8 query optimization

8/18/2019 8 Query Optimization

1/53

Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/1

Outline•Intrdu!tin

•Ba!"#rund

•Distributed Database Desi#n

•Database Inte#ratin

•Se$anti! Data Cntrl

•Distributed %uer Pr!essin# O'er'ie(

%uer de!$)sitin and l!alizatin

Distributed *uer )ti$izatin

•Multidatabase %uer Pr!essin#

•Distributed Transa!tin Mana#e$ent•Data +e)li!atin

•Parallel Database Sste$s

•Distributed Ob,e!t DBMS

•Peer-t-Peer Data Mana#e$ent

•eb Data Mana#e$ent

•Current Issues


2/53

Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/

Ste) 0 3lbal %uerO)ti$izatinIn)ut4 5ra#$ent *uer

•5ind the best 6nt ne!essaril )ti$al7 #lbal s!hedule

Mini$ize a !st un!tin

Distributed ,in )r!essin#

Bush 's. linear trees

hi!h relatin t shi) (here9

Shi)-(hle 's shi)-as-needed

De!ide n the use se$i,ins

Se$i,in sa'es n !$$uni!atin at the e:)ense $re l!al)r!essin#.

;in $ethds

nested l) 's rdered ,ins 6$er#e ,in r hash ,in7


3/53


Cst-Based O)ti$izatin

•Slutin s)a!e

The set e*ui'alent al#ebra e:)ressins 6*uer trees7.

•Cst un!tin 6in ter$s ti$e7

I/O !st < CP= !st < !$$uni!atin !st These $i#ht ha'e di>erent (ei#hts in di>erent distributed

en'irn$ents 6?@A 's @A7.

Can als $a:i$ize thru#h)ut

•Sear!h al#rith$

( d (e $'e inside the slutin s)a!e9

:hausti'e sear!h heuristi! al#rith$s 6iterati'e i$)r'e$entsi$ulated annealin# #eneti!E7


4/53

Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/F

%uer O)ti$izatin Pr!ess

Search SpaceGeneration

SearchStrategy

Equivalent QEP

Input Query

TransformationRules

Cost Model

est QEP


5/53

Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/G

Sear!h S)a!e

•Sear!h s)a!e !hara!terizedb alternati'e e:e!utin

•5!us n ,in trees

•5r N relatins there areO6NH7 e*ui'alent ,in treesthat !an be btained ba))lin# !$$utati'it andass!iati'it rules

SELECT ENAME,RESP

FROM EMP, ASG,PROJ

WHERE EMP.ENO=ASG.ENO

AND ASG.PNO=PROJ.PNO

PR!"

#SGEMP

PR!" #SG

EMP

PR!"

#SG

EMP

▷◁ P$!

▷◁E$!

▷◁ P$!

▷◁ E$!

▷◁E$!%P$!


6/53

Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/J

Sear!h S)a!e

+estri!t b $eans heuristi!s

Perr$ unar )eratins bere binar )eratins

E

+estri!t the sha)e the ,in tree Cnsider nl linear trees i#nre bush nes

&inear "oin Tree ushy "oin Tree

R 'R (

R )

R *

R 'R ( R *R )

K

KK

KK K


7/53Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/L

Sear!h Strate#

( t $'eN in the sear!h s)a!e.

Deter$inisti!

Start r$ base relatins and build )lans b addin# ne relatin atea!h ste)

Dna$i! )r#ra$$in#4 breadth-rst

3reed4 de)th-rst

+and$ized

Sear!h r )ti$alities arund a )arti!ular startin# )int

Trade )ti$izatin ti$e r e:e!utin ti$e

Better (hen 1Q relatins

Si$ulated annealin#

Iterati'e i$)r'e$ent


8/53Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/8

Sear!h Strate#ies

•Deter$inisti!

