scalar+ vector + matrix clock- done

8/17/2019 scalar+ vector + matrix clock- done

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CS4231CS4231

Parallel and Distributed AlgorithmsParallel and Distributed Al

gorithms

AY 2006/2007 Semester 2 AY 2006/2007 Semester 2

Leture 4

!nstrutor" #ai$eng Y%


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CS4231 Parallel and Distributed Algorithms AY2006/2007 Semester 2 2

&e'ie( o$ Last Leture&e'ie( o$ Last Leture


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)oda*+s &oadma,)oda

*+s &oadma,

Cha,ter 7 -.odels and Clos oal" De$ine -time in a distributed s*stem

Logial lo

etor lo

.atri lo


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Assum,tions Assum

,tions

Proess an ,er$orm three inds o$ atomi ations/e'ents Loal om,utation

Send a single message to a single ,roess

&eei'e a single message $rom a single ,roess

o atomi broadast

Communiation model

Point5to5,oint

rror5$ree in$inite bu$$er

Potentiall* out o$ order


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.oti'ation.oti'ation .an* ,rotools need to im,ose an ordering among e'ents

!$ t(o ,la*ers o,en the same treasure hest -almost at the sametime (ho should get the treasure8

Ph*sial los"

Seems to om,letel* sol'e the ,roblem

9ut (hat about theor* o$ relati'it*8

'en (ithout theor* o$ relati'it* : e$$iien* ,roblems

#o( aurate is su$$iient8

;ithout out5o$5band ommuniation" .inimum message,ro,agation dela*

;ith out5o$5band ommuniation" distane/s,eed o$ light

!n other (ords some time it has to be -


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So$t(are -ClosSo$t(are -Clos

So$t(are -los an inur muh lo(er o'erhead than maintaining=su$$iientl* aurate> ,h*sial los

Allo(s a ,rotool to in$er ordering among e'ents

oal o$ so$t(are -los" Ca,ture e'ent ordering that are 'isible to users 9ut (hat orderings are 'isible to users (ithout ,h*sial los8


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isible ?rdering to %sersisible ?rdering to %sers

A→ 9 =,roess order>

9→ C =send5reei'e order>

A→ C =transiti'it*>

user1 =,roess1>

user2 =,roess2>

user3 =,roess3>

A 9

C

D

A 8 D

9 8 D

C 8 D


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--#a,,ened59e$ore &elation#a,,ened59e$ore &elation

-#a,,ened5be$ore relation a,tures the ordering thatis 'isible to users (hen there is no ,h*sial lo

A ,artial order among e'ents

Proess5order send5reei'e order transiti'it*

@irst introdued b* Lam,ort : Considered to be the

$irst $undamental result in distributed om,uting

oal o$ so$t(are -lo is to a,ture the abo'e-ha,,ened5be$ore relation


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So$t(are -Clo 1" Logial ClosSo$t(are -Clo 1" Logial Clos ah e'ent has a single integer as its logial lo 'alue

ah ,roess has a loal ounter C !nrement C at eah -loal om,utation and -send e'ent

;hen sending a message logial lo 'alue is attahed to

the message At eah -reei'e e'ent C B ma=C > 1

user1 =,roess1>

user2 =,roess2>

user3 =,roess3>

1 2 3 4

1

3 B ma=12>1

4

1 2

3

4 B ma=33>1


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Logial Clo Pro,ertiesLogial Clo Pro,erties

)heorem" 'ent s ha,,ens be$ore t

⇒

the logial lo 'alue o$ s is

smaller than the logial lo 'alue o$ t

)he re'erse ma* not be true

user1 =,roess1>

user2 =,roess2>

user3 =,roess3>

1 2 3 4

1 4

1 2

3


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So$t(are -Clo 2" etor ClosSo$t(are -Clo 2" etor Clos Logial lo"

'ent s ha,,ens be$ore e'ent t⇒

the logial lo 'alue o$ s

is smaller than the logial lo 'alue o$ t

etor lo"

'ent s ha,,ens be$ore e'ent t the 'etor lo 'alue o$ s

is -smaller than the 'etor lo 'alue o$ t

ah e'ent has a 'etor o$ n integers as its 'etor

lo 'alue

'1 B '2 i$ all n $ields same

'1 ≤ '2 i$ e'er* $ield in '1 is less than or e


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etor Clo Protooletor Clo Protool ah ,roess i has a loal 'etor C

!nrement CGiH at eah -loal om,utation and -send e'ent

;hen sending a message 'etor lo 'alue is attahed to

the message At eah -reei'e e'ent C B ,air(ise5ma=C >I

CGiHI

user1 =,roess1>

user2 =,roess2>

user3 =,roess3>

=100> =200> =300>

=002>

=022>=010>

=001>

=232>

=233>

C B =010> B =002>

,air(ise5ma=C > B =012>


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etor Clo Pro,ertiesetor Clo Pro,erties 'ent s ha,,ens be$ore t

