A Stable Fixed-outline
Floorplanning Method
Song Chen and Takeshi Yoshimura
Graduate School of IPS, Waseda University
March, 2007
Outline
• Problem
• Previous Work
• Fixed-outline Floorplanning
– Overview
– Objective Function
– Solution Perturbation
• Experimental Results
• Conclusions
Problem
• Given
– A set of rectangular blocks among which connections
(nets) exist
– Specified width wi and height hi for each block bi
– Specified rectangular region: W0, H0. (Fixed-outline)
H0
W0
• The fixed-outline floorplanning is to determine
coordinates for each block such that
– There is no overlapping between any two blocks.
– All the blocks are placed inside the specified region
(fixed-outline)
– Some objectives, such as wire-length, etc., are
optimal.
Outline
• Problem
• Previous Work
• Fixed-outline Floorplanning
– Overview
– Objective Function
– Solution Perturbation
• Experimental Results
• Conclusions
Previous Work
• S. Adya and I. Markov, ICCD’01 TCAD’03
(Parquet)
– New objective functions; New types of move.
• C. Lin, et al., ASPDAC’04
– Evolutionary search-based robust fixed-outline
floorplanning; Fixed-outline constraint only.
• R. Liu et al., ISCAS’05.
– Instance augmentation; Fixed-outline constraint only.
• T.C. Chen and Y.W. Chang, ISPD’05.
– Adaptive Fast-SA; Weights in the cost function
changed Dynamically.
Previous Work (Cont’)
• The existing fixed-floorplanning methods
work well when fixed-outline constraint is
the only objective.
– Poor success rates when optimizing wire and
other objectives.
– And when the aspect ratios are far away from
one (W=H).
Outline
• Problem
• Previous Work
• Fixed-outline Floorplanning
– Overview
– Objective Function
– Solution Perturbation
• Experimental Results
• Conclusions
Overview of Floorplanning
• Sequence Pair is used for
floorplan representation
• Objective function
• Solution perturbation
– Remove a block randomly
– Compute the floorplan of the
blocks except the removed
one
– Select fixed number of
candidate insertion points
for the removed block by
enumerating insertion points
– Choose for the removed
block one of the candidate
insertion points randomly
Outline
• Problem
• Previous Work
• Fixed-outline Floorplanning
– Overview
– Objective Function
– Solution Perturbation
• Experimental Results
• Conclusions
Objective Function
• Objective functions used in the existing fixedoutline floorplanners.
– Low success rate when given larger aspect ratios.
– Low success rate when other objectives exist.
• since the function values hardly reach zero when competitions
from other objectives exist.
Ew
Eh
– A trade-off between area
and aspect ratios.
H0
Fixed-outline
W0
Objective Functions (Cont’)
• Calculate chip area costs for fixed-outline
floorplanning (assume λ>1)
– EW = max(W −W0, 0)
– EH = max(H − H0, 0)
– C1 and C2 are user-defined constants
– λ is the aspect ratio.
EH
Ew
• High success rates for large aspect ratios
• High success rate when Hcombined with
other objectives
0
W0
Outline
• Problem
• Previous Work
• Fixed-outline Floorplanning
– Overview
– Objective Function
– Solution Perturbation
• Experimental Results
• Conclusions
Solution Perturbation –Enhanced
Remove and Insertion
• Remove a block randomly
• Insert the block
– Select some candidate
insertion points (CIP, totally
100 here) by Enumerating
Insertion Points (EIP) (rough
estimation)
– Select from the CIPs the
insertion point for the
removed block
Enumerate Insertion Points (EIP)
• Sequence Pair (P, M)
– (…bi…bj…, …bi…bj…)  bj is left to bi
– (…bi…bj…, …bj…bi…)  bj is below bi
– An insertion point means one position in P and one
position M -- (p, m)
• In order to evaluate an insertion point, we need to
know how much inserting a block into the
insertion point will contribute to the chip width and
height
EIP – Computing x-coordinates
• Given a Sequence Pair (P, M)
– Coordinates (with origin at the bottom-left corner
of the chip) of a block bi only depend on the
blocks that are left to bi in the sequence M
( a b c e d f g, a c b d e g f )
– Coordinates of the blocks that are right to bi in
both P and M are larger than that of bi
( a b c e d f g,
acbdegf)
EIP— Computing x-coordinates (Cont’)
• Based on the previous observations, we can
compute the x-coordinates of all insertion points
– Given a sequence pair (P, M) = (f c e d b a, c b f a d e)
Distance of CIPs (p, c+) to the left
boundary: p is before c in P, 0; p is
after c in P: 2.
( f c e d b a,
cbfade)
Distance of CIPs (p, b+) to the left
boundary: p is before c in P, 0; p is
between b and c in P, 2; p is after
b: 4.
( f c e d b a, c b f a d e )
Enumerating Insertion Points
• Following pairs of sequences are scanned to
compute the distance of an insertion point to
the chip boundaries
–
–
–
–
(P, M): Distance to the left boundary
(Pr, M): Distance to the bottom boundary
(Pr, Mr): Distance to the right boundary
(P, Mr): Distance to the top boundary
P
top
left
M
Mr
right
bottom
Pr
Enumerating Insertion Points (Cont’)
• The enumerating is similar to the computation of xcoordinates, but, for each time, we have to scan
four lists simultaneously.
• Without consideration of wire length, the complexity
of enumerating is O(n2), which is linear with the
number of insertion points.
• During the enumerating, we take into account only
the nets that have connections to the removed
block.
– a linear piecewise function is used for wire-length
calculation.
Outline
• Problem
• Previous Work
• Fixed-outline Floorplanning
– Overview
– Objective Function
– Solution Perturbation
• Experimental Results
• Conclusions
Experimental Results-Success Rate
• white space percent 10%, all blocks are hard,
and the aspect ratios are chosen from the range
[1,3] with interval 0.5.
• Success rate: Parquet (SP) 60%, Parquet
(BTree) 100%, NTU-FOFP 94%, IARFP 100%.
• Runtime: IARFP is the least one. (a tenth part)
Experimental results-Wire
• White space 10%, 50 runs for n100, 10 runs for
n200 and n300.
• Success rate: IARFP 100%, NTU-FOFP 45%, and
Parquet (SP) 34%
• Wire: IARFP achieved 12% and 7% improvement
• Runtime: IARFP spent much less time.
Experimental Results-Objective Function
• Embed objective function into the existing fixedoutline floorplanner NTU-FP
– White space: 10%
– Aspect ratios: From the range [1,3] with interval 0.5
Outline
• Problem
• Previous Work
• Fixed-outline Floorplanning
– Overview
– Objective Function
– Solution Perturbation
• Experimental Results
• Conclusions
Conclusions
• We developed a stable fixed-outline
floorplanner
– A new method for calculating area costs in
fixed-outline floorplanning is proposed.
– An enhanced remove and insertion solution
perturbation method is implemented based
on enumerating insertion points.
• Compared with the existing method, the
proposed method is very effective and
efficient.
• Thanks for your attentions!