lecture4_partition2

8/12/2019 lecture4_partition2

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VLSI Physical Design Automation

Prof. David Pan

[email protected]

Office: ACES 5.434

Lecture 4. Circuit Partitioning (II)


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Recap of Kerni!an"#in$s A%orit!&

Pair-ise e!change o" no#es to re#uce cut si$e

Allo cut si$e to increase tem%orarily ithin a %ass

Com%ute the gain o" a sa%

&e%eat

Per"orm a "easi'le sa% o" ma! gainar sa%%e# no#es *loce#+,

%#ate sa% gains,

ntil no "easi'le sa%,

in# ma! %re"i! %artial sum in gain se/uence g10 g20 0 gm

ae corres%on#ing sa%s %ermanent.

Start another %ass i" current %ass re#uces the cut si$e

(usually conerge a"ter a "e %asses)

u

u

loce#


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'iduccia"(att!e)ses A%orit!&

**A #inear"ti&e +euristicsA #inear"ti&e +euristicsfor ,&provin -etor/ Partitions0for ,&provin -etor/ Partitions0

1212t!t!DAC paes 15"11 126.DAC paes 15"11 126.


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'eatures of '( A%orit!&

7 (odification of K# A%orit!&:

8 Can !and%e non"unifor& vertex ei!ts 9areas

8 A%%o un;a%anced partitions

8 Extended to !and%e !)perrap!s

8 C%ever a) to se%ect vertices to &ove run &uc! faster.


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Pro;%e& 'or&u%ation

7 ,nput: A !)perrap! it!8 Set vertices p

8 Area aufor eac! vertex u in


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,deas of '( A%orit!&

7 Si&i%ar to K#:

8 Hor/ in passes.

8 #oc/ vertices after &oved.

8 Actua%%) on%) &ove t!ose vertices up to t!e &axi&u& partia%

su& of ain.

7 Difference fro& K#:

8 -ot exc!anin pairs of vertices.

(ove on%) one vertex at eac! ti&e.8 !e use of ain ;uc/et data structure.


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Iain Juc/et Data Structure

Ce%%?

Ce%%?

(ax

Iain

Fp&ax

"p&ax

1 6 n


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"1

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'( Partitionin:


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i&e Co&p%exit) of '(

7 'or eac! pass

8 Constant ti&e to find t!e ;est vertex to &ove.

8 After eac! &ove ti&e to update ain ;uc/ets is proportiona%

to deree of vertex &oved.

8 ota% ti&e is O9p !ere p is tota% nu&;er of pins

7 -u&;er of passes is usua%%) s&a%%.


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Ratio Cut O;Lective

;) Hei and C!en

**oards Efficient +ierarc!ica% Desins ;)oards Efficient +ierarc!ica% Desins ;)Ratio Cut Partitionin0Ratio Cut Partitionin0

,CCAD paes 1:62"31 122.,CCAD paes 1:62"31 122.


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Ratio Cut O;Lective

7 ,t is not desira;%e to !ave so&e pre"defined ratio on

t!e partition sies.

7 Hei and C!en proposed t!e Ratio Cut o;Lective.

7 r) to %ocate natura% c%usters in circuit and force t!e

partitions to ;e of si&i%ar sies at t!e sa&e ti&e.

7 Ratio Cut R@B> C@B9== x =B=

7 A !euristic ;ased on '( as proposed.


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Sanc!is A%orit!&

**(u%tip%e"a) -etor/ Partitionin0(u%tip%e"a) -etor/ Partitionin0,EEE rans. Co&puters,EEE rans. Co&puters

391:N6"1 122.391:N6"1 122.


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Partitionin:

Si&u%ated Annea%in


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State Space Searc! Pro;%e&

7 Co&;inatoria% opti&iation pro;%e&s 9%i/e partitionincan ;e t!ou!t as a State Space Searc! Pro;%e&.

7 A State is Lust a confiuration of t!e co&;inatoria%

o;Lects invo%ved.

7 !e State Space is t!e set of a%% possi;%e states

9confiurations.

7 A -ei!;our!ood Structure is a%so defined 9!ic!

states can one o in one step.

7 !ere is a cost correspondin to eac! state.

7 Searc! for t!e &in 9or &ax cost state.


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Ireed) A%orit!&

7 A ver) si&p%e tec!niue for State Space Searc!Pro;%e&.

7 Start fro& an) state.

7 A%a)s &ove to a nei!;or it! t!e &in cost 9assu&e

&ini&iation pro;%e&.

7 Stop !en a%% nei!;ors !ave a !i!er cost t!an t!e

current state.


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Pro;%e& it! Ireed) A%orit!&s

7 Easi%) et stuc/ at %oca% &ini&u&.

7 Hi%% o;tain non"opti&a% so%utions.

7 Opti&a% on%) for convex 9or concave for &axi&iation

funtions.

Cost

State


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Ireed) -ature of K# '(7 K# and '( are almostreed) a%orit!&s.

7 Pure%) reed) if e consider a pass as a *&ove0.

Cut t !ere is t)pica%%) around .25

8 t > e"tt !ere is t)pica%%) around .

8 ......


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Paper ;) o!nson Araon (cIeoc! andSc!evon on Jisectionin usin SA

**Opti&iation ;) Si&u%ated Annea%in:Opti&iation ;) Si&u%ated Annea%in:

An Experi&enta% Eva%uation Part ,An Experi&enta% Eva%uation Part ,

Irap! Partitionin0Irap! Partitionin0

Operations Researc! 3:N5"26 122.Operations Researc! 3:N5"26 122.


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!e Hor/ of o!nson et a%.

7 An extensive e&pirica% stud) of Si&u%ated Annea%inversus ,terative ,&prove&ent Approac!es.

7 Conc%usion: SA is a co&petitive approac! ettin

;etter so%utions t!an K# for rando& rap!s.

Re&ar/s:8 -et%ists are not rando& rap!s ;ut sparse rap!s it! %oca%

structure.

8 SA is too s%o. So K#'( variants are sti%% &ost popu%ar.

8 (u%tip%e runs of K#'( variants it! rando& initia% so%utions&a) ;e prefera;%e to SA.


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!e se of Rando&ness

7 'or an) partitionin pro;%e&:

7 Suppose so%utions are pic/ed rando&%).

7 ,f =I==A= > r Pr9at %east 1 ood in 5r tria%s > 1"91"r5Er

7 ,f =I==A= > .1 Pr9at %east 1 ood in 5 tria%s > 1"

91".15KKK> .2233

I

A%% so%utions 9State space

Iood so%utionsA


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Addin Rando&ness to K#'(

7 ,n fact ? of ood states are extre&e%) fe. !ereforer is extre&e%) s&a%%.

7 -eed extre&e%) %on ti&e if Lust pic/in states

rando&%) 9it!out doin K#'(.

7 Runnin K#'( variants severa% ti&es it! rando&initia% so%utions is a ood idea.

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lecture4_partition2