Producing XML Documents with Guaranteed “Good” Properties David W. Embley Brigham Young...

Producing XML Documents with Guaranteed “Good” PropertiesDavid W. Embley

Brigham Young University

Wai Y. MokUniversity of Alabama in Huntsville

Sponsored in part by the National Science Foundation under grant number IIS-0083127

“Good” ~ XNF

Motivation XML is for Information Exchange. What constitutes a “good” XML document for Information Exchange?

Principles XML Document Properties

A Few Large Trees. No Redundancy.

Information Modeling Create a conceptual model. Generate “good” XML.

XNF Align XML trees with natural hierarchies in the data. Base redundancy elimination on FDs, naturally occurring MVDs, and

inclusion dependencies (IDs).

Example: XNF

GradStudent

FacultyMember

Hobby

Program

Department

GradStudent

FacultyMember

Hobby

Program

Department

F D

S P H

H

( F D ( S P ( H )* )* ( H )* )*

Kelly CS Pat PhD Hiking Hiking Skiing Skiing

Tracy MS Hiking Sailing

Chris MS

Lynn Math Sailing

Example: More Trees Than Necessary

GradStudent

FacultyMember

Hobby

Program

Department

GradStudent

FacultyMember

Hobby

Program

Department

S P F D

H F

H

( S P F ( H )* )* ( D ( F ( H )* )*

Pat PhD Kelly Hiking CS Kelly Hiking Skiing Skiing

Tracy MS Kelly Hiking Math Lynn Sailing Sailing

Chris MS Kelly

Example: Redundancy

GradStudent

FacultyMember

Hobby

Program

Department

GradStudent

FacultyMember

Hobby

Program

Department

H

S P

( H ( S P )* )*

Hiking Pat PhD Tracy MS

Skiing Pat PhD

Sailing Tracy MS

S

H

F

( S ( H ( F )* )* )*

Pat Hiking Kelly Skiing Kelly

Tracy Hiking Kelly

Sailing Lynn

Chris

XNF → XML

GradStudent

FacultyMember

Hobby

Program

Department

GradStudent

FacultyMember

Hobby

Program

Department

F D

S P H

H

( F D ( S P ( H )* )* ( H )* )*



Chris MS

Lynn Math Sailing

Naive DTD Generation

F D

S P H

H

( F D ( S P ( H )* )* ( H )* )*



Chris MS

Lynn Math Sailing

<!DOCTYPE University[<!ELEMENT University ( ( Faculty_Member, Department, ( Grad_Student, Program, ( Hobby )* )* ( Hobby )* )*, <!ELEMENT Faculty_Member (#PCDATA)> …]>

Naive DTD Generation

F D

S P H

H

<!DOCTYPE University[<!ELEMENT University ( ( Faculty_Member, Department, ( Graduate_Student, Program, ( Hobby )* )* ( Hobby )* )*, <!ELEMENT Faculty_Member (#PCDATA)> …]> <University>

<Faculty_Member>Kelly</Faculty_Member> <Department>CS</Department> <Graduate_Student>Pat</Graduate_Student> <Program>PhD</Program> <Hobby_S>Hiking</Hobby_S> <Hobby_S>Skiing</Hobby_S> <Graduate_Student>Tracy</Graduate_Student> <Program>MS</Program> <Hobby_S>Hiking</Hobby_S> <Hobby_S>Sailing</Hobby_S> <Graduate_Student>Chris</Graduate_Student> <Program>MS</Program> <Hobby_F>Hiking</Hobby_F> <Hobby_F>Skiing</Hobby_F> <Faculty_Member>Lynn</Facutly_Member> <Hobby_F>Sailing</Hobby_F></University>

Sophisticated DTD Generation

F D

S P H

H

Faculty Members

Grad_Students

Hobbies

Hobbies

<!DOCTYPE University[<!ELEMENT University (Faculty_Members)> <!ELEMENT Faculty_Members (Faculty_Member)*> <!ELEMENT Faculty_Member (Department, Grad_Students, Hobbies)> <!ATTLIST Faculty_Member value CDATA #REQUIRED> <!ELEMENT Department (#PCDATA) <!ELEMENT Grad_Students (Grad_Student)*> <!ELEMENT Grad_Student (Program, Hobbies)> …]>

<University> <Faculty_Members> <Faculty_Member value=“Kelly”> <Department>CS</Department> <Grad_Students> <Grad_Student value=“Pat”> <Program>PhD</Program> <Hobbies> <Hobby>Hiking</Hobby> <Hobby>Skiing</Hobby> </Hobbies> </Grad_Student> <Grad_Student value=“Tracy”> … </Faculty_Members></University>

→ XNF

GradStudent

FacultyMember

Hobby

Program

Department

GradStudent

FacultyMember

Hobby

Program

Department

F D

S P H

H

( F D ( S P ( H )* )* ( H )* )*



Chris MS

Lynn Math Sailing

How do we generateXNF scheme-trees?

