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DATE 2014-12-01

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MESSAGE
DATE 2014-12-12
FROM Ruben Safir
SUBJECT Subject: [LIU Comp Sci] Fwd: Re: relational algrabra division?
From owner-learn-outgoing-at-mrbrklyn.com Fri Dec 12 17:36:44 2014
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Subject: Re: relational algrabra division?
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Xref: panix comp.databases.theory:75273

Relational division is one of the eight basic operations in Codd's
relational algebra. The idea is that a divisor table is used to
partition a dividend table and produce a quotient or results table. The
quotient table is made up of those values of one column for which a
second column had all of the values in the divisor. There is a really
good presentation on four ways to do this at:
http://www.cs.arizona.edu/people/mccann/research/divpresentation.pdf

This is easier to explain with an example. We have a table of pilots and
the planes they can fly (dividend); we have a table of planes in the
hangar (divisor); we want the names of the pilots who can fly every
plane (quotient) in the hangar. To get this result, we divide the
PilotSkills table by the planes in the hangar.

CREATE TABLE PilotSkills
(pilot CHAR(15) NOT NULL,
plane CHAR(15) NOT NULL,
PRIMARY KEY (pilot, plane));

PilotSkills
pilot plane
=========================
'Celko' 'Piper Cub'
'Higgins' 'B-52 Bomber'
'Higgins' 'F-14 Fighter'
'Higgins' 'Piper Cub'
'Jones' 'B-52 Bomber'
'Jones' 'F-14 Fighter'
'Smith' 'B-1 Bomber'
'Smith' 'B-52 Bomber'
'Smith' 'F-14 Fighter'
'Wilson' 'B-1 Bomber'
'Wilson' 'B-52 Bomber'
'Wilson' 'F-14 Fighter'
'Wilson' 'F-17 Fighter'

CREATE TABLE Hangar
(plane CHAR(15) NOT NULL PRIMARY KEY);

Hangar
plane
=============
'B-1 Bomber'
'B-52 Bomber'
'F-14 Fighter'

PilotSkills DIVIDED BY Hangar
pilot
=============================
'Smith'
'Wilson'

In this example, Smith and Wilson are the two pilots who can fly
everything in the hangar. Notice that Higgins and Celko know how to fly
a Piper Cub, but we don't have one right now. In Codd's original
definition of relational division, having more rows than are called for
is not a problem.

The important characteristic of a relational division is that the CROSS
JOIN (Cartesian product) of the divisor and the quotient produces a
valid subset of rows from the dividend. This is where the name comes
from, since the CROSS JOIN acts like a multiplication operator.

Division with a Remainder

There are two kinds of relational division. Division with a remainder
allows the dividend table to have more values than the divisor, which
was Codd's original definition. For example, if a pilot can fly more
planes than just those we have in the hangar, this is fine with us. The
query can be written in SQL-89 as

SELECT DISTINCT pilot
FROM PilotSkills AS PS1
WHERE NOT EXISTS
(SELECT *
FROM Hangar
WHERE NOT EXISTS
(SELECT *
FROM PilotSkills AS PS2
WHERE (PS1.pilot = PS2.pilot)
AND (PS2.plane = Hangar.plane)));

The quickest way to explain what is happening in this query is to
imagine an old World War II movie where a cocky pilot has just walked
into the hangar, looked over the fleet, and announced, "There ain't no
plane in this hangar that I can't fly!" We are finding the pilots for
whom there does not exist a plane in the hangar for which they have no
skills. The use of the NOT EXISTS() predicates is for speed. Most SQL
systems will look up a value in an index rather than scan the whole
table. The SELECT * clause lets the query optimizer choose the column to
use when looking for the index.

This query for relational division was made popular by Chris Date in his
textbooks, but it is not the only method nor always the fastest. Another
version of the division can be written so as to avoid three levels of
nesting. While it is not original with me, I have made it popular in my
books.

