Cuts

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Cuts
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consists from an event from each process
Cut
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no messages cross the cut
Consistent cut
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messages can cross from left to right of the cut
Consistent cut
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messages cross from right to left of the cut
Inconsistent cut
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messages cross from right to left of the cut
Inconsistent cut
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Maximal Consistent Cut
Consider some (inconsistent) cut
Maximal Consistent Cut of
A consistent cut such that
and contains most recent events
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(inconsistent cut)
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maximal consistent cut
(inconsistent cut)
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Theorem
For every cut , there is a unique maximal
consistent cut
Proof
Proof by contradiction
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Assume for contradiction there are two (or more)
maximal cuts of
maximal consistent cuts
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It cannot be that and dont cross
not maximal!
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and cross
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and cross
new cut
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and cross
impossible
is consistent
since
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and cross
impossible
is consistent
since
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and cross
Contradiction!
not maximal!
not maximal!
is consistent
End of proof
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A distributed algorithm for computing the
maximum consistent cut of

• Use vector clocks
• For each processor
• Find most recent event with
• vector clock

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OK
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OK
OK
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OK
OK
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OK
OK
OK
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Distributed Snapshot

• A set of processors initiate the
• computation for obtaining a global snapshot

(these processors receive special marker
messages from the system)

• The cut contains the state of at least
• one processor in in the initiation

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A Distributed Snapshot Algorithm
Processor

• Count local events in

• Upon receiving a marker message

If then
set
send marker to all neighbors
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cut
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Theorem
The cut obtained by the algorithm is consistent
By contradiction
Proof
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Suppose the cut is incosistent
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(we assume FIFO)
It must be
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Impossible!
End of proof