1. (a) A university is organized into faculties.
1.(15) Draw an ER-diagram to describe the following real world problem.
(a) A university is organized into faculties.
(b) Each faculty has a unique name, ID and number of professors and a specific professor is chosen as the faculty head.
(c) Each faculty provides a number of courses.
(d) Each course has a unique name and courseID.
(e) Each professor has a name, SIN, address, salary, sex and courses taught by him/her.
(f) Each professor belongs to a faculty and can teach several sections of a course.
(g) Each student has a name, ID, SIN, address, GPA, sex, and major.
(h) Each student can choose one faculty as his/her major faculty and take several courses with certain credit hours. Some of the courses are mandatory and some are optional.
Feb. 27, 2017
ACS-7102 Yangjun Chen

2. ER-model: professor faculty course section student belong teach head
salary
name ID
addr.
SIN
belong N 1
professor
NoProf
F-Id
sex
F-name M
startdate 1
teach
section-IDs
faculty
head 1 L M 1
provide N 1 M
course
has
section
sectionId
choose N
couresId
name N ID
addr.
SIN
take M
student N
major
mandatory-optional
creditHours
name
sex
birthdate
Feb. 27, 2017
ACS-7102 Yangjun Chen

3. 2.(15) Given the following B+-tree, trace the deletion sequence: h, c,
e, f. Here, we assume that each internal node can contain at most two
keys and each leaf node can contain at most two value/point pairs. c b f a b c e f h
Fig. 1
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ACS-7102 Yangjun Chen

4. remove h: f e a b c remove c: f e a c b Feb. 27, 2017
ACS-7102 Yangjun Chen
ACS-7102 Yangjun Chen 4

5. remove e: c a e a b f remove f: a e a b f a b a Feb. 27, 2017
ACS-7102 Yangjun Chen

6. Find the names of employees who works on all the projects
3.(10) Given the relation schemas shown in Fig. 2, construct expressions
(using relational algebraic operations) to evaluate the following query:
Find the names of employees who works on all the projects
controlled by department ‘Applied Computer Science’.
EMPLOYEE
fname, minit, lname, ssn, bdate, address, sex, salary, superssn, dno
DEPARTMENT
Dname, dnumber, mgrssn, mgrstartdate
Fig. 2
PROJECT
WORKS_ON
Pname, pnumber, plocation, dnum
Essn pno, hours
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ACS-7102 Yangjun Chen

7. : DN dnumber(Dname = ‘Applied Computer Science’(Department))
DEPT_P PNUMBER(DNDN.dnumber = PROJECT.dnumber(PROJECT))
EMP_PNOS  ESSN,PNO(WORK_ON)
SSNS EMP_PNOS :
DEPT_P
RESULT  FNAME, LNAME(SSNS * EMPLOYEE)
Feb. 27, 2017
ACS-7102 Yangjun Chen

8. 4. (20) Construct an R-tree over a set of records for geographical
objects with the following coordinates [(x1, y1), (x2, y2)]:
[(0, 40), (60, 50)] ---- road1
[(40, 0), (60, 40)] ---- road2
[(15, 25), (35, 35)] ---- house1
[(70, 40), (80, 60)] ---- house2
[(70, 5), (90, 15)] ---- house3
[(80, 60), (100, 80)] ---- house4
Assume that each leaf node can have at most 4 pointers and
at least two pointers; and each internal node at most 2
pointers and at least 1 pointer.
Please give the computation process.
Feb. 27, 2017
ACS-7102 Yangjun Chen

9. 100 house4 house2 road1 house1 house3 road2 100 Feb. 27, 2017
100
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ACS-7102 Yangjun Chen

10. ((0, 40), (60, 50)) ((0, 0), (60, 50)) road1 road1 road2
[(15, 25), (35, 35)] ---- house1
[(70, 40), (80, 50)] ---- house2
((0, 0), (60, 50))
((0, 0), (80, 60))
Road1 road2 house1
Road1 road2 house1 house2
Feb. 27, 2017
ACS-7102 Yangjun Chen