SELECT PS1.pilot
FROM PilotSkills AS PS1, Hangar AS H1
WHERE PS1.plane = H1.plane
GROUP BY PS1.pilot
HAVING COUNT(PS1.plane) = (SELECT COUNT(plane) FROM Hangar);

There is a serious difference in the two methods. Burn down the hangar,
so that the divisor is empty. Because of the NOT EXISTS() predicates in
Date's query, all pilots are returned from a division by an empty set.
Because of the COUNT() functions in my query, no pilots are returned
from a division by an empty set.

In the sixth edition of his book, INTRODUCTION TO DATABASE SYSTEMS
(Addison-Wesley; 1995 ;ISBN 0-201-82458-2), Chris Date defined another
operator (DIVIDEBY ... PER) which produces the same results as my query,
but with more complexity.

Exact Division

The second kind of relational division is exact relational division. The
dividend table must match exactly to the values of the divisor without
any extra values.

SELECT PS1.pilot
FROM PilotSkills AS PS1
LEFT OUTER JOIN
Hangar AS H1
ON PS1.plane = H1.plane
GROUP BY PS1.pilot
HAVING COUNT(PS1.plane) = (SELECT COUNT(plane) FROM Hangar)
AND COUNT(H1.plane) = (SELECT COUNT(plane) FROM Hangar);

This says that a pilot must have the same number of certificates as
there planes in the hangar and these certificates all match to a plane
in the hangar, not something else. The "something else" is shown by a
created NULL from the LEFT OUTER JOIN.

Please do not make the mistake of trying to reduce the HAVING clause
with a little algebra to:

HAVING COUNT(PS1.plane) = COUNT(H1.plane)

because it does not work; it will tell you that the hangar has (n)
planes in it and the pilot is certified for (n) planes, but not that
those two sets of planes are equal to each other.

Note on Performance

The nested EXISTS() predicates version of relational division was made
popular by Chris Date's textbooks, while the author is associated with
popularizing the COUNT(*) version of relational division. The Winter
1996 edition of DB2 ON-LINE MAGAZINE (http://www.db2mag.com/96011ar:htm)
had an article entitled "Powerful SQL:Beyond the Basics" by Sheryl
Larsen which gave the results of testing both methods. Her conclusion
for DB2 was that the nested EXISTS() version is better when the quotient
has less than 25% of the dividend table's rows and the COUNT(*) version
is better when the quotient is more than 25% of the dividend table.



