Tombstone Transformation Functions for Ensuring Consistency in Collaborative Editing Systems

1
Tombstone Transformation Functions for Ensuring
Consistency in Collaborative Editing Systems

• Gérald Oster, Pascal Molli, Pascal Urso and
  Abdessamad Imineoster,molli,urso,imine_at_loria.fr

2
Outline

• Context
• Background (Operational Transformation)
• Model
• Correctness properties
• TTF Approach
• Summary

3
Context

• Collaborative editing systems
• Multiple users
• Distributed across space and time
• Supporting multi-synchronous editing Dourish95
• Synchronous (real-time), asynchronous
  (disconnected work), combination of Sync./Async.

4
Context

• Documents are replicated (optimistic)
• High responsiveness
• Disconnection support
• Users work on their own copy and produce
  operations
• Executed locally
• Sent to other copies
• Integrated with other operations
• Executed on remote copies
• How to maintain consistency of replicated
  documents?

5
Outline

• Context
• Background (Operational Transformation)
• Model
• Correctness properties
• TTF Approach
• Summary

6
Copies Convergence

• Concurrent order gt different integration
  orders
• gt different state of the copies of the document

abc
abc
op2Insert(2,y)
op1Insert(3,x)
abxc
aybc
op1Insert(3,x)
op2Insert(2,y)
ayxbc
aybxc
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Operational Transformation (OT) Ellis89

• From Real-time groupware
• T(op2operation, op1operation) op2
• op1 and op2 are concurrent, defined same state S
• op2 same effects as op2, but defined on state
  S.op1

abc
abc
op2Insert(2,y)
op1Insert(3,x)
abxc
aybc
op1T(op1,op2) Insert(4,x)
op2T(op2,op1) Insert(2,y)
aybxc
aybxc
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Consistency Maintenance

• Genericity of OT approach
• 2 components
• Integration algorithm
• Transformation functions
• Correctness relies on
• Correctness of integration algorithm
• Properties on transformation functions
• Different OT integration algorithms gt
  different properties

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Correctness Properties Ressel96 /1

• TP1 op1 . T(op2,op1) op2 . T(op1,op2)

op2
op1
op1T(op1,op2)
op2T(op2,op1)
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Correctness Properties Ressel96 /2

• TP2 T(op3, op1.T(op2,op1)) T(op3,
  op2.T(op1,op2))

op2
op1
op3
op1
op2
op3
op3
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Problem

• There is no published transformations (Ellis89,
  Ressel96, Sun98, Suleiman98, IMOR03) ensuring
  both
• TP1
• TP2
• Existence of such transformations?
• Guidelines to write them?

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Outline

• Context
• Background (Operational Transformation)
• Model
• Correctness properties
• TTF Approach
• Summary

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Common Problem (false-tie)
axyc? ayxc?
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Our Approach

• Keep tombstones of deleted elements
• Model sequence of (character, visibility_flag)

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Tombstone Transformation Functions (TTF)

• T(Insert(p1,el1,sid1), Insert(p2,el2,sid2))
• if(p1ltp2) return Insert(p1,el1,sid1)
• else if(p1p2 and sid1ltsid2) return
  Insert(p1,el1,sid1)
• else return Insert(p11,el1,sid1)
• T(Insert(p1,el1,sid1), Delete(p2,el2,sid2))
• return Insert(p1,el1,sid1)
• T(Delete(p1,sid1), Insert(p2,sid2))
• if(p1ltp2) return Delete(p1,sid1)
• else return Delete(p11,sid1)
• T(Delete(p1,sid1), Delete(p2,sid2))
• return Delete(p1,sid1)

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Correctness

• TTF satisfy TP1 TP2
• Proofs built using a theorem prover
• TTF are injective functions
• Reversibility property T-1( T( op1 ,op2 ), op2
  ) op1

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Inverses of Transformation Functions

• T-1(Insert(p1,el1,sid1), Insert(p2,el2,sid2))
• if(p1ltp2) return Insert(p1,el1,sid1)
• else if(p1p2 and sid1ltsid2) return
  Insert(p1,el1,sid1)
• else return Insert(p1-1,el1,sid1)
• T-1(Insert(p1,el1,sid1), Delete(p2,el2,sid2))
• return Insert(p1,el1,sid1)
• T-1(Delete(p1,sid1), Insert(p2,sid2))
• if(p1ltp2) return Delete(p1,sid1)
• else return Delete(p1-1,sid1)
• T-1(Delete(p1,sid1), Delete(p2,sid2))
• return Delete(p1,sid1)

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Compacted Storage Model (C-TTF)

• C-Model sequence of (character, abs_pos)

view2model()
Insert(5,y)
y
h
a
b
c
n
Model
View
Insert(3,y)
a
b
y
c
view2model()
Compacted Model
Insert(5,y)
a,2
b,3
y,5
c,6
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Delta Storage Model (D-TTF)

• D-Model sequence of (character, offset)

view2model()
Insert(5,y)
Compacted Model
a,2
b,3
y,5
c,6
a
View
Insert(3,y)
b
y
c
view2model()
DeltaModel
Insert(5,y)
c,1
a,2
b,1
y,2
Ce,1
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Models Comparison

• Basic Model
• Deleted characters are kept
• Size of the model is growing infinitely
• Compacted Model
• Update absolute position of all characters
  located after the effect position
• Delta Model
• Update the offset of next character
• Our observations
• View2model can be optimised (caret position)
• Overhead of view2model is not significant

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Outline

• Context
• Background (Operational Transformation)
• Model
• Correctness properties
• TTF Approach
• Summary

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Conclusion Future Work

• First set of transformation functions satisfying
• TP1TP2 properties
• Reversibility property
• Could be used with adOPTed, SOCT2-3-4-5, GOT,
  GOTO, COT,
• Guidelines to develop transformations
• Extend approach to other data-structures
• Supporting group undo
• Management of conflicts

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Gérald Oster ltoster_at_loria.frgt
CollaborateCom 2006, Atlanta, Georgia,USA,
November 2006