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Programming Distributed Systems 08 Replicated Data Types Annette - - PowerPoint PPT Presentation

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Programming Distributed Systems 08 Replicated Data Types Annette Bieniusa AG Softech FB Informatik TU Kaiserslautern Summer Term 2018 Annette Bieniusa Programming Distributed Systems Summer Term 2018 1/ 37 Motivation So far, we resolved

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Programming Distributed Systems

08 Replicated Data Types Annette Bieniusa

AG Softech FB Informatik TU Kaiserslautern

Summer Term 2018

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Motivation

So far, we resolved conflicting updates (i.e. non-commutative) updates simply by sequencing operations using arbitration order (ar). But sometimes, applications do not want to depend on a global order such as ar do want to be made aware of conflicts do want to resolve conflicts in a type-specific way.

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Example: Multi-value register

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How can we determine the state?

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Formal model

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Sequential semantics for registers

S : Op × Op∗ → V al S(rd, ǫ) = undef (read returns initial value) S(rd, wr(2) · wr(8)) = 8 (read returns last value written) S(wr(3), rd · wr(2) · wr(8)) = ok (write always returns ok)

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Operation Context

An operation context is a finite event graph C = (E, op, vis, ar). Events in E capture what prior operations are visible to the

  • peration that is to be performed.

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Concurrent semantics for Multi-Value Register

F : Op × C → V al Fmvr(wr(x), C) =

  • k

Fmvr(rd(), C) = {x| exists e in C such that op(e) = wr(x) and e is vis-maximal in C}

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Quizz: What do the read ops return?

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Return values in Abstract Executions revisited

Last lecture: Consistency Notions can be defined alternatively with concurrency semantics An abstract execution A = (E, op, rval, rb, ss, vis, ar) satisfies a concurrent semantics F if rval(e) = F(op(e), A |vis−1(e),op,vis,ar

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Semantics of a set data type

Sequential specification of abstract data type Set S: {true} add(e) {e ∈ S} {true} rmv(e) {e / ∈ S} The following pairs of operations are commutative (for two elements e, f and e = f):

{true} add(e); add(e) {e ∈ S} {true} add(e); add(f) {e, f ∈ S} {true} rmv(e); rmv(e) {e / ∈ S} {true} rmv(e); rmv(f) {e, f / ∈ S} {true} add(e); rmv(f) {e ∈ S, f / ∈ S}

For these ops, the concurrent execution should yield the same result as executing the ops in any order.

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What are the options regarding a concurrency semantics for add(e) and rmv(e)?

The operations add(e) and rmv(e) are not commutative

{true} add(e); rmv(e) {e / ∈ S} {true} rmv(e); add(e) {e ∈ S}

Options

sequential consistency / linearizability → not really. . . add-wins: e ∈ S remove-wins: e / ∈ S erroneous state last-writer wins (i.e. define arbitration order through total order, for example, via totally- ordered timestamps)

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Set Semantics

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Formal Semantics for the Add-Wins Set

Faws(add(x), C) =

  • k

Faws(rmv(x), C) =

  • k

Faws(rd(), C) = {x| exists e in C such that op(e) = add(x) and there exists no e’ in C such that

  • p(e′) = rmv(x) and e vis

− − → e′}

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Sets with odd semantics

Grow-only set

Convergence by union on element set No remove operation

2P-Set (Wuu & Bernstein PODC 1984)

Set of added elements + set of tombstones Add/remove once Violates sequential spec

c-set (Sovran et al., SOSP 2011)

Maintain add/remove counter Violates sequential spec

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Conflict-free Replicated Data Types (CRDTs) [3]

Same API as sequential abstract data type, but with concurrency semantics If operations are commutative, same semantics as in sequential execution Otherwise, need arbitration to resolve conflict

Don’t loose updates! Results should not depend on the order received Semantics close to sequential version

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CRDTs and Consistency

Strong Eventual Consistency

Eventual delivery: Every update is eventually applied at all correct replicas Termination: Update operation terminates Strong convergence: Correct replicas that have applied the same update have equivalent state

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CRDT catalogue

Register (Laster-writer wins, Multi-value) Set (Grow-Only, Add-Wins, Remove-Wins) Flags Counter (unlimited, restricted/bounded) Graph (directed, monotone DAG) Sequence / List Map, JSON

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Specification: Replicated counter

All operations commute, no conflict resolution is needed Value returned depends only on E and op, but not on vis and ar Fctr(rd(), (E, op, vis, ar)) = |{e′ ∈ E | op(e′) = inc}| Next: Operational Semantics

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State-based CRDTs

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State-based specifications

Synchronization by propagating replica state Updates must inflate the state State must form a join semi-lattice wrt merge ⇒ Merge must be idempotent, commutative, associative

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Join-semilattice

A join-semilattice S is a set that has a join (i.e. a least upper bound) for any nonempty finite subset: For all elements x, y ∈ S, the least upper bound (LUB) x ⊔ y exists. A semilattice is a commutative, idempotent and associative. A partial order on the elements of S is induced by setting x ≤ y iff x ⊔ y = y.

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Examples

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Example: Counter

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Operation-based CRDTs

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Op-based specifications

Synchronization by propagating operations and re-apply Concurrent updates must commute Requires reliable causal delivery

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Example: Counter

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Example: Add-wins Set (Observed-remove Set)

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Example: Add-wins Set (Observed-remove Set)

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Optimized version of Add-wins Set

Possible to garbage-collect the tombstone after remove Trick: Assuming causal delivery, element will never be re-introduced (with the same id)[2]

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Optimized version of Add-wins Set

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Challenges with CRDTs

Meta-data overhead for CRDTs that require causal contexts

Version vectors track concurrent modifications (O(N) ⇒ Churn!)

Monotonically growing state with state-based approach

Tombstones ⇒ Garbage collection

Composability for recursive CRDTs (Maps, Sequences; Transactions)

What is the desirable semantics of the composed entity?

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Delta-based CRDTs

State-based CRDTs suffer from monotonically growing state Op-based CRDTs require causal delivery

Delta-based CRDTs[1]

Small message comprising a set of incremental updates Work over unreliable communication channels A delta-mutator mδ is a function, corresponding to an update

  • peration, which takes a state X in a join-semilattice S as parameter

and returns a delta-mutation mδ(X), also in S. X′ = X ⊔ mδ(X)

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Adoption of CRDTs in industry

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Conclusion

CRDTs provide Strong Eventual Consistency (sometimes even more) Data-type specific conflict resolution

Deterministic (independent of local update order) Relation to sequential semantics Meta-data overhead can be substantial

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Further reading I

[1] Paulo S´ ergio Almeida, Ali Shoker und Carlos Baquero. “Delta state replicated data types”. In: J. Parallel Distrib. Comput. 111 (2018), S. 162–173. doi: 10.1016/j.jpdc.2017.08.003. url: https://doi.org/10.1016/j.jpdc.2017.08.003. [2] Annette Bieniusa u. a. “An optimized conflict-free replicated set”. In: CoRR abs/1210.3368 (2012). arXiv: 1210.3368. url: http://arxiv.org/abs/1210.3368. [3] Nuno Preguic ¸a, Carlos Baquero und Marc Shapiro. “Conflict-Free Replicated Data Types (CRDTs)”. In: Encyclopedia of Big Data

  • Technologies. Hrsg. von Sherif Sakr und Albert Zomaya. Cham:

Springer International Publishing, 2018, S. 1–10. isbn: 978-3-319-63962-8. doi: 10.1007/978-3-319-63962-8 185-1. url: https://doi.org/10.1007/978-3-319-63962-8 185-1.

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