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Attiya et al,
PODC 2016
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Standard RGA: insertion op is triple (a, t, r)
• a character being inserted
• t operation timestamp (globally unique)
• r timestamp of reference character
To fix interleaving, change to 4-tuple (a, t, r, e)
• e set of timestamps of all insertion operations
with the same reference character r
at the time the insertion was performed
(not including t itself)
I′ = I ∪ {(a, t, r, {t′|∃a′, e′. (a′, t′, r, e′) ∈ I})}
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(‘!’, τ1
, τ0
, {})
(‘ ’, τ2
, τ0
, {τ1
})
(‘ ’, τ3
, τ0
, {τ1
})
(‘ ’, τ4
, τ0
, {τ1
, τ2
})
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(a
1
, t
1
, r, e
1
) < (a
2
, t
2
, r, e
2
) if t
1
∈ e
2
(a
2
, t
2
, r, e
2
) < (a
1
, t
1
, r, e
1
) if t
2
∈ e
1
(‘!’, τ
1
, τ
0
, {}) (‘ ’, τ
2
, τ
0
, {τ
1
})
(‘ ’, τ3
, τ
0
, {τ
1
})
(‘ ’, τ4
, τ
0
, {τ
1
, τ2
})
<
< <
If (a
1
, t
1
, r, e
1
) and (a
2
, t
2
, r, e
2
) are concurrent (t
1
∉ e
2
∧ t
2
∉ e
1
):
m
1
= min({t
1
} ∪ e
1
− e
2
) m
2
= min({t
2
} ∪ e
2
− e
1
)
(a
1
, t
1
, r, e
1
) < (a
2
, t
2
, r, e
2
) if m
1
< m
2
(a
2
, t
2
, r, e
2
) < (a
1
, t
1
, r, e
1
) if m
2
< m
1
(‘ ’, τ
2
, τ
0
, {τ
1
}) (‘ ’, τ3
, τ
0
, {τ
1
})
min({τ2
} ∪ {τ1
} − {τ1
}) = τ2
min({τ3
} ∪ {τ1
} − {τ1
}) = τ3
<
(‘ ’, τ4
, τ
0
, {τ
1
, τ2
}) (‘ ’, τ3
, τ
0
, {τ
1
})
min({τ3
} ∪ {τ1
} − {τ1
, τ2
}) = τ3
min({τ4
} ∪ {τ1
, τ2} − {τ1
}) = τ2
<
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Thanks! [email protected] @martinkl
RGA proof of no interleaving: Martin Kleppmann, Victor B F Gomes, Dominic P Mulligan, and
Alastair R Beresford: “OpSets: Sequential Specifications for Replicated Datatypes,”
https://arxiv.org/abs/1805.04263, May 2018.
Logoot: Stéphane Weiss, Pascal Urso, and Pascal Molli: “Logoot: A Scalable Optimistic Replication
Algorithm for Collaborative Editing on P2P Networks,” ICDCS 2009.
LSEQ: Brice Nédelec, Pascal Molli, Achour Mostefaoui, and Emmanuel Desmontils: “LSEQ: an
Adaptive Structure for Sequences in Distributed Collaborative Editing,” DocEng 2013.
RGA: Hyun-Gul Roh, Myeongjae Jeon, Jin-Soo Kim, and Joonwon Lee: “Replicated abstract data
types: Building blocks for collaborative applications,” Journal of Parallel and Distributed
Computing, 71(3):354–368, 2011.
Treedoc: Nuno Preguiça, Joan Manuel Marques, Marc Shapiro, and Mihai Letia: “A Commutative
Replicated Data Type for Cooperative Editing,” ICDCS 2009.
WOOT: Gérald Oster, Pascal Urso, Pascal Molli, and Abdessamad Imine: “Data consistency for P2P
collaborative editing,” CSCW 2006.
Astrong
: Hagit Attiya, Sebastian Burckhardt, Alexey Gotsman, Adam Morrison, Hongseok Yang,
and Marek Zawirski: “Specification and Complexity of Collaborative Text Editing,” PODC
2016.