11. square units to the region.
[(70, 5), (80, 15)] ---- house3
((0, 0), (60, 50)) ((70, 5), (90, 60))
road1 road2 house1
house2 house3
If we expand the first subregion in the internal node, then we add 4000
square units to the region.
If we extend the other subregion in the internal, then we add 1200 square
units.
[(35, 25), (80, 35)] ---- pipeline
((0, 0), (80, 50)) ((70, 5), (100, 80))
road1 road2 house1
house2 house3 house4
Feb. 27, 2017
ACS-7102 Yangjun Chen

12. 5. (15) Please give the algorithm for transforming any XML document
to a tree structure. Apply the algorithm to the following document
and trace the computation process.
<book>
<title>
“The Art of Programming”
</title>
<author>
“D. Knuth”
</author>
<year>
“1969”
</year>
</book>
<book>
<title>
<author>
<year>
“The Art of
Programming”
“D. Knuth”
“1969”
Feb. 27, 2017
ACS-7102 Yangjun Chen

13. Transform an XML document to a tree
Read a file into a character array A:
< b o o k > < t i t l e > “ T h e A r t …
node_value
Point_to_node
stack S:
Feb. 27, 2017
ACS-7102 Yangjun Chen

14. Transform an XML document to a tree
Algorithm:
Scan array A;
If A[i] is ‘<’ and A[i+1] is a character then {
generate a node x for A[i..j],
where A[j] is ‘>’ directly after A[i];
let y = S.top().pointer_to_node;
make x be a child of y; S.push(A[i..j], x);
If A[i] is ‘ ‘‘ ’, then {
genearte a node x for A[i..j],
where A[j] is ‘ ’’ ’ directly after A[i];
make x be a child of y;
If A[i] is ‘<’ and A[i+1] is ‘/’, then S.pop();
Feb. 27, 2017
ACS-7102 Yangjun Chen

15. <book> <book> <book> <book> <title>
“The Art of Programming”
</title>
<author>
“D. Knuth”
</author>
<year>
“1969”
</year>
</book>
<book>
<book>
<book>
<book>
<title>
<title>
<book>
<title>
The Art of
Programming
<book>
The Art of
Programming
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ACS-7102 Yangjun Chen

16. <author> <book> <book> D. Knuth <year>
<title>
“The Art of Programming”
</title>
<author>
“D. Knuth”
</author>
<year>
“1969”
</year>
</book>
<book>
<author>
The Art of
Programming
<book>
The Art of
Programming
D. Knuth
<book>
<year>
The Art of
Programming
D. Knuth
Feb. 27, 2017
ACS-7102 Yangjun Chen

17. empty <year> <book> D. Knuth 1969 book title author year
“The Art of Programming”
</title>
<author>
“D. Knuth”
</author>
<year>
“1969”
</year>
</book>
<book>
<year>
The Art of
Programming
D. Knuth
1969
book
The Art of
Programming
D. Knuth
1969
<book>
The Art of
Programming
D. Knuth
1969
title
author
year
empty
Feb. 27, 2017
ACS-7102 Yangjun Chen

18. 6. (15) In order to represent XML documents as relations, we should
give each document and each element of a document a unique ID. For
each document, the ID could be its URL or path in a file system.
A possible relational database schema:
DocRoot(docID, rootElmentID)
ElementValue(elementID, value)
SubElement(parentID, childID, position)
ElementAttribute(elementID, name, value)
Please show the tables after we have put the following document into
the tables:
Feb. 27, 2017
ACS-7102 Yangjun Chen

19. <? Xml version = “1.0” encoding = “utf-8” standalone = “yes” ?>
< md : StarMoviedata xmlns : md = >
<Star starID = “cf” starredIn = “sw”>
<Name>Carrie Fishes</Name>
<Address>
<Street>123 Maple St.</Street><City>Hollywood</City>
</Address>
<Street>5 Locust Ln.</Street><City>Malibu</City>
</Star>
<Star starID = “mh” starredIn = “sw”>
<Name>Mark Hamill</Name><Street>456 Oak Rd.</Street>
<City>Brentwood</City>
<Movie movieID = “sw” starsOf = “cf mh”>
<Title>Star Wars</title><Year>1977</Year>
</Movie>
</StarMovieData> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
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ACS-7102 Yangjun Chen

