1. Schema Normalization & XML
Zachary G. Ives
University of Pennsylvania
CIS 550 – Database & Information Systems
October 12, 2004
Some slide content courtesy of Susan Davidson & Raghu Ramakrishnan

2. Announcements Project description handed out
Decide on 3-person project groups by 1 week from today (10/19)
Reading assignment on XML handed out
Homework 2 answers posted on Web
Midterm: Thursday 10/28
Right after class: Phil Bernstein, MS Research, talk on Model Management, Levine 101

3. Why Armstrong’s Axioms?
Why are Armstrong’s axioms (or an equivalent rule set) appropriate for FD’s? They are:
Consistent: any relation satisfying FD’s in F will satisfy those in F +
Complete: if an FD X  Y cannot be derived by Armstrong’s axioms from F, then there exists some relational instance satisfying F but not X  Y
In other words, Armstrong’s axioms derive all the FD’s that should hold
What is the goal of using these axioms?

4. Stuff(sid, name, serno, subj, cid, exp-grade)
Decomposition
Consider our original “bad” attribute set
We could decompose it into:
But this decomposition loses information about the relationship between students and courses. Why?
Stuff(sid, name, serno, subj, cid, exp-grade)
Student(sid, name)
Course(serno, cid)
Subject(cid, subj)

5. Lossless Join Decomposition
R1, … Rk is a lossless join decomposition of R w.r.t. an FD set F if for every instance r of R that satisfies F,
ÕR1(r) ⋈ ... ⋈ ÕRk(r) = r
Consider:
What if we decompose on (sid, name) and (serno, subj, cid, exp-grade)?
sid
name
serno
subj
cid
exp-grade 1
Sam
570103 AI
570 B 23
Nitin
550103 DB
550 A

6. Testing for Lossless Join
R1, R2 is a lossless join decomposition of R with respect to F iff at least one of the following dependencies is in F+
(R1  R2)  R1 – R2
(R1  R2)  R2 – R1
So for the FD set:
sid  name
serno  cid, exp-grade
cid  subj
Is (sid, name) and (serno, subj, cid, exp-grade) a lossless decomposition?

7. Dependency Preservation
Ensures we can check whether a FD X  Y is violated during DB updates, without using a join:
FZ, the projection of FD set F onto attribute set Z, is:
{X  Y | X  Y  F +, X  Y Í Z}
i.e., it is those FDs only applicable to Z’s attributes
A decomposition R1, …, Rk is dependency preserving if F + = (FR1 ... FRk)+ (note we need an extra closure!)
We don’t lose the ability to test the “cover” of our FDs in a single table, just because we decompose
Pay special attention to closure over the union

8. Example 1
For Schema R(sid, name, serno, cid, subj, exp-grade) and FD set:
sid  name serno  cid
cid  subj sid, serno  exp-grade
Is R1(sid, name) and R2(serno, subj, cid, exp-grade):
A lossless decomposition?
Is it dependency-preserving?
How about R1(sid, name) and R2(sid, serno, subj, cid, exp-grade)?
First example:
Not lossless: no join key
Not dep preserving: sid, serno  …
Second example:
Lossless (sid  name)
Dep-preserving

9. Example 2 Given schema R(name, street, city, st, zip, item, price),
FD set name  street, city street, city  st
street, city  zip name, item  price
and decomposition
R1(name, street, city, st, zip) and R2(name, item, price)
Is it lossless?
Is it dependency preserving?
What if we replaced the first FD with name, street  city?
Lossless: name  street, city, st, zip
Dep-preserving: name  street, city; street, city  st, zip

10. A More Disturbing Example…
Given schema R(sid, fid, subj)
and FD set: fid  subj sid, subj  fid
Consider the decomposition
R1(sid, fid) and R2(fid, subj)
Is it lossless?
Is it dependency preserving?
If it isn’t, can you think of a decomposition that is? Can you do this non-redundantly?
Lossless: fid  subj
Not dep-preserving: sid, subj are split
Decomposition would be: R1(sid, fid), R2(fid, sid, subj) which is redundant

