Merging Uncertain Multi-Version XML Documents

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Merging Uncertain Multi-Version XML Documents

M. Lamine BA, Talel Abdessalem & Pierre Senellart

ACM DocEng 2013 - 1st International Workshop on Document Changes (Florence, Italy)

September 10^th, 2013

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Merging feature: a need in open environments

I Merging documents related to the same topic or sharing a large common part, e.g., Wikipedia articles

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Merging feature: a need in open environments

I Merging documents related to the same topic or sharing a large common part, e.g., Wikipedia articles

I Recommend the outcome of the merging of contributions of the most trustworthy contributors

☛ Proposal of a merging operation over multi-version tree-structured documents with uncertain data

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Usual Merging Process over Documents

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Usual Merging Process over Documents

(i) Change Detection (diff algorithm): {u₁, u₂} and{u₃, u₄}

u1:Update A to A⁰ u2:Insert C

u3:Remove A u4:Insert D

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Usual Merging Process over Documents

(i) Change Detection (diff algorithm): {u₁, u₂} and{u₃, u₄}

(ii) Three merge scenarios: {A’, B, C, D},{B, C, D} and{A, B, C, D}

u1:Update A to A⁰ u2:Insert C

u3:Remove A u4:Insert D

merge outcome

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State-of-the-art XML Merging algorithms

I Diff algorithms, for instance [Lindholm et al., 2006], for documents having tree-like structure

I Two-way merging [Suzuki, 2002], [Ma et al., 2010] vs. Three-way merging [Lindholm, 2004], [Abdessalem et al., 2011]

I All deterministic approaches require human input in the presence of uncertainties, e.g. conflicts handling, for the merge outcome

I Probabilistic merging, proposed in [Ma et al., 2010], does not retain enough information for retrieving back individual merged versions

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State-of-the-art XML Merging algorithms

Outline

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Uncertain Tree-Structured Data

Probabilistic XML [Kimelfeld & Senellart.(2013)]

I Unordered, unranked, and labeledXML treeswith annotated edges

− annotations are propositional formulasof random Boolean variables

c P) r

p1 e1∨e2

t1 p2

¬e2

t2 PrXML^fiep-Document d1) r

p1

t1 p2

t2 F₁₁={e1}

d₂) r

p1

t1 F₂₁={e2} F₂₂={e1,e₂}

Pr(e1) = 0.2 Pr(e2) = 0.8

Pr(d1) =Pr(e1)×Pr(¬e2)

Pr(d2) = (Pr(¬e1)×Pr(e2)) + (Pr(e1)×Pr(e2))

Possible worlds and their probabilities

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Uncertain Tree-structured Multi-version Documents

Uncertain Tree-Structured Data

c P) r

p1 e1∨e2

t1 p2

¬e2

p1

t1 p2

t2 F₁₁={e1}

d₂) r

p1

t1 F₂₁={e2} F₂₂={e1,e₂}

Pr(e1) = 0.2 Pr(e2) = 0.8 Pr(d1) = 0.04 Pr(d2) = 0.80

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Uncertain Tree-Structured Data

c P) r

p1 e1∨e2

t1 p2

¬e2

p1

t1 p2

t2 F₁₁={e1}

d₂) r

p1

t1 F₂₁={e2} F₂₂={e1,e₂}

Pr(e1) = 0.2 Pr(e2) = 0.8 Pr(d1) = 0.04 Pr(d2) = 0.80

− Enumerating all possible worlds and their probabilities

− Enable also to model uncertain updates on (uncertain) nodes [Kharlamov et al.(2010)]

☞ Integrate such a representation in a typical version control process

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Uncertain Multi-Version XML Document

Uncertain Version Control Model

Defines two equivalent views over any uncertain multi-version XML tree

I set V of random variablese₀,e₁. . .e_n modeling the tree states

I infinite set D of all (unordered) XML trees including the versions

(G,Ω): Logical View

• DAGG built on variables inV

• Mapping Ω : 2^V^\{e⁰^}→D which computes the possible versions according to sets of valid events

