FaultTolerant SemiFast Implementations of Atomic ReadWrite Registers

1
Fault-Tolerant SemiFast Implementations of
Atomic Read/Write Registers

• Nicolas Nicolaou, University of Connecticut
• Joint work with
• C. Georgiou, University of Cyprus
• A. A. Shvartsman, University of Connecticut

2
What is an Atomic R/W Register?
Register
Read
Write(7)
Write(0)
3
Prior Results

• Attiya et al. 1995 - Single Writer Multiple
  Reader (SWMR) model where lt1/2 of processes may
  crash
• Pairs ltvalue, taggt are used for ordering
  operations
• Writer increases tag and sends ltvalue, taggt to a
  majority
• Reader
• Phase 1 obtains maximum tag from a majority
• Phase 2 propagates the tag to a majority and then
  returns the value associated with that tag
• Lynch, Shvartsman 1997 and Englert, Shvartsman
  2000 extend the above result for MWMR
• Quorums instead of majorities
• 2 round protocols for read/write operations

4
Fast Implementations

• Dutta, Guerraoui, Levy, Chakraborty 2004
• SWMR model
• Single communication round for all write and read
  operations
• Requires R lt (S/t) 2
• R readers, S servers, t max server
  failures
• Not applicable to MWMR

Question Can one introduce SemiFast
Implementations (with fast reads or fast writes)
to relax the bound on the number of readers?
5
Our Contributions

• Formally define semifast implementations
• Develop a semifast implementation
• Based on Fast implementation of Dutta et al. 04
• Introduce the notion of virtual nodes
• Bounds On the Number of Virtual Nodes
• Show that no SemiFast implementations are
  possible for MWMR
• Simulation Results
• A small percentile of read operations require a
  second communication round.

6
Model
Writer
Reliable communication channels (For
performance, not for safety)
Servers
Up to t Failures tlt(S/2)
sS
s2
s1
Readers
Any subset of readers /writer may fail by crash.
r2
r1
Siblings
rR
Virtual Nodes Vlt(S/t)-2
vrV
vr2
vr1
7
Semifast Implementations

• Def. An implementation I is semifast if it
  satisfies the following properties (informally)
• All writes are fast
• All complete read operations perform one or two
  communication rounds
• ?f a read operation ?1 performs two communication
  rounds, then all read operations that precede or
  succeed ?1 and return the same value as ?1 are
  fast
• ?here exists some execution of I which contains
  only fast read and write operations
• Assuming all written values are unique

8
SF Implementation

• Replica consists of
• Timestamp associated with 2 values
• Current value and Previous value
• Writer
• Send the new timestamp to S-t servers
• Increase its own timestamp

ts1
ts2
S-t WACKs receivedgt ts, ret(O.K.)
WRITE, ts1, w
WACK, ts1
ts0 ps0
ts0 ps0
ts0 ps0
ts1 ps0 w
ts1 ps0 w
ts0 ps0
ts0 ps0
ts1 ps0 w
ts1 ps0 w
s3
s4
s5
s1
s2
9
SF Implementation (Cont.)

• Reader
• Inquire timestamp from S-t servers
• Server on receipt of a read/write message
• Record Virtual Identifiers of nodes inquire the
  servers timestamp ts, into a set (seen set).
• If tsltts gt seen vid ts ts
• If tsgtts gt seen seen U vid
• If msgType Inform gt postit ts

10
The servers(Example)
11
The servers(Example)
12
SF Implementation (Cont.)

• Reader
• Consider return of timestamps
• Return timestamp as follows
• If Predicate True return Maximum Timestamp
• If Postit MaxTS return Maximum Timestamp
• Otherwise return Maximum Timestamp -1
• The definition of the Predicate will be given
  later

13
Predicate(Key Idea)
Completed
ts0 ps0 vr1
ts1 ps0 w,vr1
ts1 ps0 w,vr1
ts1 ps0 w
ts1 ps0 w,vr1
s5
s1
s2
s3
s4
I have to return 1
S-2t servers with ts1
ts0 r1(vr1)
14
Predicate(Key Idea)
ts1 ps0 w,vr1,vr2
ts1 ps0 w,vr1
ts1 ps0 w,vr1,vr2
ts0 ps0 vr2
ts0 ps0 vr1,vr2
s2
s3
s1
s4
s5
MS S-3t
Completed, returned 1
I have to return 1
ts0 r2(vr2)
ts1 r1(vr1)
15
Predicate(Final Form)

• Predicate is true if a read operation
• Receives maxTS from MS S-at servers (i.e.
  S-3t)
• Observes that (i.e. )
• Formally

16
Sibling Problem
ts1 ps0 w,vr1
ts1 ps0 w,vr1
ts0 ps0 vr1
ts0 ps0 vr1
ts1 ps0 w,vr1
s2
s3
s1
s4
s5
MS S-3t
Completed, returned 1
Predicate is false! return 0
ts0 r2(vr1)
ts1 r1(vr1)
17
SF Implementation (Cont.)

• Reader must perform second comm. round if
• Predicate True nm.seena
• Postit MaxTS Postits lt t1

18
Which readers must write?

• Observation
• Two read operations r1 and r2
• MS1 gt servers replied with maxTS to r1
• MS2 gt servers replied with maxTS to r2
• Then MS1-MS2 t gtIf MS1S-at
  then MS2 S-(a1)t
• If r1 and r2 are siblings
• Let si ? MS1nMS2
• si sent m1 and m2 to r1 and r2 resp.
• It may be the case m1.seen m2.seen
• Thus if then

19
Correctness

• We need to show the following
• Writes are globally ordered
• If a read() returns a value x then a write(x)
  operation immediately precedes or is concurrent
  with that read
• A read operation does not return an older value
  than a preceding read operation
• Reads done by sibling readers
• Reads done by non-siblings readers

20
Impossibility

• Consider Algorithms
• With no virtual nodes
• With grouping mechanisms similar to our approach
• Theorem There is no semifast implementation if
  the number of virtual nodes is V (S/t) - 2.

