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SES Algorithm SES: Schiper-Eggli-Sandoz Algorithm. No

need for broadcast messages. Each process maintains a vector V_P of size

N - 1, N the number of processes in thesystem. V_P is a vector of tuple (P,t): P the

destination process id and t, a vectortimestamp.

Tm: logical time of sending message m Tpi: present logical time at pi

Initially, V_P is empty.

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SES Algorithm ... What does the condition t Tp2 imply?

t is message vector time stamp. t > Tp2 -> For all j, t[j] > Tp2[j] This implies some events occurred without P2s

knowledge in other processes. So P2 decides to buffer themessage.

When t < Tp2, message is delivered & Tp2 isupdated with the help of V_P2 (after the mergeoperation).

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SES Buffering Example

P1

P2

P3

M1

(0,2,1)

(0,1,0) (0,2,0)

(2,2,2)(1,1,0)

(0,2,2)

M2

M3

V_P2empty

V_P2:(P1, )

V_P3:(P1,)

Tp1:

Tp2:

Tp3:

(0,0,0)

M4V_P3:(P1,)

V_P2:

(P1, )(P3, )

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SES Buffering Example... M1 from P2 to P1: M1 + Tm (=) + Empty

V_P2 M2 from P2 to P3: M2 + Tm () + (P1,

) M3 from P3 to P1: M3 + + (P1, ) M3 gets buffered because:

Tp1 is , t in (P1, t) is & so Tp1 < t

When M1 is received by P1: Tp1 becomes , by rules 1 and 2 of vector clock.

After updating Tp1, P1 checks buffered M3. Now, Tp1 > t [in (P1, ]. So M3 is delivered.

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SES Algorithm ...

On delivering the message: Merge V_M (in message) with V_P2 as follows.

If (P,t) is not there in V_P2, merge.

If (P,t) is present in V_P2, t is updated with max(t[i] inVm, t[i] in V_P2). {Component-wise maximum}.

Message cannot be delivered until t in V_M isgreater than t in V_P2

Update site P2s local, logical clock. Check buffered messages after local, logical

clock update.

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SES Algorithm

P1

P2

P3

M2

M1(0,0,1)

(0,1,1)

(0,2,1)

(1,2,1) (2,2,1)

(0,2,2)

V_P3 isempty

V_P2 isempty

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Global State

$500 $200

A B

C1: Empty

C2: Empty

Global State 1

$450 $200

A B

C1: Tx $50

C2: Empty

Global State 2

$450 $250

A B

C1: Empty

C2: Empty

Global State 3

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Recording Global State... Similarly, for consistency m = m m: no. of messages received along channel before Bs state

recording m: no. of messages received along channel by B before

channels state was recorded.

Also, n >= m, as in no system no. of messages sentalong the channel be less than that received

Hence, n >= m Consistent global state should satisfy the above

equation. Consistent global state:

Channel state: sequence of messages sent before recordingsenders state, excluding the messages received before

receivers state was recorded. Only transit messages are recorded in the channel state.

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Recording Global State Send(Mij): message M sent from Si to Sj rec(Mij): message M received by Sj, from Si time(x): Time of event x

LSi: local state at Si send(Mij) is in LSi iff (if and only if) time(send(Mij)) cj) and !(cj-> ci).

S1

S2

S3

S4

c1

c2c3

c4

VTc=

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Time of a Cut C = {c1, c2, .., cn} with vector time stamp VTci.

Vector time of the cut, VTc = sup (VTc1, VTc2, ..,VTcn).

sup is a component-wise maximum, i.e., VTci =

max(VTc1[i], VTc2[i], .., VTcn[i]). Now, a cut is consistent iff VTc = (VTc1[1], VTc2[2],

.., VTcn[n]).

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Termination Detection Termination: completion of the sequence of algorithm. (e.g.,)

leader election, deadlock detection, deadlock resolution. Use a controlling agent or a monitor process. Initially, all processes are idle. Weight of controlling agent is 1

(0 for others).

Start of computation: message from controller to a process.Weight: split into half (0.5 each).

Repeat this: any time a process send a computation messageto another process, split the weights between the twoprocesses (e.g., 0.25 each for the third time).

End of computation: process sends its weight to the controller. Add this weight to that of controllers. (Sending processsweight becomes 0).

Rule: Sum of W always 1. Termination: When weight of controller becomes 1 again.

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Huangs Algorithm B(DW): computation message, DW is the weight. C(DW): control/end of computation message; Rule 1: Before sending B, compute W1, W2 (such that W1 + W2 is

W of the process). Send B(W2) to Pi, W = W1.

Rule 2: Receiving B(DW) -> W = W + DW, process becomesactive. Rule 3: Active to Idle -> send C(DW), W = 0. Rule 4: Receiving C(DW) by controlling agent -> W = W + DW, If W

== 1, computation has terminated.

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Huangs Algorithm

P1

P2 P3

P4 P5

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P1

P2 P3

P4 P5

0.5

0.5

0

0

0