[PPT] - Decentralized Consensus Proto cols 1 Goals of the lecture PowerPoint Presentation

SLIDE 1 Decentralized Consensus Proto cols 1 Goals

f

the lecture

Decentralized

Consensus Proto cols

V

erication

f

Synchronous Proto cols

Algo

rithms fo r computing functions

f

global state. Bermond, Konig, and Ra ynal c Vija y K. Ga rg Distributed Systems F all 94

SLIDE 2 Decentralized Consensus Proto cols 2 Consensus Proto cols

Systems
X

X X X T ransfo rmation Reactive

n

no des

connected

top

logy
bi-directional

channels

m

channels

D

diameter

no

sha red mem

ry/

clo ck

message-based

comm unication

reliable

delivery

each

no de kno ws its identit y and channels adjacent to it c Vija y K. Ga rg Distributed Systems F all 94

SLIDE 3 Decentralized Consensus Proto cols 3 Consensus Proto cols

@

@ @ @ @ @

initial

data distributed

n

the no des

required

symmetric algo rithm

aim

is to compute a global function/p redicate such p roto cols a re called Consensus p roto cols. c Vija y K. Ga rg Distributed Systems F all 94

SLIDE 4 Decentralized Consensus Proto cols 4 Ideas in the algo rithm

Computation

in phases: Init, phase 1 , phase 2 ,

;

phase k , term.

Logical

synchronization induced

w

ak eup

n

receivinga message

T

ermination : no de iterates phase so long as it receives new info rmation ) dierent no des ma y terminate at dierent times If D is kno wn, the algo rithm stops after D phases. c Vija y K. Ga rg Distributed Systems F all 94

SLIDE 5 Decentralized Consensus Proto cols 5 Filtering Notions 1. In phase p send

nly

the new info rmation that is received in phase p

1.

2. if sent(c) = r eceiv ed(c) then p ro cesses connected thru that channel can never lea rn any new info rmation along that channel. 3. A t phase p:

P

lea rns r eceiv ed(c)

sent(c).
Send

\end" message if this is already kno wn. c Vija y K. Ga rg Distributed Systems F all 94

SLIDE 6 Decentralized Consensus Proto cols 6 Algo rithm to compute the routing table Pro cess P :

D

kno wn

p

: numb er

f

the current phase

c

: any channel incident

n

P Inf : global info rmation kno wn b y P f identities

f

the no des fo r which P kno ws a sho rtest route g New : new info rmation

btained

since the b eginnin g

f

this phase. sen t(c) : message sent

n

channel c at the current phase. receiv e(c) : message received through channel c. c Vija y K. Ga rg Distributed Systems F all 94

SLIDE 7 Decentralized Consensus Proto cols 7 Algo rithm [Contd.] Init p Inf f identit y

f

the no de g sent(c) Inf fo r all c Phases while p < D do p p + 1 sendhsent (c)i

n

all channels c New

F
r

every channel c do receive h received (c)i

n

c 8y 2 received(c)

Inf
New

: Rout (c) Rout (c) [fy g New New [ (received(c )

Inf

) Inf Inf [ New sent(c) New

received(c)

T erm Rout : minimum routing table Inf : identities

f

all no des c Vija y K. Ga rg Distributed Systems F all 94

SLIDE 8 Decentralized Consensus Proto cols 8 General Algo rithm

D

not kno wn

OPEN

: set

f

channels still

p

en Init : p 0; Inf finitial data g New Inf ; OPEN set

f

all channels 8c : received(c)

Phases

: while OPEN 6=

do

p p + 1 8c 2 OPEN do sent(c0 New

received(c)

send hsend (c)i

n

c New

8c

2 OPEN do received hreceived (c)i

n

c if (received(c) = send(c)) then OPEN OPEN fcg New New [ (received(c )

Inf

) call compute Inf Inf [ New c Vija y K. Ga rg Distributed Systems F all 94

SLIDE 9 Decentralized Consensus Proto cols 9 Pro

f

Idea

During

phase p a no de P receives the info rmation contained in the no des at distance exactly p from itself.

closed(c)

at the end

f

phase p

T

p1 (P ) = T p1 (Q) !

T

i (P ) = set

f

no des at distance at most i from P . c Vija y K. Ga rg Distributed Systems F all 94

SLIDE 10 Decentralized Consensus Proto cols 10 Pro

f

[Contd.] Notation : N i (P ) = set

f

no des at distance i from P . T i (P ) = [ j i N i (P ) c = channel (P ; Q) c Vija y K. Ga rg Distributed Systems F all 94

SLIDE 11 Decentralized Consensus Proto cols 11 8c 2

p

en p1 : sent p (c) new p1

r

ecd p1 (c) 8c 2

p

en p1 : received p (c) sent p (c )

p

en p

p

en p1

f

c j sent p (c) = received p (c)g new p [ received p (c)

inf

p1 inf p inf p1 [ new p Theo rem : new p = N p (P ) sent p (c) = N p1 (P )

N

p2 (Q) received p (c) = N p1 (Q)

N

p2 (P )

p

en p = f (P ; Q) j T p1 (P ) 6= T p1 (Q)g inf p = T p (P ) c Vija y K. Ga rg Distributed Systems F all 94

SLIDE 12 Decentralized Consensus Proto cols 12 Lemma closed p = f (P ; Q) j T p1 (P ) = T p1 (Q)g (B) ) Given N p1 (P )

N

p2 (Q) = N p1 (Q)

N

p2 (P ). t t t t t t p-3 P Q p-2 p-1 p-2 T p1 (P ) = T p2 (Q) [ N p1 (P ) [ N p2 (P ) = T p2 (Q) [

N

p1 (P )

N

p2 (Q)

[

N p2 (P ) = T p2 (Q) [

N

p1 (Q)

N

p2 (P )

[

N p2 (P ) = T p2 (Q) [ N p1 (Q) = T p1 (Q) c Vija y K. Ga rg Distributed Systems F all 94

SLIDE 13 Decentralized Consensus Proto cols 13 ( Given

T

p1 (P ) 6= T p1 (Q)

T
sho

w that N p1 (P )

N

p2 (Q) = N p1 (Q)

N

p2 (P ) t t t x Q p-1 p-2 x p-1 x P c Vija y K. Ga rg Distributed Systems F all 94