  1. 2014-12-02 Ruben <ruben.safir-at-my.liu.edu> Subject: [LIU Comp Sci] Arch Study tonight
  2. 2014-12-02 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Memory Notes et al
  3. 2014-12-02 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Re: Sorry for the last reply
  4. 2014-12-06 Maneesh Kongara <maneeshkongara-at-gmail.com> Re: [LIU Comp Sci] All the notes through External Memory
  5. 2014-12-06 Maneesh Kongara <maneeshkongara-at-gmail.com> Re: [LIU Comp Sci] Parity Bit Algebra
  6. 2014-12-06 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Parity Bit Algebra
  7. 2014-12-06 Maneesh Kongara <maneeshkongara-at-gmail.com> Re: [LIU Comp Sci] Parity Bit Algebra
  8. 2014-12-06 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Parity Bit Algebra
  9. 2014-12-06 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Parity Bit Algebra
  10. 2014-12-06 Maneesh Kongara <maneeshkongara-at-gmail.com> Re: [LIU Comp Sci] Parity Bit Algebra
  11. 2014-12-06 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Parity Bit Algebra
  12. 2014-12-06 Maneesh Kongara <maneeshkongara-at-gmail.com> Re: [LIU Comp Sci] Parity Bit Algebra
  13. 2014-12-06 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Parity Bit Algebra
  14. 2014-12-06 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Parity Bit Algebra
  15. 2014-12-06 Maneesh Kongara <maneeshkongara-at-gmail.com> Re: [LIU Comp Sci] Parity Bit Algebra
  16. 2014-12-06 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Parity Bit Algebra
  17. 2014-12-06 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Parity Bit Algebra
  18. 2014-12-06 Maneesh Kongara <maneeshkongara-at-gmail.com> Re: [LIU Comp Sci] Parity Bit Algebra
  19. 2014-12-06 Maneesh Kongara <maneeshkongara-at-gmail.com> Re: [LIU Comp Sci] Parity Bit Algebra
  20. 2014-12-06 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Parity Bit Algebra
  21. 2014-12-06 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Parity Bit Algebra
  22. 2014-12-06 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] All the notes through External Memory
  23. 2014-12-06 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Parity Bit Algebra
  24. 2014-12-07 Maneesh Kongara <maneeshkongara-at-gmail.com> Re: [LIU Comp Sci] Computer Available
  25. 2014-12-07 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Computer Available
  26. 2014-12-07 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Computer Available
  27. 2014-12-07 mrbrklyn-at-panix.com Subject: [LIU Comp Sci] Upcoming Events for Oracle Professionals
  28. 2014-12-08 Maneesh Kongara <maneeshkongara-at-gmail.com> Re: [LIU Comp Sci] Memorize Optcode
  29. 2014-12-08 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Memorize Optcode
  30. 2014-12-08 Maneesh Kongara <maneeshkongara-at-gmail.com> Re: [LIU Comp Sci] Memorize Optcode
  31. 2014-12-08 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Memorize Optcode
  32. 2014-12-08 Maneesh Kongara <maneeshkongara-at-gmail.com> Re: [LIU Comp Sci] Memorize Optcode
  33. 2014-12-08 Kamran <kamran.mirzayev-at-my.liu.edu> Re: [LIU Comp Sci] Memorize Optcode
  34. 2014-12-08 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Memorize Optcode
  35. 2014-12-08 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Memorize Optcode
  36. 2014-12-08 Maneesh Kongara <maneeshkongara-at-gmail.com> Re: [LIU Comp Sci] Memorize Optcode
  37. 2014-12-08 Ruben <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Memorize Optcode
  38. 2014-12-08 Ruben <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Memorize Optcode
  39. 2014-12-08 Ruben <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Memorize Optcode
  40. 2014-12-08 Kamran <kamran.mirzayev-at-my.liu.edu> Re: [LIU Comp Sci] Memorize Optcode
  41. 2014-12-08 Maneesh Kongara <maneeshkongara-at-gmail.com> Re: [LIU Comp Sci] UPerclassmen
  42. 2014-12-08 Ruben <ruben.safir-at-my.liu.edu> Re: [LIU Comp Sci] UPerclassmen
  43. 2014-12-08 Maneesh Kongara <maneeshkongara-at-gmail.com> Re: [LIU Comp Sci] UPerclassmen
  44. 2014-12-08 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] UPerclassmen
  45. 2014-12-08 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Arch Problem Solution for the final HW question
  46. 2014-12-08 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Foundation for OPTCODE and Machine Instruction
  47. 2014-12-08 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Memorize Optcode
  48. 2014-12-08 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Notes Done on In and Out, Operating Systemsm Modules and Memoery
  49. 2014-12-08 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] UPerclassmen
  50. 2014-12-09 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Anyone in school
  51. 2014-12-09 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] CPU Instructions - Notes for Chapter 14
  52. 2014-12-09 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Machine Instructions notes
  53. 2014-12-09 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Relative - PC addressing
  54. 2014-12-09 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] wifi
  55. 2014-12-10 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Answers to the final review questions
  56. 2014-12-10 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] database Hoem Work
  57. 2014-12-10 duodujames <duodujames-at-gmail.com> RE: [LIU Comp Sci] noone in class?