R 'R (

R )

R *

R 'R ( R 'R (

R )

R 'R (

R )

R )R (

R '

•+and$ized

KK

K

K

K

K

KK K

K


9/53Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/R

Cst 5un!tins

• Ttal Ti$e 6r Ttal Cst7

+edu!e ea!h !st 6in ter$s ti$e7 !$)nent indi'iduall

D as little ea!h !st !$)nent as )ssible

O)ti$izes the utilizatin the resur!es

In!reases sste$ thru#h)ut

•+es)nse Ti$e

D as $an thin#s as )ssible in )arallel Ma in!rease ttal ti$e be!ause in!reased ttal a!ti'it


10/53Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/1Q

Ttal Cst

Su$$atin all !st a!trs

Ttal !st CP= !st < I/O !st < !$$uni!atin !st

CP= !st unit instru!tin !st ∗ n. instru!tins

I/O !st unit dis" I/O !st ∗ n. dis" I/Os

!$$uni!atin !st $essa#e initiatin < trans$issin



Ttal Cst 5a!trs

•ide area net(r"

Messa#e initiatin and trans$issin !sts hi#h

?!al )r!essin# !st is l( 6ast $ainra$es r

$ini!$)uters7 +ati !$$uni!atin t I/O !sts Q41

•?!al area net(r"s

C$$uni!atin and l!al )r!essin# !sts are $re r less

e*ual +ati 141.J



+es)nse Ti$e

la)sed ti$e bet(een the initiatin and the !$)letin a *uer

+es)nse ti$e CP= ti$e < I/O ti$e < !$$uni!atin ti$e

CP= ti$e unit instru!tin ti$e n. se*uentialinstru!tins

I/O ti$e unit I/O ti$e n. se*uential I/Os

!$$uni!atin ti$e unit $s# initiatin ti$e n.

se*uential $s#< unit trans$issin ti$e n. se*uential

btes



:a$)le

@ssu$e that nl the !$$uni!atin !st is !nsidered

Ttal ti$e ×$essa#e initializatin ti$e < unit trans$issin ti$e 6 x+y 7

+es)nse ti$e $a: Uti$e t send x r$ 1 t 0 ti$e t send y r$ t 0

ti$e t send x r$ 1 t 0 $essa#e initializatin ti$e< unit trans$issin ti$e x

ti$e t send y r$ t 0 $essa#e initializatin ti$e< unit trans$issin ti$e y

Site (

Site '

x units

y units

Site )


14/53Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/1F

O)ti$izatin Statisti!s

•Pri$ar !st a!tr4 size inter$ediate relatins Aeed t esti$ate their sizes

•Ma"e the$ )re!ise ⇒$re !stl t $aintain

•Si$)liin# assu$)tin4 unir$ distributin attribute 'alues in

a relatin


15/53Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/1G

Statisti!s

•5r ea!h relatin RW A1 A E AnX ra#$ented as R1 E Rr len#th ea!h attribute4 length6 Ai7

the nu$ber distin!t 'alues r ea!h attribute in ea!hra#$ent4 card6Π AiR j7

$a:i$u$ and $ini$u$ 'alues in the d$ain ea!h attribute4min6 Ai7 ma:6 Ai7

the !ardinalities ea!h d$ain4 card6domW AiX7

• The !ardinalities ea!h ra#$ent4 card6R j7 Sele!ti'it a!tr

ea!h )eratin r relatins 5r ,ins

SF K 6RS7

card6R

KS7card6R7 ∗ card6S7


16/53Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/1J

Inter$ediate +elatin Sizes

Sele!tin

size6R7 card6R7 ×length6R7

card6σF 6R77 SF σ6F 7 ×card6R7

(here S F σ6 A value7 card6Y A6R77

1

S F σ6 A value7 max 6 A7 min6 A7

max 6 A7 value

S F σ

6 A Zvalue7 max 6 A7 min6 A7

value – max 6 A7

SF σ6 p6 Ai7∧ p6 A j77 SF σ6 p6 Ai77 ×SF σ6 p6 A j77

SF σ6 p6 Ai7 ∨ p6 A j77 SF σ6 p6 Ai77 < SF σ6 p6 A j77 6SF σ6 p6 Ai77 ×SF σ6 p6 A j777

