Improved Cut Sequences for Partitioning Based Placement

Mehmet Can YILDIZ and Patrick H. Madden State University of New York at Binghamton

Computer Science Department DAC 2001

Outline

Introduction Previous Work Optimal generation of cut

sequences Experimental results Conclusion

Introduction Placement by recursive partitioning is

one of the oldest approaches Cut sequence appears to have

increasing impact as circuit sizes grow. Use mathematical foundation to find an

optimal cut sequence with some assumptions

Previous Work Placement problem

Inputs: a set of cells, a netlist. Goal: Find the best position for each cell accordi

ng to appropriate cost functions. Circuit placement approaches

Linear programming Force directed Partitioning based methods (focus on here)

Previous Work

Previous Work A number of cut sequence

(a) VHHVVVV (b) QQQQQ (c) HHHHVVVV (d)

Previous Work

Other cut sequence Capo - based on the relative height and w

idth of a region Feng Shui - utilizes an aspect ratio (height to

width) to determine cut direction

Optimal generation of cut sequences

Goal : Obtain optimal cut sequences for

placement by partitioning. Sequences determine the direction of

cuts to perform, and the balance between partitions.

Optimal generation of cut sequences Assume only two pin nets and Rent’s r

ule holds Rent’s rule

pCkT T : propagated terminalsC : areaP : generally between 0.3 and 0.7K : constant

C

Estimation of Cut Sizes

C0

c1 c2cut nets = 2/)( 021 TTT

p

p

p

CkT

CkT

CkT

22

11

00

Estimation of Wire Lengths

Cut length function CL(r1,c1,r2,c2) compute the wire length f

or nets cut by partition

estimate of the wire length for any sequence of cuts by counting the wirelength of each net the first time that it is cut.

CL(r,2,r,c-2) C0 c2c1r

c2 c-2

cutsize * ( x * weightH + y * weightV) )

Dynamic Programming Formulation For the r by c region, wish to minimize the t

otal estimated wire length. consider a variety of possible horizontal an

d vertical cut locations. Each partition

Total wire length = (subregions’ wire length) + (contribution of nets cut by the partition)

C0c1 c2

Optimal generation of cut sequences WL(r,c) : optimal wire length for r by c region CL : cut length function

C0 c2c1r

c

2 c-2

An optimal cut sequence table

• record the direction and balance of an optimal cut to minimize total wire length

An optimal cut sequence table Two properties

In all cases, optimal sequences include bisections, and not partitions of arbitrary balance.

If the ratio of rows to column exceeds a threshold value, and optimal sequence partitions horizontally.

Change the estimated Rent parameter or wire length estimation function, the general nature of the tables does not change.

An optimal cut sequence table We can choose an appropriate cut direction

by simply considering the ratio of region height to width.

This is the method employed by Feng Shui Lack an method to find an appropriate aspe

ct ratio, and determine by experiment.

Experimental results

• Capo - aspect-ratio(1) based sequence• Modified Capo - modified cut sequences more closely to Feng Shui.• Feng Shui - aspect-ratio(2) based sequence

cut sequence has greatest impact on the largest benchmarks

Each tool run 10 times of benchmark

Conclusion resolved the problem of cut sequence generati

on for partitioning based placement show that bisection is preferable to unbalance

d partitions Anticipate similar changes can result in signific

ant improvements on other partitioning-based placement tools.