  58. 2014-12-10 Ruben <ruben.safir-at-my.liu.edu> Re: [LIU Comp Sci] UPerclassmen
  59. 2014-12-10 Maneesh Kongara <maneeshkongara-at-gmail.com> Subject: [LIU Comp Sci] Answers to the final review questions
  60. 2014-12-10 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] database Hoem Work
  61. 2014-12-10 Ruben <ruben.safir-at-my.liu.edu> Subject: [LIU Comp Sci] Fwd: MINIPROJECT
  62. 2014-12-10 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] HW 6
  63. 2014-12-10 mrbrklyn-at-panix.com Subject: [LIU Comp Sci] MINIPROJECT
  64. 2014-12-10 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] noone in class?
  65. 2014-12-10 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] welcome jame
  66. 2014-12-10 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] [mrbrklyn-at-panix.com: HW Last one maybe 6?]
  67. 2014-12-11 Ruben Safir <mrbrklyn-at-panix.com> Fwd: Re: [LIU Comp Sci] Database Class concepts which are still unclear
  68. 2014-12-11 Ruben Safir <mrbrklyn-at-panix.com> Re: Fwd: Re: [LIU Comp Sci] Database Class concepts which are still
  69. 2014-12-11 Ruben <ruben.safir-at-my.liu.edu> Re: [LIU Comp Sci] Database Class concepts which are still unclear
  70. 2014-12-11 Ruben <ruben.safir-at-my.liu.edu> Re: [LIU Comp Sci] Database Class concepts which are still unclear
  71. 2014-12-11 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Database Class concepts which are still unclear
  72. 2014-12-11 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Database Class concepts which are still unclear
  73. 2014-12-11 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Fwd: Invitation: Flatiron Alumni Present!
  74. 2014-12-11 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Fwd: Re: Database Class concepts which are still unclear
  75. 2014-12-11 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Fwd: turning attibute values into relations?
  76. 2014-12-11 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] jobs
  77. 2014-12-12 James Kwabena Duodu <duodujames-at-gmail.com> Re: [LIU Comp Sci] Answers to the final review questions
  78. 2014-12-12 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] .NET and C# free implimentation
  79. 2014-12-12 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Calling Upper Classman
  80. 2014-12-12 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Fwd: Re: n-ary operations
  81. 2014-12-12 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Fwd: Re: Oracle XE Web Server
  82. 2014-12-12 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Fwd: Re: relational algrabra division?
  83. 2014-12-12 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] jobs
  84. 2014-12-12 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] lerning tools
  85. 2014-12-12 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] liu mailing list
  86. 2014-12-12 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Re: turning attibute values into relations?
  87. 2014-12-12 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Sunday Arch Finals Review Study Session
  88. 2014-12-13 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Answers to the final review questions
  89. 2014-12-13 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] (fwd) Re: relational algrabra division?
  90. 2014-12-13 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Base Conversations
  91. 2014-12-13 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Gates HW problems
  92. 2014-12-13 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Logic Gates
  93. 2014-12-13 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] old homework question
  94. 2014-12-14 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Answers to the final review questions
  95. 2014-12-14 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] NOTE ERROR:****Error in the Hamming notes on the final review
  96. 2014-12-15 Ruben <ruben.safir-at-my.liu.edu> Re: [LIU Comp Sci] Answers to the final review questions
  97. 2014-12-15 Kamran <kamran.mirzayev-at-my.liu.edu> Re: [LIU Comp Sci] study hall today
  98. 2014-12-15 Ruben <ruben.safir-at-my.liu.edu> Re: [LIU Comp Sci] study hall today
  99. 2014-12-15 Kamran <kamran.mirzayev-at-my.liu.edu> Re: [LIU Comp Sci] study hall today
  100. 2014-12-15 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] study hall today
  101. 2014-12-15 Kamran <kamran.mirzayev-at-my.liu.edu> Re: [LIU Comp Sci] study hall today
  102. 2014-12-15 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] study hall today
  103. 2014-12-15 Maneesh Kongara <maneeshkongara-at-gmail.com> Re: [LIU Comp Sci] study hall today
  104. 2014-12-15 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] study hall today
  105. 2014-12-15 Maneesh Kongara <maneeshkongara-at-gmail.com> Re: [LIU Comp Sci] study hall today
  106. 2014-12-15 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] study hall today
  107. 2014-12-15 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] study hall today
  108. 2014-12-15 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] errror in the hamming notes.
  109. 2014-12-15 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] [Samir.Iabbassen-at-liu.edu: RE: NOTE ERROR:****Error in the Hamming
  110. 2014-12-16 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Study Hall
