📖Delta State Replicated Data Types

January 24, 2021

authors: Almeida, Paulo Sérgio and Shoker, Ali and Baquero, Carlos
year: 2016
url: http://arxiv.org/abs/1603.01529v1

I think most of these data structures are available in Riak via riak_dt
Excerpts:
- Instead of shipping the whole state, ship only deltas (δ-state) generated by δ-mutators.
- Definition 1 (Delta-mutator). A delta-mutator $m^δ$ is a function, corresponding to an update operation, which takes a state $X$ in a join-semilattice $S$ as parameter and returns a delta-mutation $m^δ(X)$ , also in $S$ .
- Definition 2 (Delta-group). A delta-group is inductively defined as either a delta-mutation or a join of several delta-groups.
- Definition 3 (δ-CRDT). A δ-CRDT consists of a triple $(S, M^δ, Q)$ , where $S$ is a join-semilattice, $M^δ$ is a set of delta-mutators, and $Q$ a set of query functions, where the state transition at each replica is given by either joining the current state $X ∈ S$ with a delta-mutation: $X' = X ⊔ m^δ(X)$ , or joining the current state with some received delta-group $D$ : $X' = X ⊔ D$ .
- it will be useful to find a non-trivial decomposition such that delta-states returned by delta-mutators in $M^δ$ are smaller than the resulting state: $size(m^δ(X))≪size(m(X))$
- Definition 4 (Delta-interval). Given a replica $i$ progressing along the states $X^0_i, X^1_i, . . .$ , by joining delta $d^k_i$ (either local delta-mutation or received delta-group) into $X^k_i$ to obtain $X^{k+1}_i$ , a delta-interval $\Delta^{a,b}_i$ is a delta-group resulting from joining deltas $d^a_i, . . . , d^{b-1}_i$ : $\Delta^{a,b}_i=⊔\{d^k_i | a ≤ k < b\}$
- Definition 5 (Delta-interval-based anti-entropy algorithm). A given anti-entropy algorithm for δ-CRDTs is delta-interval-based, if all deltas sent to other replicas are delta-intervals.
- Definition 6 (Causal delta-merging condition). A delta-interval based anti-entropy algorithm is said to satisfy the causal delta-merging condition if the algorithm only joins $\Delta^{a,b}_j$ from replica $j$ into state $X_i$ of replica $i$ that satisfy: $X_i ⊒ X^a_j$
- Portfolios contains the following data types:
  - G-Set
  - 2P-Set
  - LWW-Set (Add-Wins or Remove-Wins)
  - PN-Counter
  - Lexicographic Counter
    - state = a lexicographic pair for each replica
  - Causal delta-CRDTs
    - DotSet, DotFun, DotMap
    - Enable-Wins Flag
    - Multi-Value Register
    - Add-Wins Set (this can be seen as a map from elements to enable-wins flags, but with a single causal context)
    - Remove-Wins Set
    - Nesting CRDTs in a map

Backlinks

📝 CRDT