SF σ6 A∈{value7 SF σ6 A value7 card6Uvalues7


17/53Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/1L

Inter$ediate +elatin Sizes

Pr,e!tin

card6Π A6R77card6R7

Cartesian Prdu!t

card6R ×S7 card6R7 card6S7=nin

u))er bund4 card6R ∪ S7 card6R7 < card6S7

l(er bund4 card6R ∪ S7 max Ucard6R7 card6S7

Set Di>eren!eu))er bund4 card6RS7 card6R7

l(er bund4 Q



Inter$ediate +elatin Size

;in

S)e!ial !ase4 A is a "e R and B is a rei#n "e S

card6R K AB S7 card6S7

Mre #eneral4card6R K S7 SF K card6R7 ×card6S7

Se$i,in

card6R [ A S7 SF [6S!A7 card6R7

(here

SF [6R [ A S7 SF [6S!A7 card6Y A6S77card6domW AX7


19/53Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/1R

ist#ra$s r Sele!ti'itsti$atin•5r s"e(ed data the unir$ distributin assu$)tin attribute

'alues ields ina!!urate esti$atins

•=se an hist#ra$ r ea!h s"e(ed attribute @

ist#ra$ set bu!"ets

a!h bu!"et des!ribes a ran#e 'alues @ (ith its a'era#e

re*uen! " 6nu$ber tu)les (ith @ in that ran#e7 and nu$ber

distin!t 'alues d

Bu!"ets !an be ad,usted t di>erent ran#es

•:a$)les *ualit )redi!ate

ith 6'alue in +an#ei7 (e ha'e4 SF σ 6 A value7 1 #di

+an#e )redi!ate

+e*uires identiin# rele'ant bu!"ets and su$$in# u) their

re*uen!ies


20/53Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/Q

ist#ra$ :a$)le

5r @S3.D=+184 (e ha'e S51/1 s the !ard sele!tin is0QQ/1 G tu)les

5r @S3.D=+\184 (e ha'e $in6ran#e071 and$a:6ran#e

0

7F s the !ard. sele!tin is 1QQ



Centralized %uerO)ti$izatin•Dna$i! 6In#res )r,e!t at =CB7

Inter)reti'e

•Stati! 6Sste$ + )r,e!t at IBM7

:hausti'e sear!h

•brid 6Vl!an )r,e!t at O3I7

Chse nde (ithin )lan


22/53Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/

Dna$i! @l#rith$

De!$)se ea!h $ulti-'ariable *uer int a se*uen!e $n-'ariable *ueries (ith a !$$n 'ariable

Pr!ess ea!h b a ne 'ariable *uer )r!essr Chse an initial e:e!utin )lan 6heuristi!s7

Order the rest b !nsiderin# inter$ediate relatin sizes

A statisti!al inr$atin is $aintained



Dna$i! @l#rith$De!$)sitin•+e)la!e an n 'ariable *uer $ b a series *ueries

$1→$ → E → $n

(here $i uses the result $i-1.

•Deta!h$ent %uer $ de!$)sed int $% → $& (here $% and $& ha'e a !$$n

'ariable (hi!h is the result $%

• Tu)le substitutin

+e)la!e the 'alue ea!h tu)le (ith a!tual 'alues and si$)li the*uer

$6' 1 ' ... ' n7 → 6$% 6t 1 ' ' ... ' n7 t 1∈R7


24/53Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/F

Deta!h$ent

$4 SELECT V 2.A

2,V

3.A

3, …,V

n.A

n

FROM R1V 1, …,R

nV n

WHERE P 1(V

1.A

1’) AND P

2(V

1.A

1,V

2.A

2,…, V

n.A

n)

⇓$%4 SELECT V

1.A

1INTO R

1'

FROM R1V 1

WHERE P 1(V 1.A 1)

$&4 SELECT V 2.A

2, …,V

n.A

n

FROM R1' V

1, R

2V 2, …,R

nV n

WHERE P 2(V

1.A

1, V

2.A

2, …,V

n.A

n)


