net-centric post processing techniques are very
  effective to minimize congestion.
• Congestion at the global placement level,
  correlates well with congestion of detailed
  placement.

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Shapes of Cost Functions
net-cut cost
wirelength
congestion
Solution Space
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Relationships Between the Three Cost Functions

• The net-cut objective function is more smooth
  than the wirelength objective function
• The wirelength objective function is more smooth
  than the congestion objective function
• Local minimas of these three objectives are in
  the same neighborhood.

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Crossing A routability estimator?

• Replace each crossing with a gate
• A planar netlist
• Easy to place

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Timing Cost
Critical Path

• Delay of the circuit is defined as the longest
  delay among all possible paths from primary
  inputs to primary outputs.
• Interconnection delay becomes more and more
  important in deep sub-micron regime.

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Timing Analysis
How do we get the delay numbers on the
gate/interconnect?
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Approaches

• Budgeting
• In accurate information
• Fast
• Path Analysis
• Most accurate information
• Very slow
• Path analysis with infrequent path substitution
• Somewhere in between

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Timing Metrics

• How do we assess the change in a delay due to a
  potential move during physical design?
• Whether it is channel routing or area routing,
  the problem is the same
• translate geometrical change into delay change

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Others costs Coupling Cost

• Hard to model during placement
• Can run a global router in the middle of
  placement
• Even at the global routing level it is hard to
  model it

Avoid it
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Coupling Solutions

• Once we have some metrics for coupling, we can
  calculate sensitivities, and optimize the
  physical design...

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Other Performance Costs

• Power usage of the chip.
• Weighted nets
• Dual voltages (severe constraint on placement)
• Very little known about these cost functions and
  their interaction with other cost functions
• Fundamental research is needed to shed some light
  on the structure of them

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Netlist Granularity Problem Size and Solution
Space Size

• The most challenging part of the placement
  problem is to solve a huge system within given
  amount of time
• We need to effectively reduce the size of the
  solution space and/or reduce the problem size
• Netlist clustering Edge extraction in the
  netlist

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Layout Coarsening

• Reduce Solution Space
• Edge extraction in the solution space
• Only simple things have been tried
• GP, DP (Twolf)
• 2x1, 2x2, .
• Coarsen only easy parts

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Incremental Placement

• Given an optimal placement for a given netlist,
  how to construct optimal placements for netlists
  modified from the given netlist.
• Very little research in this area.
• Different type of incremental changes (in one
  region, or all over)
• Methods to use
• How global should the method be
• An extremely important problem.

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Incremental Placement

• A placement move changes the interconnect
  capacitance and resistance of the associated net
• A net topology approximation is required to
  estimate these changes

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Placynthesis Algorithms
buffering
resizing
restructuring
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Many other Design MetricsPower Supply and Total
Power
Source The Incredible Shrinking Transistor,
Yuan Taur, T. J. Watson Research Center, IBM,
IEEE Spectrum, July 1999
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Dual Voltages A harder problem

• Layout synthesis with dual voltages major
  geometric constraints

VL
VH
VH
GND
feedthrough
VL
H
L
OUT
IN
H
L
? ? ?
GND
H -- High Voltage Block L -- Low Voltage Block
Cell Library with Dual Power Rails
Layout Structure
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Placement References

• C. J. Alpert, T. Chan, D. J.-H. Huang, I. Markov,
  and K. Yan, Quadratic Placement Revisited,Proc.
  34th IEEE/ACM Design Automation Conference, 1997,
  pp. 752-757
• C. J. Alpert, J.-H Huang, and A. B. Kahng,
  Multilevel Circuit Partitioning, Proc. 34th
  IEEE/ACM Design Automation Conference, 1997, pp.
  530-533
• U. Brenner, and A. Rohe, An Effective Congestion
  Driven Placement Framework, International
  Symposium on Physical Design 2002, pp. 6-11
• A. E. Caldwell, A. B. Kahng, and I.L. Markov,
  Can Recursive Bisection Alone Produce Routable
  Placements,Proc. 37th IEEE/ACM Design Automation
  Conference, 2000, pp 477-482
• M.A. Breuer, Min-Cut Placement, J. Design
  Automation and Fault Tolerant Computing, I(4),
  1997, pp 343-362
• J. Vygen, Algorithms for Large-Scale Flat
  Placement, Proc. 34th IEEE/ACM Design Automation
  Conference, 1988,pp 746-751
• H. Eisenmann and F. M. Johannes, Generic Global
  Placement and Floorplanning, Proc. 35th IEEE/ACM
  Design Automation Conference, 1998, pp. 269-274
• S.-L. Ou and M. Pedram, Timing Driven Placement
  Based on Partitioning with Dynamic Cut-Net
  Control, Proc. 37th IEEE/ACM Design Automation
  Conference, 2000, pp. 472-476
• C.M. Fiduccia and R.M. Mattheyses, A linear time
  heuristic for improving network partitions, Proc.
  ACM/IEEE Design Automation Conference. (1982) pp.
  175 - 181.