Sharing Memory
in a Self-stabilizing Manner
Noga Alon, Hagit Attiya, Shlomi Dolev,
Swan Dubios, Maria Gradinariu, Sebastien
Tixeuil
DISC, 2010
Talk Outline
• Bounded Time Stamp
• Guessing Game
• Quorum System
• Integration
Quorum Based SWMR
• Writer has a sequence number seq
• Sends messages to all the participants
with NewValue seq+1
• The write of NewValue terminates, once
acknowledged by more than half of the
participants
• (Fast) Self-stabilizing, for unbounded
seq, first ask for the largest seq known
to the participants
Bounded Time Stamps
• {Sting, (AntiSting1, Antisting2,…, AntistingK)}
• {3,(4,5,7)} > {4,(2,10,5)}
• {3,(4,5,7)} ? {4,(3,10,5)}
Given any K timestamps, a timestamp greater
than them all can be constructed.
Take all the K stings as Antistings and non
existing value as a sting.
Guessing Game
• Hider hides H (ts1, ts2,…,tsH) timestamps
unknown to the finder
Guessing Game
• Hider hides H (ts1, ts2,…,tsH) timestamps
unknown to the finder
• Finder would like to introduce a timestamp
tsF greater than all the H (unrevealed
timestamps)
• Finder introduces a timestamp tsF the Hider
pulls out tsI from (ts1, ts2,...,tsH) not smaller
than tsF and may replace tsI by tsF in (ts1,
ts2,…,tsH)
• Finder repeatedly tries,
• Does the Finder have a winning strategy?
Guessing Game
• Finder maintains a fifo Queue of 2H
timestamps
Guessing Game
• Finder maintains a fifo Queue of 2H
timestamps
• Introduces a timetamp tsF greater than all
the timestamps in the Queue
• Whenever the Hider reveals a non smaller
timestamp tsI, both tsF and tsI are
enqueued.
• The Finder WINS!
• After at most H turns.
Quorum Systems for SWMR
• Label is a timestamp (epoch) and sequence
number (tsF,sn)
• The sequence number starts in 1 and grows
until 2^64… practically infinite
• Finder is the writer that introduces a new
epoch (tsF) every time a non smaller epoch is
found.
• Writer increments the sequence number and
uses it (within the same epoch) as the time
stamp for a new value for the SWMR value…
Thank You!