25/53


Deta!h$ent :a$)leAa$es e$)lees (r"in# n C@D/C@M )r,e!t

$14 SELECT EMP.ENAME

FROM EMP, ASG, PROJ


AND ASG.PNO=PROJ.PNO

AND PROJ.PNAME="CAD/CAM"

⇓$114 SELECT PROJ.PNO INTO JVAR

FROM PROJ

WHERE PROJ.PNAME="CAD/CAM"

$%4 SELECT EMP.ENAMEFROM EMP,ASG,JVAR


AND ASG.PNO=JVAR.PNO


26/53

Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/J

Deta!h$ent :a$)le6!nt^d7

$%4 SELECT EMP.ENAME

FROM EMP,ASG,JVAR


AND ASG.PNO=JVAR.PNO

⇓$14 SELECT ASG.ENO INTO GVAR

FROM ASG,JVAR

WHERE ASG.PNO=JVAR.PNO


FROM EMP,GVAR

WHERE EMP.ENO=GVAR.ENO


27/53

Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/L

Tu)le Substitutin

$11 is a $n-'ariable *uer

$1 and $10 is sub,e!t t tu)le substitutin

@ssu$e GVAR has t( tu)les nl4 〈 E1 〉 and 〈 E2〉

Then $10 be!$es$1014 SELECT EMP.ENAME

FROM EMP

WHERE EMP.ENO="E1"


FROM EMP

WHERE EMP.ENO="E2"


28/53


Stati! @l#rith$

Si$)le 6i.e. $n-relatin7 *ueries are e:e!uted a!!rdin# t thebest a!!ess )ath

:e!ute ,ins

Deter$ine the )ssible rderin# ,ins Deter$ine the !st ea!h rderin#

Chse the ,in rderin# (ith $ini$al !st


29/53

Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/R

Stati! @l#rith$

5r ,ins t( alternati'e al#rith$s 4

•Aested l)s

for each tu)le external relatin 6!ardinalit n17

for each tu)le internal relatin 6!ardinalit n7

,in t( tu)les i the ,in )redi!ate is true

end

end

C$)le:it4 n1 n

•Mer#e ,in

srt relatins

$er#e relatins

C$)le:it4 n1< n i relatins are )re'iusl srted and e*ui,in


30/53

Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/0Q

Stati! @l#rith$ :a$)le

Aa$es e$)lees (r"in# n the C@D/C@M )r,e!t

@ssu$e

MP has an inde: n AO

@S3 has an inde: n PAO

P+O; has an inde: n PAO and an inde: n PA@M

P$!E$!

PR!"

#SG

EMP


31/53


:a$)le 6!nt^d7 Chse the best a!!ess )aths t ea!h relatin

MP4 se*uential s!an 6n sele!tin n MP7

@S34 se*uential s!an 6n sele!tin n @S37

P+O;4 inde: n PA@M 6there is a sele!tin n P+O; based n

PA@M7Deter$ine the best ,in rderin#

MP ▷◁ @S3 ▷◁ P+O;

@S3 ▷◁P+O; ▷◁ MP

P+O;▷◁

@S3▷◁

MP @S3 ▷◁MP ▷◁ P+O;

MP P+O; ▷◁ @S3

P+O ;MP ▷◁@S3

Sele!t the best rderin# based n the ,in !sts e'aluateda!!rdin# t the t( $ethds


32/53


Stati! @l#rith$

Best ttal ,in rder is ne

66@S3 K MP7 K P+O;766P+O; K @S37 K MP7

#SGEMP PR!"

EMP PR!"pruned

PR!" EMPpruned

@lternati'es

EMP K #SGpruned

+#SG

KEMP,

KPR!"

#SG K EMP#SG K PR!"pruned

PR!" K #SG

+PR!"