20. DocRoot(docID, rootElmentID)
[1, md: StarMoviedata]
[2, Star]
[3, Name]
[4, “Carrie Fishes”]
[5, Address]
[6, Street]
[7, “123 Maple St.”]
[8, City]
[9, Hollywood]
[10, address]
[11, Street]
[12, 5 Locus Ln.]
[13, City]
[14, Malibu]
[15, Star]
[16, name]
[17, Mark Hamill]
[18, Street]
[19, 456 Oak Rd.]
[20, City]
[21, Brentwood]
[22, Movie]
[23, Title]
[24, Star wars]
[25, Year]
[26, 1977]
DocRoot(docID, rootElmentID)
[1, 1]
ElementValue(elementID, value)
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ACS-7102 Yangjun Chen

21. ElementAttribute(elementID, name, value)
[1, xnmns: md, …]
[2, starID, “cf”]
[2, starredIn, “sw”]
[15, starID, “mh”]
[15, starredIn, “sw”]
[22, movieID, “sw”]
[22, starsOf, “cf mh”]
SubElement(parentID, childID, position)
[1, 2, 1]
[1, 15, 2]
[1, 22, 3]
[2, 3, 1]
[2, 5, 2]
[2, 10, 3]
[3, 4, 1]
[5, 6, 1]
[5, 8, 2]
[6, 7, 1]
[8, 9, 1]
[10, 11, 1]
[10, 13, 2]
[11, 12, 1]
[13, 14, 1]
[15, 16, 1]
[15, 18, 2]
[15, 20, 3]
[16, 17, 1]
[18, 19, 1]
[20, 21, 1]
[22, 23, 1]
[22, 25, 2]
[23, 24, 1]
[25, 26, 1]
Feb. 27, 2017
ACS-7102 Yangjun Chen

22. 7. In Fig. 3, we show a network, in which each node stands for a
page and each arc for a link from a page to another.
Please give the transition matrix for the network. (3)
Also, explain why the solution to the equation: (7)
A = MA can be used as the estimation of page importance,
where A is a vector of n variables (with each representing a
page) and M is an n  n transition matrix.
Fig. 3
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ACS-7102 Yangjun Chen

23. 7. (i) p1 p2 p3 ½ ½ ½ ½ 0 ½ M = 0 ½ 0 (ii) y ½ ½ ½ a ½ 0 ½ m = 0 ½ 0
½ ½ ½
½ 0 ½
0 ½ 0
M =
(ii)
½ ½ ½
½ 0 ½
0 ½ 0 = y a m
Feb. 27, 2017
ACS-7102 Yangjun Chen

24. 7. (ii) y: event – navigation stays on Yahoo
y-y: event – go to Yahoo from Yahoo
y-a: event – go to Yahoo from Amazon
y-m: event – go to Yahoo from Microsoft
a-y: event – go to Amazon from Yahoo
a-a: event – go to Amazon from Amazon
a-m: event – go to Amazon from Microsoft
a: event – navigation stays on Amazon
m-y: event – go to Microsoft from Yahoo
m-a: event – go to Microsoft from Amazon
m-m: event – go to Microsoft from Microsoft
m: event – navigation stays on Microsoft
P(y) = P(y-y|y) + P(y-a|a) + P(y-m|m)
P(a) = P(a-y|y) + P(a-a|a) + P(a-m|a)
P(m) = P(m-y|y) + P(m-a|a) + P(m-m|m)
= P(y-y)P(y) + P(y-a)P(a) + P(y-m)P(m)
= P(a-y)P(y) + P(a-a)P(a) + P(a-m)P(a)
= P(m-y)P(y) + P(m-a)P(a) + P(m-m)P(m)
Feb. 27, 2017
ACS-7102 Yangjun Chen