11. Redundancy vs. FDs
Ideally, we want a design s.t. for each nontrivial dependency X  Y, X is a superkey for some relation schema in R
We just saw that this isn’t always possible in a non-redundant way…
Thus we have two kinds of normal forms, Boyce-Codd and Third Normal Form

12. Two Important Normal Forms
Boyce-Codd Normal Form (BCNF). For every relation scheme R and for every X  A that holds over R,
either A  X (it is trivial) ,or
or X is a superkey for R
Third Normal Form (3NF). For every relation scheme R and for every X  A that holds over R,
either A  X (it is trivial), or
X is a superkey for R, or
A is a member of some key for R
BCNF: the only functional dependencies are from the key. Partial dependencies aren’t allowed: if AB  CD and B  D then we fail on B  R. Ditto for our previous example, which was of the form A  C, BC  A.
3NF: the same but we allow for partial dependencies. This allows for the above example to be expressed as (A,B,C) because A  R and B & C both  R.
We still disallow partial keys, AB  CD, B  D because B isn’t a key for R. We also disallow transitive keys, AB  C, C  D because C isn’t a key for R.

13. Normal Forms Compared
BCNF is preferable, but sometimes in conflict with the goal of dependency preservation
It’s strictly stronger than 3NF
Let’s see algorithms to obtain:
A BCNF lossless join decomposition (nondeterministic)
A 3NF lossless join, dependency preserving decomposition

14. BCNF Decomposition Algorithm (from Korth et al
BCNF Decomposition Algorithm (from Korth et al.; our book gives a recursive version)
result := {R}
compute F+
while there is a relation schema Ri in result that isn’t in BCNF {
let A  B be a nontrivial FD on Ri s.t. A  Ri is not in F+ and A and B are disjoint
result:= (result – Ri)  {(Ri - B), (A,B)} }
R = (sid, name, serno, cid, subj, exp-grade)
Compute F+:
sid  name
sid, serno  exp-grade
serno  cid, subj
cid  subj
sid, serno  R
(many trival deps, augmented deps)
Step 1: result := Ra(sid, serno, cid, subj, exp-grade) U R1(sid, name)
Step 2: result := Rb(sid, serno, cid, subj) U R2(sid, serno, exp-grade)
U R1(sid, name)
Step 3: result := Rc(sid, serno) U R3a(serno, cid, subj) U
R2(sid, serno, exp-grade) U R1(sid, name)
Step 4: result := Rc(sid, serno) U R4(cid, subj) U R3b(serno, cid) U
Can get different decomp with different ordering; can also get redundancy across relations (e.g., Rc)

15. 3NF Decomposition Algorithm
Let F be a minimal cover
i:=0
for each FD A  B in F {
if none of the schemas Rj, 1 j  i, contains AB {
increment i
Ri := (A, B) }
if no schema Rj, 1  j  i contains a candidate key for R {
Ri := any candidate key for R
return (R1, …, Ri)
Build dep.- preserving
decomp.
R = (sid, name, serno, cid, subj, exp-grade)
Minimal cover:
sid  name
serno  cid
cid  subj
sid, serno  exp-grade
R1 = (sid, name)
R2 = (serno, cid)
R3 = (cid, subj)
R4 = (sid, serno, exp-grade)
Ensure lossless decomp.

16. Summary of Normalization
We can always decompose into 3NF and get:
Lossless join
Dependency preservation
But with BCNF we are only guaranteed lossless joins
BCNF is stronger than 3NF: every BCNF schema is also in 3NF
The BCNF algorithm is nondeterministic, so there is not a unique decomposition for a given schema R

17. XML: A Semi-Structured Data Model

18. Why XML? XML is the confluence of several factors:
The Web needed a more declarative format for data
Documents needed a mechanism for extended tags
Database people needed a more flexible interchange format
“Lingua franca” of data
It’s parsable even if we don’t know what it means!
Original expectation:
The whole web would go to XML instead of HTML
Today’s reality:
Not so… But XML is used all over “under the covers”

19. Why DB People Like XML Can get data from all sorts of sources
Allows us to touch data we don’t own!
This was actually a huge change in the DB community
Interesting relationships with DB techniques
Useful to do relational-style operations
Leverages ideas from object-oriented, semistructured data
Blends schema and data into one format
Unlike relational model, where we need schema first
… But too little schema can be a drawback, too!

