Post on 17-Jan-2016
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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)
• 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.
W0
H0
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 fixed-outline 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.
– A trade-off between area and aspect ratios.
Ew
Eh
H0
W0
Fixed-outline
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.
• High success rates for large aspect ratios• High success rate when combined with
other objectives
Ew
EH
H0
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
– 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, a c b d e g f )
( a b c e d f g, a c b d e g f )
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)
( f c e d b a, c b f a d e )( 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.
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.
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
M
Mr
Pr
top
left
bottom
right
Enumerating Insertion Points (Cont’)
• The enumerating is similar to the computation of x-coordinates, 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 fixed-
outline 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!