Refined Quorum Systems

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Refined Quorum Systems
Rachid Guerraoui and Marko Vukolic
Ecole Polytechnique Federale de Lausanne School
of Computer and Communication Sciences EPFL / IC
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• " Plan for the worst, hope for the best. 
• English proverb

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Distributed algorithms

• Plan for
• Many failures
• Asynchrony
• Contention

• Hope for
• Few (no) failures
• Synchrony
• No Contention

• Optimistic algorithms
• optimize w.r.t complexity
• (e.g., latency)

• Resilient algorithms

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Contribution

• An abstraction to devise
• resilient optimistic algorithms

Refined Quorum Systems (RQS)
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The paper

• RQS definition
• Optimal algorithms built around RQS
• Atomic storage (register abstraction)
• Consensus (state machine replication)

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This talk

• Why RQS?
• What is RQS?
• How to use RQS?

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A simple example

• Single writer crash-tolerant atomic storage
• Implemented over 5 servers
• Any majority is a quorum (2 servers may crash)

WRITE (v1)
W
S E R V E R S
1
2
3
4
5
R1 R2
READ -gt v1
READ
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A simple example

• What if we want to expedite only best-case
  operations
• that access all (5) servers?

WRITE (v1)
W
S E R V E R S
1
2
3
4
5
R1 R2
READ -gt v1
READ
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A simple example

• Do we really need to access all servers?
• Is it sufficient to access only 4?

WRITE (v1)
W
S E R V E R S
1
2
3
4
5
R1 R2
READ -gt v1
READ
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What is really going on?

• Traditional quorum intersections are too small
  for building optimistic, yet resilient, atomic
  storage

W Quorum
R1 Quorum
3
4
2
5
1
R2 Quorum
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What is really going on?

• Intuitively, if all servers are accessed
  operations can be expedited

W Quorum
R1 Quorum
3
4
2
5
1
R2 Quorum
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What is really going on?

• In a set of 5 servers, an intersection of any 2
  subsets of 4 servers, intersects with a subset of
  3 servers

R1 Quorum
W Quorum
3
4
2
5
1
R2 Quorum
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Question

• What mathematical abstraction captures these
  "larger" intersections in the general context of
• Byzantine failures (w/o authentication)?
• Non-threshold quorums/failures?
• Graceful degradation?

Answer Refined Quorum Systems
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Refined Quorum Systems

• Consider object O implemented over a set of
  processes S
• RQS 3 classes of refined quorums (subsets of S)
• Class 3 ? Class 2 ? Class 1
• Let l1 be the best possible latency for O no
  failures, synchrony and no-contention
• Let l2, l3 be the next best possible latencies

Class j quorum correct
Synchrony
no contention




Latency lj is achieved!
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Back to the example

• Any quorum that contains at least 4 servers is
  class 1
• Other quorums (simple majorities) are class 2

W quorum (Class 1)
R1 quorum (Class 1)
3
4
2
5

• l1 1 round trip
• l2 2 round trips

1
R2 quorum (Class 2)
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Refined Quorum Systems(definition)

• Consider a set S, let RQS be any set of quorums
  (subsets of S)
• Consider an adversary structure B for S
• B is a set of subsets of S such that ?B?B
  B? B ? B?B
• RQS is a refined quorum system, if
• ? QC1, QC2 QC1 ? QC2 ? QC3 RQS, such that
• (elements of QCi are called class i quorums)
• P1) ? Q3, Q3 ? QC3 Q3 ? Q3 ? B
• P2) ? Q1, Q1 ? QC1, ? Q3 ? QC3 , ? B1, B2 ? B
• Q1 ? Q1 ? Q3 ? B1 ? B2
• P3) ? Q2 ? QC2, ? Q3 ? QC3 , ? B1, B2 ? B
• ? Q2 ? Q3 ? B1 ? B2
• ? ? Q1 ? QC1 Q1 ? Q2 ? Q3 ? B

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Application 1 Storage

• Single writer atomic storage (register)
• Clients
• Crash faulty (non-Byzantine)
• Servers
• RQS formed around servers
• Do not communicate among themselves
• Send messages only in response to clients
• Safety
• Byzantine server failures adversary B
• Any number of crash failures!
• Liveness
• As long as there is (any) quorum of correct
  servers

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Application 1 Storage
Client (reader or writer)
2nd round-trip
3rd round-trip
Class 2 quorum
S E R V E R S
Class 3 quorum
Class 1 quorum
li i round-trips (i1..3)
Synchrony no contention
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Application 2 Consensus

• Consensus (Lamports SMR framework)
• Proposers, learners
• Any number may be Byzantine
• Acceptors
• RQS formed around acceptors
• may communicate among each other
• Safety
• Byzantine acceptor failures adversary B
• Liveness
• As long as there is (any) quorum of correct
  acceptors
• Eventual synchrony (FLP)

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Application 2 Consensus
propose(v)
proposer
Class 1 quorum
Class 2 quorum
Class 3 quorum
A C C E P T O R S
learners
learn v
learn v
learn v
li i1 message delays (i1..3)
Synchrony no contention
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(Some) Open questions

• Authentication and weaker semantics
• Number of RQS given a set S and adversary
• Opaque RQS

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Summary
Refined Quorum Systems (RQS)

• An abstraction to devise
• resilient optimistic algorithms

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• Thank you