20. XML Anatomy Processing Instr. Open-tag Element Attribute Close-tag
<?xml version="1.0" encoding="ISO " ?>
<dblp>
<mastersthesis mdate=" " key="ms/Brown92">
  <author>Kurt P. Brown</author>
  <title>PRPL: A Database Workload Specification Language</title>
  <year>1992</year>
  <school>Univ. of Wisconsin-Madison</school>
  </mastersthesis>
<article mdate=" " key="tr/dec/SRC ">
  <editor>Paul R. McJones</editor>
  <title>The 1995 SQL Reunion</title>
  <journal>Digital System Research Center Report</journal>
  <volume>SRC </volume>
  <year>1997</year>
  <ee>db/labs/dec/SRC html</ee>
  <ee>
  </article>
Open-tag
Element
Attribute
Close-tag

21. Well-Formed XML A legal XML document – fully parsable by an XML parser
All open-tags have matching close-tags (unlike so many HTML documents!), or a special:
<tag/> shortcut for empty tags (equivalent to <tag></tag>
Attributes (which are unordered, in contrast to elements) only appear once in an element
There’s a single root element
XML is case-sensitive

22. XML as a Data Model XML “information set” includes 7 types of nodes:
Document (root)
Element
Attribute
Processing instruction
Text (content)
Namespace:
Comment
XML data model includes this, plus typing info, plus order info and a few other things

23. XML Data Model Visualized (and simplified!)
root
attribute
p-i
element
Root
text
?xml
dblp
mastersthesis
article
mdate
mdate
key
key
2002…
author
title
year
school
editor
title
journal
volume
year ee ee
2002…
1992
1997
ms/Brown92
The…
tr/dec/…
PRPL…
Digital…
db/labs/dec
Kurt P….
Univ….
Paul R.
SRC…

24. What Does XML Do? Serves as a document format (super-HTML)
Allows custom tags (e.g., used by MS Word, openoffice)
Supplement it with stylesheets (XSL) to define formatting
Data exchange format (must agree on terminology)
Marshalling and unmarshalling data in SOAP and Web Services

25. XML as a Super-HTML (MS Word)
<h1 class="Section1"> <a name="_top“ />CIS 550: Database and Information Systems</h1>
<h2 class="Section1">Fall 2003</h2>
<p class="MsoNormal">
<place>311 Towne</place>, Tuesday/Thursday
<time Hour="13" Minute="30">1:30PM – 3:00PM</time>
</p>

26. XML Easily Encodes Relations
Student-course-grade
sid
serno
exp-grade 1
570103 B 23
550103 A
<student-course-grade>
<tuple><sid>1</sid><serno>570103</serno><exp-grade>B</exp-grade></tuple>
<tuple><sid>23</sid><serno>550103</serno><exp-grade>A</exp-grade></tuple>
</student-course-grade>

27. But XML is More Flexible… “Non-First-Normal-Form” (NF2)
<parents>
<parent name=“Jean” >
<son>John</son>
<daughter>Joan</daughter>
<daughter>Jill</daughter>
</parent>
<parent name=“Feng”>
<daughter>Felicity</daughter> …

28. XML and Code
Web Services (.NET, recent Java web service toolkits) are using XML to pass parameters and make function calls
Why?
Easy to be forwards-compatible
Easy to read over and validate (?)
Generally firewall-compatible
Drawbacks? XML is a verbose and inefficient encoding!
XML is used to represent:
SOAP: the “envelope” that data is marshalled into
XML Schema: gives some typing info about structures being passed
WSDL: the IDL (interface def language)
UDDI: provides an interface for querying about web services

29. Integrating XML: What If We Have Multiple Sources with the Same Tags?
Namespaces allow us to specify a context for different tags
Two parts:
Binding of namespace to URI
Qualified names
<tag xmlns:myns=“
<thistag>is in namespace myns</thistag>
<myns:thistag>is the same</myns:thistag> <otherns:thistag>is a different tag</otherns:thistag>
</tag>