(G,Pc): Probabilistic XML Encoding

• Similar DAGG of random variables inV

• Probabilistic XML treePcwhich defines the same probability distribution as Ω mapping

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Uncertain Multi-Version XML Document

Uncertain Version Control Model (Example)

d₂) person

name

“Obama”

origin

“Tanzania”

F₂={e1, e2}

d₄) person

name

“Obama

origin

“Tanzania”

function

“US. President”

F₄={e1,e2, e4} d₁) person

name

“Obama”

F₁={e1}

d₃) person

name

“B. Obama”

origin

“Kenya”

F₃={e1, e3}

e₂

e₃

e₄

G)

e2 e4 e₀ e₁

e₃

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Uncertain Multi-Version XML Document

d₂) person

name

“Obama”

origin

“Tanzania”

F₂={e1, e2}

d₄) person

name

“Obama

origin

“Tanzania”

function

“US. President”

name

“Obama”

F₁={e1}

d₃) person

name

“B. Obama”

origin

“Kenya”

F₃={e1, e3}

d₅) person

name

“B. Obama”

origin

“Kenya”

function

“US. President”

F₅={e1, e3,e4}

e₂

e₃

e₄

G)

e2 e4 e₀ e₁

e₃

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Uncertain Multi-Version XML Document

d₂) person

name

“Obama”

origin

“Tanzania”

F₂={e1, e2}

d₄) person

name

“Obama

origin

“Tanzania”

function

“US. President”

name

“Obama”

F₁={e1}

d₃) person

name

“B. Obama”

origin

“Kenya”

F₃={e1, e3}

d₅) person

name

“B. Obama”

origin

“Kenya”

function

“US. President”

F₅={e1, e3,e4}

e₂

e₃

e₄

G)

e2 e4 e₀ e₁

e₃

c

P) person

name

e₁

“Obama”

¬e3

“B. Obama”

e3

origin e₂∨e₃

“Tanzania”

¬e3

“Kenya”

e₃

function e₄

“US. President”

Encode uncertain changes over nodes with formulas on edges

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Uncertain XML Merging Operation Edit Detection

Uncertain XML Merging Operation

Edit Detection

I Three-way procedurediff3() detecting node insertions and deletions based on diff2() sub-routines

diff3(T₁,T₂,T_a) =diff2(T_a,T₁)∪diff2(T_a,T₂)

I diff3() output is an edit script consisting of equivalent, conflicting and independent edits

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Uncertain XML Merging Operation

Edit Detection

T₁) r

s2

p2

t2 T_a) r

s1 p1

t1

T₂) r

s1

p1

t1 p’1

t’1 u2:Delete the subtree s1

u4:Insert the subtree s2

u3:Insert the subtree p⁰1 at the node s1

diff2(T_a,T₁) ={u2,u4} diff2(T_a,T₂) ={u3}

diff3(T₁,T₂,T_a) ={u2,u4,u3}

u2and u3are conflicting edits u₄is an independent edit s1 is a conflicting node

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Uncertain XML Merging Operation Edit Detection

Uncertain XML Merging Operation

Edit Detection

I Three-way procedurediff3() detecting node insertions and deletions based on diff2() sub-routines

diff3(T₁,T₂,T_a) =diff2(T_a,T₁)∪diff2(T_a,T₂)

I diff3() output is an edit script consisting of equivalent, conflicting and independent edits

I ∆^C is considered as the restriction ofdiff3() to the set of conflicting edits (over conflicting nodes) for the merging

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Uncertain XML Merging Operation

Formal Definition(I)

Given the triple (e₁,e₂,e⁰), an uncertain merge operation is formalized as MRG_e

1,e2,e⁰

I eventse₁ ande₂ identify the two (uncertain) versions to be merged

I e⁰ (a merge event) is a new event assessing the amount of uncertainty in the merge

An uncertain merging operation MRG_e

1,e2,e⁰ onT_mv maps in a logic sense to the formula below

MRG_e

1,e₂,e⁰(T_mv) := (G ∪({e⁰},{(e₁,e⁰),(e₂,e⁰)}), Ω⁰).

