A New Effective Congestion Model in Floorplan Design

1
A New Effective Congestion Model in Floorplan
Design

• Yi-Lin Hsieh and Tsai-Ming Hsieh
• Department of Information and Computer
  Engineering
• Chung Yuan Christian University
• Chung-Li, Taiwan, R.O.C.
• DATE 04
• Feb. 19 , 2004

2
Outline

• Introduction
• Problem Formulation
• Probabilistic Analysis
• Motivation
• Irregular-Grid Congestion Model
• Experimental results
• Conclusion

3
Introduction

• Floorplanning in physical design
• Problem
• Given a set of modules, find a non-overlapping
  placement of modules
• Expressions and algorithms
• Normalized Polish expression, sequence pair,
  Btree, , etc.
• Simulated annealing algorithm, genetic algorithm,
  simulated tempering algorithm, , etc.

4
Introduction(cont.)

• Objectives
• Minimize
• Area
• Total interconnection length
• Wire congestion
• Delay
• With constraints
• Boundary
• Alignment and abutment
• Frame shape

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Introduction
Introduction(cont.)

• Wire congestion
• Influence
• Decrease the performance of circuits
• Cause an unroutable design
• Affect timing constraint and delay constraint
• Congestion model for estimation
• Accuracy - correspond to the post-route result
• Efficiency - be embedded in iterative algorithms

6
Problem Formulation

• Input
• Areas and aspect ratios of m soft modules M1, M2,
  , Mm
• Netlist of n nets N1, N2, , Nn
• Output
• A legal floorplan which achieves some
  optimization objects
• Objectives
• Minimize the area of floorplan
• Minimize the interconnection length
• Minimize the estimated cost of wire congestion
• Major work
• Propose a new effective congestion model to
  estimate the congestion of a floorplan solution

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Problem Formulation(cont.)

• Beforehand specification
• Floorplanning methodology
• Normalized Polish expression
• Simulated annealing algorithm
• Determination of pin locations
• Intersection-to-intersection
• Multi-pin net
• Divided into 2-pin nets by minimum spanning tree

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Problem Formulation(cont.)

• Assumption of routing
• Routing with Manhattan distance
• Definition
• The region which may be passed through by a net
  is
• A point -
• ignored
• A line -
• excluded from our computing formulas
• A rectangular range -
• called the routing range of the net

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Problem Formulation(cont.)

• Type of a net
• Type I
• One pin p1i is lower-left to the other pin p2i
• Type II
• One pin p1i is upper-left to the other pin p2i

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Probabilistic Analysis

• Proposed by
• J. Lou et al.(16ISPD 2001) originally in
  placement
• C. W. Sham et al.(25ISPD 2002) in floorplanning
• Estimating steps
• Divide a floorplan solution into 2-D array with
  fixed-size grids

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Probabilistic Analysis (cont.)

• Compute the routes for a net passing through a
  grid
• Example

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Probabilistic Analysis (cont.)

• Assume Ni covers g1i g2i grids. Assign the most
  lower-left grid to be (0, 0). For a grid at (x,
  y) where
• 0 ? x lt g1i and 0 ? y lt g2i , we define Tai(x, y)
  to be the number of routes starting from the grid
  including p1i (lower-left) to (x,y),
• and Tbi(x, y) to be the number of routes starting
  from the grid including p2i (upper-left) to
  (x,y).
• Tai(x, y) Tbi(x, y) is the number of routes for
  a net
• passing through a grid at (x, y)
• Tbi(x, y) Tai(g1i 1 x, g2i 1 y)

(g1i-1, g2i-1)
g2i
(x, y)
(0, 0)
g1i
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Probabilistic Analysis (cont.)

• Compute the probability for a net passing through
  a grid
• For a Type 1 net
• The number of total routes is Tai(g1i 1, g2i
  1)
• The probability for Ni passing through a grid at
  
• (x, y) is

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Probabilistic Analysis (cont.)

• Process all the nets and obtain the summation of
  probabilities for passing through a grid to be
  the congestion cost of that grid
• Use the average cost of the top 10 most
  congested grids to be the congestion cost of the
  floorplan solution
• Time complexity O(n G1 G2)
• n the number of nets
• G1 G2 the partitioning grids of the floorplan

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Motivation

• Weakness of previous model
• The number of fixed-size grids affects the
  accuracy greatly
• The number of fixed-size grids is completely
  determined by users

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Motivation (cont.)

• Waste time on estimating the meaningless and less
  congested regions

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Motivation (cont.)