⇒

'etor lo 'alue o$ s E 'etor lo 'alue o$ t"

)here must be a hain $rom s to t

'ent s ha,,ens be$ore t 'etor lo 'alue o$ s E 'etor lo 'alue o$ t

!$ s and t on same ,roess done

!$ s is on , and t is on


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am,le A,,liation o$ etor Cloam,le A,,liation o$ etor Clo

ah user has an order ,laed b* a ustomer ;ant all users to no( all orders

ah order has a 'etor lo 'alue

user1 =,roess1>

user2 =,roess2>

user3 =,roess3>

D1 =100> =200> =300>

=002>

=022>D2 =010>

D3 =001>

=232>

=233>

D1

D3 D1 D2 D3

! ha'e seen all orders (hose 'etor lo is smaller than

=232>"

! an a'oid linear searh $or eistene testing


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So$t(are -Clo 3" .atri ClosSo$t(are -Clo 3" .atri Clos

.oti'ation

.* 'etor lo desribe (hat ! -see

!n some a,,liations ! also (ant to no( (hat other ,eo,le see

.atri lo"

ah e'ent has n 'etor los one $or eah ,roess

)he i th 'etor on ,roess i is alled ,roess i +s ,rini,le 'etor

Prini,le 'etor is the same as 'etor lo be$ore

on5,rini,le 'etors are Just ,igg*baed on messages to u,date -no(ledge


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.atri Clo Protool.atri Clo Protool

@or ,rini,le 'etor C on ,roess i

!nrement CGiH at eah -loal om,utation and -send e'ent

;hen sending a message all n 'etors are attahed to the message

At eah -reei'e e'ent let be the ,rini,le 'etor o$ the sender C B ,air(ise5ma=C >I CGiH

I

@or non5,rini,le 'etor C on ,roess i su,,ose it orres,onds to ,roess J

At eah -reei'e e'ent let be the 'etor orres,onding to ,roess J as in the reei'ed

message C B ,air(ise5ma=C >


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.atri Clo am,le.atri Clo am,le

user1 =,roess1>

user2 =,roess2>

user3 =,roess3>

=100>

=000>

=000>

=000>

=010>

=000>

=000>

=000>

=001>

=200>

=000>

=000>

=300>

=000>

=000>

=000>

=000>

=002>

=000>

=022>

=002>

=200>

=232>

=002>

=200>=232>

=233>


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.atri Clo am,le.atri Clo am,le

=100>

=000>

=000>

=000>

=010>

=000>

=000>

=000>

=001>

=200>

=000>

=000>

=300>

=000>

=000>

=000>

=000>

=002>

=000>

=022>

=002>

=200>

=232>

=002>

=200>

=232>

=233>

)heorem"

?n an* gi'en

,roess an*non5,rini,le

'etor is

smaller than

the ,rini,le

'etor


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A,,liation o$ .atri Clo A,,liation o$ .atri Clo

user1 =,roess1>

order D1 B =100>

user2 =,roess2>

order D2 B =010>

user3 =,roess3>

order D3 B =001>

=100>

=000>

=000>

=000>

=010>

=000>

=000>

=000>

=001>

=200>

=000>

=000>

=300>

=000>

=000>

=000>

=000>

=002>

=000>

=022>

=002>

=200>

=232>

=002>

=200>

=232>

=233>

D1

D3D1 D2 D3

user3 no(

no(s

that all 3users

ha'e seen

D1


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A Sna $or .ind A Sna $or .ind

etor lo tells me (hat ! no( one5dimensional data struture

.atri lo tells me (hat ! no( about (hat other

,eo,le no( )(o5dimensional data struture

88 tells me (hat ! no( about (hat other ,eo,le

no( about (hat other ,eo,le no( 885dimensional data struture


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Summar*Summar *

Cha,ter 7 -.odels and Clos

oal" De$ine -time in a distributed s*stem

Logial lo

-ha,,ened be$ore⇒ smaller lo 'alue

etor lo

-ha,,ened be$ore⇔ smaller lo 'alue

.atri lo

i'es a ,roess no(ledge about (hat other ,roesses no(


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#ome(or Assignment#ome(or Assignment Pro'e the $ollo(ing"

!$ e'ent s ha,,ens be$ore t then the logial lo 'alue o$ s

is smaller than the logial lo 'alue o$ t

Page 126

Problem 72 : gi'e a ounter5eam,le

Problem 74

Problem 77 : Pro'e that the solution satis$ies the ,ro,ert*

o$ logial los

#ome(or due a (ee $rom toda*

scalar+ vector + matrix clock- done

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