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!