java concurrent programming consensus

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Multicore Programming

Consensus

Tutorial 6CS 0368-3469Spring 2010


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Summary

Consensus

Queue

Atomic( n, n(n+1)/2)

Approximate agreement

Trinary register Team consensus


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Consensus

Consistent: all threads decide the samevalue

Valid: the common decision value issome thread's input


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Generic Consensus Protocol

abstract classConsensusProtocolimplementsConsensus {protectedObject[] proposed =newObject[N];private voidpropose Object value) {proposed[ThreadID.get )] = value;}abstractpublicObjectdecide object value);}}

(4) (4)


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Consensus Numbers

An object X has consensus numbern If it can be used to solve n-thread

consensus Take any number of instances of X

together with atomic read/write registers

and implement n-thread consensus

But not (n+1)-thread consensus


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Queue

Suppose we augmentthe FIFOQueueclass with a peek()method

that returns but does not removethefirst element in the queue.

Show that the augmentedqueue hasinfinite consensus number.


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public classQueueConsensusextendsConsensusProtocol {privateQueue queue;publicdecide object value) {propose value);this.queue.enq threadID);returnproposed[this.queue.peek )];}

Queue implementation

This is correct because if X is the first indexto beenqueued, later enq() calls will not change X's position,and X stored its value in proposed[] before calling enq().


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Atomic (n,n(n+1)/2)

Atomic (n,n(n+1)/2)-registerassignment for n>1 has consensus

number at least n.


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Reminder: Atomic (2,3)

Writesto 0 and1

Writesto 1 and2

A

B


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Atomic (n,n(n+1)/2)

n fields r0rn-1

n(n-1)/2 fields rij, where i > j.

Each thread i atomically assigns itsinput value to n fields (with its index).


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Atomic (n,n(n+1)/2)

Read rij . If the value is null, then neitherassignment has occurred.

Otherwise, read ri and rj . If rivalue isnull, thenj precedes i, and similarly for rj .

If neither ri nor rj is null, reread rij . Ifits value is equal to the value read from ri,thenj precedes i, else vice-versa.


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b


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b


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The two-threadapproximateagreement class for a given :

Call decide(xi)=yi(xiis a real number). yi in [min(xa, xb), max(xa, xb)]

|ya -yb| < for > 0

What is the consensus number?


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solution Can be implemented using atomic

registers consensus == 1

yixiIf yj= return yiwhile(|yi-yj|>)

yi(yi+yj)/2 //average


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Trinary register

Holds values [,0,1], providescompareAndSet() and get().

Solve n-consensus for K-bitsvalues: n trinary registers

k trinary registers


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Trinary register solution

Solution n trinaty registers

yi.cas(,1)

For each jiy

j

.cas(,0)

return smallest xjsuch that yj=1


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Trinary register solution

Solution k trinaty registers

Idea: try to set your bit or help.

1. Try to set the all k bits

2. If fails help to help another thread.

Look in the announce array for a matchingvalue.

Replace yours with the other, goto 1.

3. return current value.


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Team consensus

A Team consensus object provides the samepropose() and decide() methods as consensus.

A team consensus object solves consensusas long as no more than two distinct values areever proposed. (If more than two are proposed,the results are undefined.)

Show how to solve wait-free n-thread consensus,with up to n distinct input values, from a supply ofteam consensus objects.


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Team consensus Solution

174

4 5 7

1 3 5 7

4

82 4 6

2 threads

4 threads
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java concurrent programming consensus

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