K #SG,

KEMP


33/53


Stati! @l#rith$

•66P+O; K @S37 K MP7 has a useul inde: n the sele!t attributeand dire!t a!!ess t the ,in attributes @S3 and MP

• Therere !hse it (ith the ll(in# a!!ess $ethds4

sele!t P+O; usin# inde: n PA@M

then ,in (ith @S3 usin# inde: n PAO

then ,in (ith MP usin# inde: n AO


34/53

Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/0F

brid )ti$izatin

•In #eneral stati! )ti$izatin is $re e_!ient than dna$i!)ti$izatin

@d)ted b all !$$er!ial DBMS

•But e'en (ith a s)histi!ated !st $del 6(ith hist#ra$s7

a!!urate !st )redi!tin is di_!ult

•:a$)le

Cnsider a )ara$etri! *uer (ith )redi!ate

+ +.@ `a / `a is a )ara$eter

The nl )ssible assu$)tin at !$)ile ti$e is unir$ distributin 'alues

•Slutin4 brid )ti$izatin

Chse-)lan dne at runti$e based n the a!tual )ara$eterbindin#


35/53

Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/0G

brid O)ti$izatin :a$)le

-a.#

-a.#


36/53

Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/0J

;in Orderin# in 5ra#$ent%ueries•Orderin# ,ins

Distributed IA3+S

Sste$ +

T(-ste)

•Se$i,in rderin#

SDD-1


37/53

Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/0L

;in Orderin#

•Multi)le relatins $re di_!ult be!ause t $an alternati'es.

C$)ute the !st all alternati'es and sele!t the best ne. Ae!essar t !$)ute the size inter$ediate relatins (hi!h is

di_!ult.

=se heuristi!s

R

if size+R , / size+S,

if size+R , 0 size+S, S

•Cnsider t( relatins nl


38/53


;in Orderin# :a$)le

Cnsider

P+O; KPAO @S3 KAO MP

Site '

Site )Site (

P$!E$!

PR!"

#SG

EMP


39/53

Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/0R

;in Orderin# :a$)le:e!utin alternati'es41.MP→ Site . @S3 → Site 1

Site !$)utes MPMP K @S3 Site 1 !$)utes MPMP K@S3

MP→ Site 0 MP → Site 0Site 0 !$)utes MP K P+O; Site 0 !$)utes MP^ K P+O;

0.@S3 → Site 0F. P+O; → Site

Site 0 !$)utes @S3@S3 K P+O; Site !$)utes P+O;P+O;

K @S3@S3 → Site 1 P+O; → Site 1

Site 1 !$)utes @S3 ▷◁ MP Site 1 !$)utes P+O; K MP

G.MP → Site


40/53

Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/FQ

Se$i,in @l#rith$s

•Cnsider the ,in t( relatins4

RW AX 6l!ated at site 17

SW AX6l!ated at site 7

•@lternati'es4

1. D the ,in R K AS

. Perr$ ne the se$i,in e*ui'alents

R K A

S ⇔ 6R [ A

S7 K A

S

⇔ R K A 6S [ A R7

⇔ 6R [ A S7 K A 6S [ A R7


41/53

Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/F1

Se$i,in @l#rith$s

•Perr$ the ,in

send R t Site

Site !$)utes R K A S

•Cnsider se$i,in 6R [ AS7 K AS

S% Π A6S7

S% → Site 1

Site 1 !$)utes R% R [ AS%

R%→ Site Site !$)utes R% K AS

Se$i,in is better i

size6Π A6S77 < size6R [ AS77 Z size6R7


42/53

Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/F

Distributed Dna$i!@l#rith$1. :e!ute all $nrelatin *ueries 6e.#. sele!tin )r,e!tin7. +edu!e the $ultirelatin *uer t )rdu!e irredu!ible

sub*ueries$1→ $ →E → $nsu!h that there is nl ne relatin bet(een $i

and $i


43/53

Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/F0

Stati! @))ra!h

•Cst un!tin in!ludes l!al )r!essin# as (ell as trans$issin

•Cnsiders nl ,ins

•:hausti'eN sear!h

•C$)ilatin

•Published )a)ers )r'ide slutins t handlin# hrizntal and'erti!al ra#$entatins but the i$)le$ented )rtt)e des nt