30. XML Isn’t Enough on Its Own
It’s too unconstrained for many cases!
How will we know when we’re getting garbage?
How will we query?
How will we understand what we got?
We also need:
Some idea of the structure
Our focus next
Presentation, in some cases – XSL(T)
We’ll talk about this soon
Some way of interpreting the tags…?
We’ll talk about this later in the semester

31. Structural Constraints: Document Type Definitions (DTDs)
The DTD is an EBNF grammar defining XML structure
XML document specifies an associated DTD, plus the root element
DTD specifies children of the root (and so on)
DTD defines special significance for attributes:
IDs – special attributes that are analogous to keys for elements
IDREFs – references to IDs
IDREFS – a nasty hack that represents a list of IDREFs

32. An Example DTD Example DTD: … Example use of DTD in XML file:
<!ELEMENT dblp((mastersthesis | article)*)>
<!ELEMENT mastersthesis(author,title,year,school,committeemember*)>
<!ATTLIST mastersthesis(mdate CDATA #REQUIRED key ID #REQUIRED
advisor CDATA #IMPLIED>
<!ELEMENT author(#PCDATA)> …
Example use of DTD in XML file:
<?xml version="1.0" encoding="ISO " ?>
<!DOCTYPE dblp SYSTEM “my.dtd">
<dblp>…

33. Representing Graphs in XML
<?xml version="1.0" encoding="ISO " ?>
<!DOCTYPE graph SYSTEM “special.dtd">
<graph>
<author id=“author1”>
<name>John Smith</name>
</author>
<article>
<author ref=“author1” /> <title>Paper1</title>
</article>
<author ref=“author1” /> <title>Paper2</title> …

34. Graph Data Model Root graph ?xml !DOCTYPE article article author id
title
author
title
author
name
author1
Paper1
ref
Paper2
ref
John Smith
author1
author1

35. Graph Data Model Root graph ?xml !DOCTYPE article article author id
title
author
title
author
name
author1
Paper1
ref
Paper2
ref
John Smith

36. DTDs Aren’t Enough for Some People
DTDs capture grammatical structure, but have some drawbacks:
Not themselves in XML – inconvenient to build tools for them
Don’t capture database datatypes’ domains
IDs aren’t a good implementation of keys
Why not?
No way of defining OO-like inheritance
No way of expressing FDs

37. XML Schema Aims to address the shortcomings of DTDs Features:
XML syntax
Can define keys using XPaths
Type subclassing that’s more complex than in a programming language
Programming languages don’t consider order of member variables!
Subclassing “by extension” and “by restriction”
… And, of course, domains and built-in datatypes

38. Simple Schema Example
<xsd:schema xmlns:xsd="
<xsd:element name=“mastersthesis" type=“ThesisType"/>
<xsd:complexType name=“ThesisType">
<xsd:attribute name=“mdate" type="xsd:date"/>
<xsd:attribute name=“key" type="xsd:string"/>
<xsd:attribute name=“advisor" type="xsd:string"/>
<xsd:sequence>
<xsd:element name=“author" type=“xsd:string"/>
<xsd:element name=“title" type=“xsd:string"/>
<xsd:element name=“year" type=“xsd:integer"/>
<xsd:element name=“school" type=“xsd:string”/>
<xsd:element name=“committeemember" type=“CommitteeType” minOccurs=“0"/>
</xsd:sequence>
</xsd:complexType>

39. Designing an XML Schema/DTD
Not as formalized as relational data design
We can still use ER diagrams to break into entity, relationship sets
ER diagrams have extensions for “aggregation” – treating smaller diagrams as entities – and for composite attributes
Note that often we already have our data in relations and need to design the XML schema to export them!
Generally orient the XML tree around the “central” objects
Big decision: element vs. attribute
Element if it has its own properties, or if you *might* have more than one of them
Attribute if it is a single property – or perhaps not!

40. XML as a Data Model
XML is a non-first-normal-form (NF2) representation
Can represent documents, data
Standard data exchange format
Several competing schema formats – esp., DTD and XML Schema – provide typing information
Next time: querying XML