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Uncertain XML Merging Operation Formal Definition

Uncertain XML Merging Operation

Formal Definition(II)

Let A_e

1={e |e ∈G, e ≺e₁},A_e

2 ={e |e ∈G, e ≺e₂}, A_s=A_e

1 ∩A_e

2

For all subset F ∈2^V^∪{e⁰^}, Ω⁰ is computed based on Ω mapping as follows

I ife⁰6∈F: Ω⁰(F) := Ω(F);

I if{e1,e2,e⁰} ⊆F: Ω⁰(F) := Ω(F\ {e⁰});

I if{e1,e⁰} ⊆F∧e26∈F: Ω⁰(F) := [Ω((F \ {e⁰})\(A_e₂\A_s))]^∆²^−∆^C; I if{e2,e⁰} ⊆F∧e16∈F: Ω⁰(F) := [Ω((F \ {e⁰})\(A_e

1\A_s))]^∆¹^−∆^C; I if{e1,e2} ∩F =∅ ∧e⁰∈F:

Ω⁰(F) := [Ω((F\ {e⁰})\((A_e

1\A_s)∪(A_e

2\A_s)))]^∆³^−∆^C;

th

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Uncertain XML Merging Operation

T₁) r

s2

p2

t2 {e1,e₂,e₄} T_a) r

s1

p1

t1 {e1}

T₂) r

s1

p1

t1 p’1

t’1 {e1,e3} u2:Delete the subtree s1

u3:Insert the subtree p⁰₁ at the node s1

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Uncertain XML Merging Operation

T₁) r

s2

p2

t2 {e1,e₂,e₄} T_a) r

s1

p1

t1 {e1}

MRGe3,e4,e0

r s2 p2 t2 {e⁰} T₂) r

s1

p1

t1 p’1

t’1 {e1,e3} u2:Delete the subtree s1

(evente’)

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Uncertain XML Merging Operation

T₁) r

s2

p2

t2 {e1,e₂,e₄} T_a) r

s1

p1

t1 {e1}

MRGe3,e4,e0

r s2 p2 t2 {e⁰}

r

s2

p2

t2 F={e1,e₂,e₄,e⁰}

Ω⁰(F) = [T₁]^{∅}

T₂) r

s1

p1

t1 p’1

t’1 {e1 e₃} u2:Delete the subtree s1

(evente’) Propagateu2

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Uncertain XML Merging Operation

T₁) r

s2

p2

t2 {e1,e₂,e₄} T_a) r

s1

p1

t1 {e1}

MRGe3,e4,e0

r s2 p2 t2 {e⁰}

r

s1

p1

t1 p’1

t’1 s2

p2

t2 F={e1,e₃,e⁰} Ω⁰(F) = [T₂]^{u⁴^} T₂) r

s1

p1

t1 p’1

(evente’) Propagateu3

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Uncertain XML Merging Operation

T₁) r

s2

p2

t2 {e1,e₂,e₄} T_a) r

s1

p1

t1 {e1}

MRGe3,e4,e0

r s2 p2 t2 {e⁰}

r

s1

p1

t1 s2

p2

t2 F={e1,e⁰} Ω⁰(F) = [T_a]^{u⁴^} T₂) r

s1

p1

t1 p’1

(evente’) Rejectu2andu3

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Merging over Probabilistic XML Conflicting and Non-conflicting Nodes

Merging Probabilistic XML (MergePrXML)

Conflicting and Non-conflicting Nodes

I MergePrXML distinguishes conflicting nodes to non-conflicting ones Under the probabilistic XML EncodingTc_mv, a givenx in Pcis a conflicted node with respect to MRG_e