44/53

Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/FF

Stati! @))ra!h Perr$in# ;ins•Shi) (hle

?ar#er data transer

S$aller nu$ber $essa#es

Better i relatins are s$all•5et!h as needed

Au$ber $essa#es (6!ardinalit e:ternal relatin7

Data transer )er $essa#e is $ini$al

Better i relatins are lar#e and the sele!ti'it is #d

i h


45/53

Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/FG

Stati! @))ra!h Verti!al Partitinin# & ;ins1. M'e uter relatin tu)les t the site the inner relatin

6a7 +etrie'e uter tu)les

6b7 Send the$ t the inner relatin site

6!7 ;in the$ as the arri'e

Ttal Cst !st6retrie'in# *ualied uter tu)les7< n. uter tu)les et!hed !st6retrie'in#

*ualied inner tu)les7< $s#. !st 6n. uter tu)les et!hed a'#.

uter tu)le size7/$s#. size

i h


46/53

Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/FJ

Stati! @))ra!h Verti!al Partitinin# & ;ins. M'e inner relatin t the site uter relatin

Cannt ,in as the arri'e the need t be stred

Ttal !st !st6retrie'in# *ualied uter tu)les7< n. uter tu)les et!hed !st6retrie'in#

$at!hin# inner tu)les r$ te$)rarstra#e7< !st6retrie'in# *ualied inner tu)les7< !st6strin# all *ualied inner tu)les inte$)rar stra#e7

< $s#. !st n. inner tu)les et!hed a'#. inner tu)le size/$s#. size

S i @ h


47/53

Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/FL

Stati! @))ra!h Verti!al Partitinin# & ;ins0. M'e bth inner and uter relatins t anther site

Ttal !st !st6retrie'in# *ualied uter tu)les7< !st6retrie'in# *ualied inner tu)les7

< !st6strin# inner tu)les in stra#e7< $s#. !st ×6n. uter tu)les et!hed a'#. uter tu)le size7/$s#. size< $s#. !st 6n. inner tu)les et!hed a'#. inner tu)le size7/$s#. size

< n. uter tu)les et!hed !st6retrie'in#inner tu)les r$ te$)rar stra#e7


48/53

D i St ti


49/53

Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/FR

Dna$i! 's. Stati! 'sSe$i,in•Se$i,in

SDD1 sele!ts nl l!all )ti$al s!hedules

•Dna$i! and stati! a))ra!hes ha'e the sa$e ad'anta#es anddra(ba!"s as in !entralized !ase

But the )rble$s a!!urate !st esti$atin at !$)ile-ti$e are$re se'ere

Mre 'ariatins at runti$e

+elatins $a be re)li!ated $a"in# site and !) sele!tin i$)rtant

•brid )ti$izatin Chse-)lan a))ra!h !an be used

-ste) a))ra!h si$)ler


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Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/GQ

-Ste) O)ti$izatin

1. @t !$)ile ti$e #enerate a stati! )lan (ith )eratin rderin#and a!!ess $ethds nl

. @t startu) ti$e !arr ut site and !) sele!tin and all!ate)eratins t sites


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Distributed DBMS © M. T. Özsu & P. Valduriez Ch.8/G1

-Ste) Prble$ Denitin

•3i'en

@ set sites S Us1 s Esn (ith the lad ea!h site

@ *uer ) U$1* $* $0* $F su!h that ea!h sub*uer $i is the$a:i$u$ )r!essin# unit that a!!esses ne relatin and

!$$uni!ates (ith its nei#hbrin# *ueries 5r ea!h $i in ) a easible all!atin set sites S$Us1 s Es

(here ea!h site stres a !) the relatin in $i

• The b,e!ti'e is t nd an )ti$al all!atin ) t S su!h that

the lad unbalan!e S is $ini$ized The ttal !$$uni!atin !st is $ini$ized


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-Ste) @l#rith$

• 5r ea!h $ in ) !$)ute lad 6S$7

• hile ) nt e$)t d

1. Sele!t sub*uer a (ith least all!atin ce:ibilit

. Sele!t best site b r a 6(ith least lad and best benet7

0. +e$'e a r$ ) and re!$)ute lads i needed


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