A Study on Unroutable Placement Recognition

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A Study on Unroutable Placement Recognition

• ISPD 2014
• Wen-Hao Liu1,2, Tzu-Kai Chien2,and Ting-Chi
  Wang2
• 1Cadence Design Systems
• 2National Tsing Hua University, Taiwan

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Outline

• Introduction
• Unroutable Region Recognition
• Window-based Layout Scanning
• Window Dimension Determination
• Lower Bound of Total Overflow Identification
• Experimental Results
• Conclusions

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Motivation

• Routing is difficult and time-consuming

hours
days

• Routability estimation is critical

This placement is routable or not?
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Motivation

• If we can know a placement is unroutable earlier,
  we can avoid wasting time on routing the design.
• Recently, many routability estimation works are
  published, but no one can guarantee a design must
  be unroutable

Get an feasible routing result
Impossible
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Objective

• ISPD11, DAC12, and ICCAD12 placement contests
  release many placement results to public domain
• For some hard-to-route placements, no global
  router has been able to obtain overflow-free
  routing results so far
• This work attempts to recognize these placements
  are routable or not to global routers

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Global Routing Model

• A placement will be modeled into a 3D grid graph
• The goal of global routing is to identify global
  routing paths to connect each pin of each net
• The objective of global routing is to minimize
  overflows and wirelength

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Outline

• Introduction
• Unroutable Region Recognition
• Window-based Layout Scanning
• Window Dimension Determination
• Lower Bound of Total Overflow Identification
• Experimental Results
• Conclusions

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Unroutable Region

• If any unroutable region exist, the placement
  must have no overflow-free routing result

• Given a region R
• S(R) the set of the outgoing nets of R
• c(R) total capacity of the bridge edges of R
• If S(R)gtc(R), R is unroutable because overflow
  must happen

Outgoing net
Intra net
bridge edge
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Window-based Layout Scanning

• We propose a window-based layout scanning
  algorithm to find out unroutable regions
• This method can find out every region whose
  dimensions are not larger than the sliding window
• How to decide the window dimension is critical

R1
R5
R3
R6
R7
W 3 H 3
R8
R4
R2
R9
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Sliding Window Scanning

• Use a sliding window to scan the entire layout
• Explore every possible rectangular region at the
  bottom-left corner in the sliding window

.
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Fast Unroutable Region Determination

• If S(R)gtc(R), we can recognize that R is
  unroutable. However, how to obtain S(R) and
  c(R) faster is an issue
• A lookup table is built so that querying c(R) can
  be done in a constant time
• S(R3) S(R1)?S(R2)-I(R3), where R3 comprises R1
  and R2, I(R3) is the set of intra nets in R3

R1
R2
R3
Intra net
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Building S(R)

• We explore each rectangular region in a
  particular order
• When a region is processed, its sub-regions are
  processed already
• Thus, the outgoing net set of a region can be
  obtained by merging the outgoing net set of its
  sub-regions

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Outline

• Introduction
• Unroutable Region Recognition
• Window-based Layout Scanning
• Window Dimension Determination
• Lower Bound of Total Overflow Identification
• Experimental Results
• Conclusions

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Window Dimension Determination

• Different widths and heights of a sliding window
  will largely impact the recognition rate of
  unroutable regions
• We propose a two-stage method to decide a width w
  and a height h for the sliding window such that w
  x h ? Amax
• Region sampling, and then dimension selection

Unroutable regions
Sliding windows whose areas are not larger than 9
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Best Dimension
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Region Sampling

• The goal of this stage is to identify a set of
  sampling regions with higher weights
• The weight of a region is the ratio of S(R) to
  c(R)
• Sampling process
• Select n regions whose size is 1x1 with the
  highest weights
• Expand each selected region iteratively until any
  extension would make its area exceed Amax
• Insert the final expanded region and the regions
  whose weights are larger than 1 into the sampling
  region set

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Width and Height Selection

• The goal of the next stage is to decide the
  windows dimension such that the total weight of
  the sampling regions covered by the sliding
  window is maximized and w x h ? Amax
• We present a dynamic programming algorithm to
  solve this problem

Amax lt 30
OurAlgorithm
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Outline

• Introduction
• Unroutable Region Recognition
• Window-based Layout Scanning
• Window Dimension Determination
• Lower Bound of Total Overflow (LBTO)
  Identification
• Experimental Results
• Conclusions

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LBTO Identification

• The intrinsic overflow of unroutable region R is
  S(R) c(R)
• If every unroutable region is independent, we can
  add up the intrinsic overflow of every region to
  obtain the LBTO
• If more than one region shares a bridge edge, we
  only count the intrinsic overflow of one of the
  regions

R1
R3
R4
R2
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LBTO Identification

• Build a conflict graph, a conflict edge between
  vi and vj means that Ri and Rj share at least a
  bridge edge
• The weight of vi denotes the intrinsic overflow
  of Ri
• Solve the maximum-weight independent set problem
  on the conflict graph to identify LBTO

v1
v3
v2
v7
v5
v4
v9
v6
v8
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Outline

• Introduction
• Unroutable Region Recognition
• Window-based Layout Scanning
• Window Dimension Determination
• Lower Bound of Total Overflow Identification
• Experimental Results
• Conclusions

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Unroutable Placement Recognition

• Select 23 hard-to-route placements from ISPD08
  global routing and ISPD11 placement contests
• So far no global router can obtain overflow-free
  routing results for these hard-to-route testcases

Wins W x H 5 x 5 15 x 15 30 x 30 50 x 50 100 x 100
Uroutable placements 3 11 13 15 16
Unroutable regions 0.2 x 104 2.5 x 104 11.9 x 104 30.3 x 104 137.1 x 104
Time (sec) 5.62 90 638 3014 25374
running with 16 threads on 2.4GHz Intel
Xeon-based Linux server with 96GB memory
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Window Dimension Determination

• We manually set different widths and heights for
  the sliding window such that its area is 900 to
  see the difference of recognition rates
• Then, we use the proposed method to automatically
  determine the window dimension to compare with
  the manual method

WindowsW x H 15 x 60 20 x 45 30 x 30 45 x 20 60 x 15 Auto.
Uroutable placements 11 12 13 12 11 13
Unroutable regions 13 x 104 14.6 x 104 11.9 x 104 6.5 x 104 3.7 x 104 14.8 x 104
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LBTO Identification

• Use NCTUgr to route unroutable placements to see
  the gap between the total overflow identified by
  NCTUgr and the lower bound of total overflow
  (LBTO) identified by this work

The placements withsmall total overflow gap
The placements withlarge total overflow gap
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Outline

• Introduction
• Unroutable Region Recognition
• Window-based Layout Scanning
• Window Dimension Determination
• Lower Bound of Total Overflow Identification
• Experimental Results
• Conclusions

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Conclusions

• We propose a window-based layout scanning
  algorithm to recognize unroutable regions
• The proposed two-stage method can identify a good
  window dimension for the sliding window
• Region sampling
• Window dimension selection
• This work uses a maximum-weight independent set
  algorithm to identify the lower bound of total
  overflow for unroutable layouts

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Solving MWIS Problem

• We adopt a heuristic algorithm to solve MWIS
  problem
• Sort nodes based on the following scoring
  function in a nonincreasing order
• Select each unmarked node one-by-one and mark its
  neighbors.
• If a node is marked, it will not be selected.
• If more powerful MWIS algorithm is adopted,
  tighter LBTO can be obtained

(a is set to 0.1 )
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