21
MWMR model

• Theorem There is no semifast implementation for
  the MWMR model
• Proved in the case of 2 writers, 2 readers and 1
  failure
• We consider n communication rounds

22
Simulation Results

• NS2 Simulator
• Only 10 of read operations need to perform 2nd
  communication round
• Stochastic Environment
• Fix Interval Environment

23
Conclusions

• Semifast implementation is defined
• Only one complete read operation has to perform 2
  comm. rounds for every write operation
• SF implementation presented
• Virtual Nodes lt (S/t) - 2
• No semifast implementation possiblefor MWMR
  model

24
References

• Partha Dutta, Rachid Gerraoui, Ron R. Levy and
  Arindam Chakraborty, How Fast can a Distributed
  Atomic Read be, Proceedings of the 23rd annual
  ACM Symposium on Principles of distributed
  computing (PODC 2004), pp. 236- 245, ACM press
  2004.
• S. Dolev, S. Gilbert, N.A.Lynch,A.A.Shvartsman,J.
  L.Welch GeoquorumsImplementing Atomic Memory in
  Mobile Ad-Hoc Networks, Technical Report
  LCS-TR-900, MIT (2003)
• Nancy Lynch and Alex Shvartsman. Rambo A
  reconfigurable atomic memory service for dynamic
  networks. In Proceedings of the 16th
  International Symposium on Distributed Computing,
  pages 173-- 190, 2002
• H.Attiya, A.Bar-Noy, and D.Dolev Sharing memory
  robustly in message-passing systems, Journal of
  the ACM, January 1995.
• B. Englert and A. A. Shvartsman. Graceful quorum
  reconfiguration in a robust emulation of shared
  memory.In International Conference on Distributed
  Computing Systems, pages 454463, 2000
• N. A. Lynch and A. A. Shvartsman. Robust
  emulation of shared memory using dynamic
  quorumacknowledged broadcasts. In Symposium on
  Fault-Tolerant Computing, pages 272281, 1997

25

• Questions?

26
Atomicity

• Lynch96
• Valid Executions
• Invalid Executions

write(8)
write(8)
ack( )
Time
Time
read( )
ret(0)
read( )
read( )
ret(0)
ret(8)
write(8)
ack( )
write(8)
Time
Time
read( )
ret(0)
read( )
ret(0)
read( )
ret(8)
read( )
ret(0)
27
Definitions

• Each process invokes 1 operation at a time.
• Each operation consists of
• Invocation Step
• Matching Response Step
• Incomplete Operation no matching response for
  the invocation. Complete operation
• op1 precedes op2 gt response for op1 precedes
  invocation for op2.
• If op is a read we write rd
• If op is a write we write wr

28
Definitions (Cont.)

• Algorithm implements a register gt satisfies
  termination and atomicity properties
• Termination Every operation by correct process
  completes.
• Atomicity (SWMR, wrkkth write)
• If rd returns x then there is wrk s.t. valkx
• If wrk precedes rd and rd returns valj, then j
  k
• If rd returns valk then wrk precedes or is
  concurrent to rd
• If rd1 returns valk and a succeeding rd2 returns
  valj then j k

29
Atomic vs Shared Register

• Shared Register
• Accessible from Single Process
• Write(v) Stores the value v and returns OK
• Read() Read the last value stored
• Atomic Register
• A distributed data structure
• Accessed by multiple processes concurrently
• Behaves as a sequential register.
• (Recall Atomicity)

30
Atomic vs Shared Register(Graphical)

• Sequential Register
• Atomic Register

Register0
Register8
Read(0)
WriteAck()
Read(8)
Register
Write(8)
WriteAck( )
ReadAck2(0)
Read1( )
ReadAck1(8)
Read2( )
31
Non-Triviality

• A semifast implementation is not trivial if
• For any execution of , if contains the
  operations and some , performs 2comm.
  rounds, then any , , must be fast.
• For any execution of , if two read
  operations rd1 and rd2 return the same value and
  rd

32
Strict Communication Scheme

• Only messages from the invoking processes to the
  servers are delivered.
• No messages between any servers
• No messages between any invoking processes

33
When a SemiFast Impl. is Impossible?

• When Vlt(S/t)-2
• If V(S/t)-1 then No fast implementation even in
  the case of a skip-free write operation.
  (violates non-triv. Property 3)
• If V(S/t)-2 then there is an execution where we
  need 2 complete read operations to perform 2 com.
  rounds. (violates Property 1)
• When V(S/t)-2
• There exists an execution where 2 read operations
  return the same value and they both perform 2
  com. rounds (violates Prop. 2).

34
No Semifast for MWMR model.

• Proof Sketch
• Split multiple round operations into
• Read phases
• Write phases
• Show that as soon as an operation performs a
  write phase cannot change its return value.
• Show a construction where W2, R2 and t1 and
  atomicity is violated.

35
Challenge

• How fast can a general implementation of an
  Atomic Register can be?
• Dynamic Environment (Mobility)
• Hybrid implementations with some read and write
  operations to perform multiple roundtrips.
• Communication Overhead in such impl.?
• Quorum based algorithms. How fast can they be?