Congestion Reduction During Placement Based on Integer Programming

1
Congestion Reduction During Placement Based on
Integer Programming

• Xiaojian Yang Ryan Kastner Majid
  Sarrafzadeh
• Embedded and Reconfigurable System Lab
• Computer Science Department, UCLA

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Outline

• Introduction
• Previous Work on Congestion
• Integer Linear Programming(ILP) Formulation
• Approximation Algorithms
• Congestion Reduction based on ILP solution
• Experimental Results
• Conclusion

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Introduction

• Main Goals in Placement
• Minimizing Chip Area (old)
• Routability and Timing (modern)
• Objectives/Cost for Routability
• Cut, Wirelength, Congestion
• Why congestion?
• Shorter Bounding Box ? Better Routability
• Congestion models routability better

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Previous Work on Congestion

• Mayrhofer and Lauther, ICCAD90.
• Partitioning based method
• Cheng, ICCAD94
• RISA model used in Simulated Annealing
• Parakh et. al., DAC98
• Quadratic Placement combined with Area Router
• Wang and Sarrafzadeh, ISPD99, ISPD00
• Post-processing after global placement
• Congestion Estimation
• Yang et.al, Congestion Estimation at early
  placement based on Rents Rule
• Lou et. al, Congestion Estimation at late
  placement stages using probabilistic analysis

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Our Contribution

• Work Summary
• Post-processing step to reduce congestion
• Routing-estimation for congestion cost
• Reduce congestion in an enlarged area by moving
  cells
• Our Main Contribution
• Global Picture for Congestion Problem
• ILP based congested spot expansion to alleviate
  congestion
• Approximation algorithm for ILP

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Congestion Cost

• Routing Estimation --- Bounding Box Model

k-termimal nets Net weight q(k)
Cheng ICCAD94
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Congestion Cost

• Routing Estimation --- Bounding Box Model

k-termimal nets Net weight q(k)
Cheng ICCAD94
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Congestion Cost

• Congestion Cost Function

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Congested Spot

• Identify congested spots
• Alleviate congestion in the expanded area

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Congestion Alleviation

• Conflict between expanded areas
• How big the expanded area should be?

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Problem

• Two expansion areas for each congested spot
• Congestion degree after expanding
• Minimize the maximum congestion degree over the
  entire area

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ILP Based Approach

• For congested spot k
• xk0 small expansion, xk1 large expansion
• For bin (i, j), define incremental degree

bin(i,j)
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ILP Based Approach
Minimize
Subject to
bin(i,j)
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Approximation Algorithm
Threshold Rounding
Relaxation
Solve the LP
Rounding
2-approximation algorithm
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a-Approximation Algorithm
a-approximation algorithm
Proof
a 1.5 at p0.22
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Congestion Reduction Flow
Wirelength Minimization Placement
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Experimental Setup
(Dragon)
(Labyrinth)
Wirelength Minimization
Congestion Reduction
Global Routing
Circuits
output1
Dragon produces comparable placement with
commercial tools
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Experimental Results
Congestion reduction in placement affects routing
result Runtime 11s389s for circuit size 12,000
67,000 (Pentium 733MHz)
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Bounding Box Wire Length
Wirelength is no longer a good measurement of
routability
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Routed Wire Length
Congestion models routability better
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Experimental Results (contd)
Comparison between single expansion and double
expansion
circuit ibm02
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Summary

• Congestion reduction as a post-processing
• ILP based congestion reduction control
• Approximation algorithms with good bound
• Future Work
• Extend the approach using ILP instead of 0-1 ILP
• Web site http//www.cs.ucla.edu/xjyang/iccad