  111. 2014-12-16 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Study Hall
  112. 2014-12-16 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] [mrbrklyn-at-panix.com: HW Last one maybe 6?]
  113. 2014-12-17 Maneesh Kongara <maneeshkongara-at-gmail.com> Re: [LIU Comp Sci] database class
  114. 2014-12-17 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] database class
  115. 2014-12-17 James Kwabena Duodu <duodujames-at-gmail.com> Re: [LIU Comp Sci] database class
  116. 2014-12-17 Maneesh Kongara <maneeshkongara-at-gmail.com> Re: [LIU Comp Sci] database class
  117. 2014-12-17 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] database class
  118. 2014-12-17 duodujames <duodujames-at-gmail.com> Re: [LIU Comp Sci] database class
  119. 2014-12-17 Maneesh Kongara <maneeshkongara-at-gmail.com> Re: [LIU Comp Sci] database class
  120. 2014-12-17 James Kwabena Duodu <duodujames-at-gmail.com> Re: [LIU Comp Sci] database class
  121. 2014-12-17 Maneesh Kongara <maneeshkongara-at-gmail.com> Re: [LIU Comp Sci] database class
  122. 2014-12-17 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] database class
  123. 2014-12-17 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] database class
  124. 2014-12-17 Ruben <ruben.safir-at-my.liu.edu> Re: [LIU Comp Sci] database class
  125. 2014-12-17 Ruben <ruben.safir-at-my.liu.edu> Re: [LIU Comp Sci] study hall today
  126. 2014-12-17 Kamran <kamran.mirzayev-at-my.liu.edu> Re: [LIU Comp Sci] study hall today
  127. 2014-12-17 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] why is this textbook just off the look
  128. 2014-12-17 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] why is this textbook just off the look
  129. 2014-12-17 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] database class
  130. 2014-12-17 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Fwd: Database HW6
  131. 2014-12-17 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] the silence
  132. 2014-12-17 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Traffic Lights Diagram
  133. 2014-12-17 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] why is this textbook just off the look
  134. 2014-12-18 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] in coming
  135. 2014-12-18 Ruben <ruben.safir-at-my.liu.edu> Re: [LIU Comp Sci] Need tutoring on Relational Calculus
  136. 2014-12-18 Ruben <ruben.safir-at-my.liu.edu> Re: [LIU Comp Sci] Need tutoring on Relational Calculus
  137. 2014-12-18 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Need tutoring on Relational Calculus
  138. 2014-12-18 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Need tutoring on Relational Calculus
  139. 2014-12-18 Sergei Glikstein <serge.gl-at-gmail.com> Re: [LIU Comp Sci] Normalization review
  140. 2014-12-18 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Normalization review
  141. 2014-12-18 Sergei Glikstein <serge.gl-at-gmail.com> Re: [LIU Comp Sci] Normalization review
  142. 2014-12-18 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Normalization review
  143. 2014-12-18 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Normalization review
  144. 2014-12-18 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Normalization review
  145. 2014-12-18 maneeshkongara <maneeshkongara-at-gmail.com> Re: [LIU Comp Sci] Normalization review
  146. 2014-12-18 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Normalization review
  147. 2014-12-18 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Normalization review
  148. 2014-12-18 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Normalization review
  149. 2014-12-18 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Normalization review
  150. 2014-12-18 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Normalization review
  151. 2014-12-18 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Normalization review
  152. 2014-12-18 Sergei Glikstein <serge.gl-at-gmail.com> Re: [LIU Comp Sci] Normalization review
  153. 2014-12-18 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Normalization review
  154. 2014-12-18 From: <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Normalization review
  155. 2014-12-18 Sergei Glikstein <serge.gl-at-gmail.com> Re: [LIU Comp Sci] Normalization review
  156. 2014-12-18 From: <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Normalization review
  157. 2014-12-18 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] BCNF
  158. 2014-12-18 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] in coming
  159. 2014-12-18 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] lunch
  160. 2014-12-18 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Need tutoring on Relational Calculus
  161. 2014-12-18 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Normalization review
  162. 2014-12-18 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Re: relational calculus
  163. 2014-12-18 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] relational calculus
  164. 2014-12-19 Ruben <ruben.safir-at-my.liu.edu> Subject: [LIU Comp Sci] Oracle Files for the Homework and Oracle Resources
  165. 2014-12-22 Ruben <ruben.safir-at-my.liu.edu> Subject: [LIU Comp Sci] Operating Systems Class
  166. 2014-12-30 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Creating a New OS: Final Projects for MS degree

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