Alg. 1

GradStudent

FacultyMember

Hobby

Program

Department

GradStudent

FacultyMember

Hobby

Program

Department

F D

S P H

H


Algorithm 1Until all vertices and edges are included: Find a start vertex: -- included in most enclosures -- back off by one, if possible Grow a tree as large as possible: -- cut out hierarchy (watch out for optionals) -- add adjacent vertices: -- within node (for functional edges) -- below node (for non-functional edges)

Alg. 1: Start

GradStudent

FacultyMember

Hobby

Program

Department

GradStudent

FacultyMember

Hobby

Program

Department

F D

S P H

H



1

2 3

1 2

Alg. 1: Start

GradStudent

FacultyMember

Hobby

Program

Department

GradStudent

FacultyMember

Hobby

Program

Department

F D

S P H

H


Algorithm 1Until all vertices and edges are included: Find a start vertix: -- included in most enclosures -- back off by one, if possible Grow a tree as large as possible: -- cut out hierarchy (watch out for optionals) -- add adjacent vertices: -- within node (for functional edges) -- below node (for non-functional edges)

1

2 3

1 2

GradStudent

FacultyMember

Hobby

Program

Department

GradStudent

FacultyMember

Hobby

Program

DepartmentAlg. 1: Grow

F D

S P H

H



Alg. 1: Grow

GradStudent

FacultyMember

Hobby

Program

Department

GradStudent

FacultyMember

Hobby

Program

Department

F D

S P H

H



√

Alg. 1: Grow

GradStudent

FacultyMember

Hobby

Program

Department

GradStudent

FacultyMember

Hobby

Program

Department

F D

S P H

H



√

√

Algorithm 1 Yields XNF

Theorem. Given a canonical, binary conceptual-model (CM)hypergraph H, Algorithm 1 generates an XNF scheme-treeforest with respect to the FDs and MVDs of H.

Proof: Based on NNF (Mok, et al., TODS, 1996)

What is this restriction?

Can we relax this constraint?

Can we enlarge the set of dependencies?

Non-Canonical CM Hypergraphs

GradStudent

DepartmentFacultyMember

Hobby

ProgramGradStudent

DepartmentFacultyMember

Hobby

Program

If the input CM hypergraph has redundancy, Algorithm 1generates scheme trees with potential redundancy.

D

F S

S P H

H

The set of studentsmust be the samefor every department.

F D

S P D H

H

A faculty member’sdepartment is the sameas the faculty member’sstudents’ department.A CM hypergraph is canonical if:

(1) No edge is redundant,(2) No edge is losslessly decomposable, and(3) No vertex is redundant.

Non-Binary CM Hypergraphs

Address DayTime

Name Course

Phone

Major

Address DayTime

Name Course

Phone

Major

Address

Name Course

DayTimePhone

Major

Address

Name Course

DayTimePhone

Major

Not Canonical:Decomposable

Generating Scheme Trees fromNon-Binary CM Hypergraphs

Address

Name Course

DayTimePhone

Major

Address

Name Course

DayTimePhone

Major

N A M

C

C

D

T

C

D Tor or …

A P

Alg. 2

Address

Name Course

DayTimePhone

Major

Address

Name Course

DayTimePhone

Major

N A M

C

C

D

T

A P Algorithm 2Until all vertices and edges are included: Find a start edge and configure it Grow a tree as large as possible -- cut out hierarchy (watch out for optionals) -- add and configure edges

Alg. 2: Start

Address

Name Course

DayTimePhone

Major

Address

Name Course

DayTimePhone

Major

N A M

C

C

D

T


√

Alg. 2: Grow

Address

Name Course

DayTimePhone

Major

Address

Name Course

DayTimePhone

Major

N A M

C

C

D

T


Alg. 2: Start Again & Grow

Address

Name Course

DayTimePhone

Major

Address

Name Course

DayTimePhone

Major

N A M

C

C

D

T


√

Alg. 2: Start Again and Grow

Address

Name Course

DayTimePhone

Major

Address

Name Course

DayTimePhone

Major

N A M

C

C

D

T


√


Theorem. Given a canonical conceptual-model (CM)hypergraph H, Algorithm 2 generates an XNF scheme-treeforest with respect to the FDs and MVDs of H.


Inclusion Dependencies (IDs)

Hobby

FacultyMemberwith Hobby

GradStudentwith Hobby

FacultyMember

GradStudent

Advisor

Department

Program

Hobby



FacultyMember

GradStudent

Advisor

Department

Program

optionalconnections

Inclusion Dependencies (IDs)

Hobby

Grad-StudentHobbies

Faculty-MemberHobbies



FacultyMember

GradStudent

Advisor

Department

Program

Hobby

Grad-StudentHobbies




FacultyMember

GradStudent

Advisor

Department

Program

This constraint makesthis vertex redundant.

Canonical CM Hypergraph with IDs

Grad-StudentHobbies




FacultyMember

GradStudent

Advisor

Department

ProgramGrad-StudentHobbies




FacultyMember

GradStudent

Advisor

Department

Program

Generating Scheme Trees fromCanonical CM Hypergraph with IDs

Grad-StudentHobbies




FacultyMember

GradStudent

Advisor

Department





FacultyMember

GradStudent

Advisor

Department

Program

F D

S P HF

HS

Algorithm 3Collapse G/S hierarchiesIf the edges are all binary Execute Algorithm 1Else Execute Algorithm 2

Alg. 3: Collapse

Grad-StudentHobbies




FacultyMember

GradStudent

Advisor

Department





FacultyMember

GradStudent

Advisor

Department

Program

F D

S P HF

HS


Alg. 3: Collapse

F D

S P HF

HS


GradStudent

Grad-StudentHobbies

FacultyMember


Department

ProgramGradStudent

Grad-StudentHobbies

FacultyMember


Department

Program

Alg. 3: Execute

F D

S P HF

HS


GradStudent

Grad-StudentHobbies

FacultyMember


Department

ProgramGradStudent

Grad-StudentHobbies

FacultyMember


Department

Program


Theorem. Given a canonical conceptual-model (CM)hypergraph H, Algorithm 3 generates an XNF scheme-treeforest with respect to the FDs, MVDs, and IDs of H.


Conclusions

XNF ~ “Good” XML No redundancy As few trees as possible

Elegant DTD generation Algorithms to generate XNF Proofs of correctness

[email protected]@email.uah.edu

Producing XML Documents with Guaranteed “Good” Properties David W. Embley Brigham Young...

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