1. Normal Forms and XML Zachary G. Ives October 10, 2007
University of Pennsylvania
CIS 550 – Database & Information Systems
October 10, 2007
Some slide content courtesy of Susan Davidson & Raghu Ramakrishnan

2. Announcements Homework 3 will be due Monday10/22
Midterm: Wednesday 10/24
Please start forming into project groups of 4, with a list of names due 10/24

3. 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

4. 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?

5. Dependency Preservation
Ensures we can “easily” check whether a FD X  Y is violated during an update to a database:
The projection of an FD set F onto a set of attributes Z, FZ is
{X  Y | X  Y  F +, X  Y Í Z}
i.e., it is those FDs local to Z’s attributes
A decomposition R1, …, Rk is dependency preserving if F + = (FR1 ... FRk)+
The decomposition hasn’t “lost” any essential FD’s, so we can check without doing a join

6. Example of Lossless and Dependency-Preserving Decompositions
Given relation scheme
R(name, street, city, st, zip, item, price)
And FD set name  street, city
street, city  st
street, city  zip
name, item  price
Consider the 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 by name, street  city?

7. Another Example Given scheme: 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?

8. FD’s and Keys
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
Hence we have two kinds of normal forms

9. 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.

10. 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

11. 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)} }
i.e., A doesn’t form a key
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)

12. An Example Given the schema: And FDs:
Stuff(sid, name, serno, classroom, cid, fid, prof)
And FDs:
sid  name serno  classroom, cid, fid
fid  prof
Find the Boyce-Codd Normal Form for this schema
What if instead:
sid  name classroom, cid  serno fid  prof serno  cid

13. 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.

14. An Example Given the schema: And FDs:
Stuff(sid, name, serno, classroom, cid, fid, prof)
And FDs:
sid  name serno  classroom, cid, fid
fid  prof
Find the Third Normal Form for this schema
What if instead:
sid  name classroom, cid  serno fid  prof serno  cid

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

16. Normalization Is Good… Or Is It?
In some cases, we might not mind redundancy, if the data isn’t directly updated:
Reports (people like to see breakdowns by semester, department, course, etc.)
Warehouses (archived copies of data for doing complex analysis)
Data sharing (sometimes we may export data into object-oriented or hierarchical formats)

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 2004</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> …
Coincides with “semi-structured data”, invented by DB people at Penn and Stanford

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
<root xmlns=“ xmlns:otherns=“…”>
<tag xmlns:myns=“
<thistag>is in the default namespace (aspace)</thistag>
<myns:thistag>is in myns</myns:thistag> <otherns:thistag>is a different tag in otherns</otherns:thistag>
</tag>
</root>