• Observation
• The way to partition estimating grids is
  important to a congestion model
• The information provided by nets is related to
  the condition of wire congestion
• Our new congestion model
• According to the routing ranges
  of nets to divide the floorplan
• Provide a more accurate and
  rapid congestion model

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Irregular-GridCongestion Model

• Overview
• Introduction to Irregular-Grid and our estimating
  steps
• The computation of the probability for a net
  passing through an IR-grid
• Accurate approximating formulas for the
  computation of the probabilities
• Analysis of the accuracy of the approximating
  formulas
• The summary of the characteristics and
  excellences in our Irregular-Grid congestion model

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Irregular-GridCongestion Model (cont.)

• Irregular-Grid
• Partitioned by routing ranges of nets
• IR-grid
  The partitioned rectangular grids
  with irregular sizes
• Each pin will be always on the partitioning lines
• Each net will pass through several IR-grids

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Irregular-GridCongestion Model (cont.)

• The congestion cost of an IR-grid is related to
• The summation of the probabilities for all nets
  passing through the IR-grid
• The size of the IR-grid
• Estimating steps
• 1) Divide a floorplan solution into
  Irregular-grid
• with IR-grids
• 2) Compute the routes for a net passing through
  
• an IR-grid
• 3) Compute the probability for a net passing
• through an IR-grid

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Irregular-GridCongestion Model (cont.)

• 4) Process all the nets and obtain the summation
  of
• probabilities for all nets passing through a
  grid
• 5) The congestion cost of a unit area in an
  IR-grid is
• determine by
• sum of probabilities for all nets
  passing through the IR-grid
• the size of the
  IR-grid
• 6) Use the average cost of the top 10 most
• congested unit area to be the congestion cost
  of
• the floorplan solution

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Irregular-GridCongestion Model (cont.)

• Compute the routes for a net passing through an
  IR-grid
• Example
• The number of routes passing through the IR-grid
  is (5x115x1)(4x510x420x3)(35x3) 245

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Irregular-GridCongestion Model (cont.)

• There exists an IR-grid I in the routing range
  of Ni. The lower-left corner is at (x1I, y1I) and
  the upper-right corner is at (x2I, y2I)
• Ni is Type I
• the probability for Ni passing through I is
• Ni is Type II
• the probability for Ni passing through I is

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Irregular-GridCongestion Model (cont.)

• Accurate approximating formulas
• Goal
• Find an accurate approximating formula to the
  probability formula for a net passing through an
  IR-grid, and
• make the time complexity of the computation be
  constant time
• Inducing process
• For a Type I net Ni

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Irregular-GridCongestion Model (cont.)
Original formula gtgt Hypergeometric Distribution
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Irregular-GridCongestion Model (cont.)
Hypergeometric Distribution gtgt Normal
Distribution
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Irregular-GridCongestion Model (cont.)
The definite integral can be easily calculated
by Simpsons rule of integration in constant
time.
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Irregular-GridCongestion Model (cont.)

• Analysis of accuracy and modification
• Accuracy of approximating formulas
• Observation

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Irregular-GridCongestion Model (cont.)

• Advantages
• Provide a unified basis to partition estimated
  region
• Reduce the dependence between the number of grids
  and accuracy
• Reduce the run time and increase the accuracy
• Induce effective approximating formulas and make
  the time complexity of the computation be
  constant time
• Total time complexity is O(n3) O(n G1 G2)

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Experiment results

• Platform
• Pentium IV 2.4GHz PC with 256 RAM
• Microsoft Windows XP
• Microsoft Visual C 6.0
• MCNC Benchmarks

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Experiment results (cont.)

• Experiment I
• Improvement of congestion

Optimize area and wire length only VS
Optimize area, wire length and congestion with
Irregular-Grid model
Comparison results
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Experiment results (cont.)

• Experiment II
• Covergency of congestion costs in SA
• process (ami 33)
• A IR-grid
• B 10 10 µm2
• fixed grid
• C 50 50 µm2
• fixed grid

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Experiment results (cont.)

• Experiment III Run time(ami33)

Optimize congestion only with Irregular-Grid model
Optimize congestion only with Fixed-grid model
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Conclusion

• We propose a concept of irregular-grid to build
  up a new effective congestion model in
  flooplanning design.
• Our new model could estimate congestion of a
  floorplan more accurately in less run time and
  could be embedded into a floorplanner.
• Three experimental results validate our
  theoretical work and our model performs well in
  congestion estimating of floorplans.
• In the future, we want to test the results of our
  model by a real global router to verify the
  practical efficiency.

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• Thank You !