1,e2,e⁰ when its lineagefie^↑(x) is such that –

1. fie^↑(x)|=νs;

2. fie^↑(x)6|=ν1(orfie^↑(x)6|=ν2) and;

3. ∃y∈Pc,desc(x, y): fie^↑(y)6|=νs andfie^↑(y)|=ν2(orfie^↑(y)|=ν1)

I fie^↑(x) =V

z∈Pc,zx(fie(z)) and ν_s,ν₁, ν₂ are valuations over A_s, A_e

1,A_e

2 respectively

I MergePrXML implements MRG_e

1,e2,e⁰ as an update operation inPc that only modifies formulas of non-conflicting nodes of the merge

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Merging Probabilistic XML (MergePrXML)

Merge Algorithm (I)

Input: (G,Pc), e₁,e₂,e⁰

Output: Merging Uncertain XML Versions in Tc_mv G :=G ∪({e⁰},{(e₁,e⁰),(e₂,e⁰)});

foreach non-conflicted node x inPc\Pc_|_C

{e1, e2} do replace(fie(x), e₁,(e₁∨e⁰));

replace(fie(x), e₂,(e₂∨e⁰));

return(G,Pc)

✉ MergePrXML performs the merge in time proportional to the size of the formulas of nodes impacted by the updates in merged branches

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Merging over Probabilistic XML Merge Algorithm

Merging Probabilistic XML (MergePrXML)

Merge Algorithm (II)

c

P) r

s1

e1∧ ¬e2

p1

t1

p’1

e3

t’1

s2

e4

p2

t2

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Merging Probabilistic XML (MergePrXML)

c

P) r

s1

e1∧ ¬e2

p1

t1

p’1

e3

t’1

s2

e4

p2

t2

MRG_e

3,e₄,e⁰

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Merging over Probabilistic XML Merge Algorithm

Merging Probabilistic XML (MergePrXML)

c

P) r

s1

e1∧ ¬e2

p1

t1

p’1

e3

t’1

s2

e4

p2

t2

c

P⁰) r

s1

e₁∧ ¬e₂

p1

t1

p’1

e3

t’1

s2

e4∨e⁰

p2

t2

MRG_e

3,e₄,e⁰

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Conclusion and Further Works

I Merging operation over tree-structured multi-version documents with uncertain data

I implementation of the common deterministic merge scenarios

I modelling of the amount of uncertainty in the merged versions

I Efficient merging algorithm over Probabilistic XML encoding

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Conclusion and Further Works

References I

Abdessalem, T., Ba, M. L., and Senellart, P. (2011).

A probabilistic XML merging tool.

InProc. EDBT.

Ba, M. L., Abdessalem, T., and Senellart, P. (2011).

Towards a version control model with uncertain data.

InPIKM.

Ba, M. L., Abdessalem, T., and Senellart, P. (2013).

Uncertain version control in open collaborative editing of tree-structured documents.

InProc. DocEng.

Kharlamov, E., Nutt, W., and Senellart, P. (2010).

Updating Probabilistic XML.

InProc. Updates in XML.

Kimelfeld, B. and Senellart, P. (2013).

Probabilistic XML: Models and Complexity.

InAdvances in Probabilistic Databases for Uncertain Information Management. Springer-Verlag.

Lindholm, T. (2004).

A three-way merge for XML documents.

InProc. DocEng.

Lindholm, T., Kangasharju, J., and Tarkoma, S. (2006).

Fast and simple XML tree differencing by sequence alignment.

InProc. DocEng.

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References II

Ma, J., Liu, W., Hunter, A., and Zhang, W. (2010).

An XML based framework for merging incomplete and inconsistent statistical information from clinical trials.

In Ma, Z. and Yan, L., editors,Software Computing in XML Data Management. Springer-Verlag.

Suzuki, N. (2002).

A Structural Merging Algorithm for XML Documents.

InProc. ICWI.