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DATE 2014-12-01

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MESSAGE
DATE 2014-12-13
FROM Ruben Safir
SUBJECT Subject: [LIU Comp Sci] (fwd) Re: relational algrabra division?
From owner-learn-outgoing-at-mrbrklyn.com Sat Dec 13 23:26:57 2014
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From: Ruben Safir
To: learn-at-nylxs.com
Subject: [LIU Comp Sci] (fwd) Re: relational algrabra division?
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Subject: Re: relational algrabra division?
From: -CELKO-
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Xref: panix comp.databases.theory:75273

Relational division is one of the eight basic operations in Codd's relation=
al algebra. The idea is that a divisor table is used to partition a dividen=
d 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/divpresentatio=
n.pdf

This is easier to explain with an example. We have a table of pilots and th=
e 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.=20

CREATE TABLE PilotSkills=20
(pilot CHAR(15) NOT NULL,=20
plane CHAR(15) NOT NULL,=20
PRIMARY KEY (pilot, plane));
=20
PilotSkills=20
pilot plane=20
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D
'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'
=20
CREATE TABLE Hangar
(plane CHAR(15) NOT NULL PRIMARY KEY);
=20
Hangar
plane=20
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
'B-1 Bomber'
'B-52 Bomber'
'F-14 Fighter'
=20
PilotSkills DIVIDED BY Hangar
pilot
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D
'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 relationa=
l division, having more rows than are called for is not a problem.=20

The important characteristic of a relational division is that the CROSS JOI=
N (Cartesian product) of the divisor and the quotient produces a valid subs=
et of rows from the dividend. This is where the name comes from, since the =
CROSS JOIN acts like a multiplication operator.=20

Division with a Remainder

There are two kinds of relational division. Division with a remainder allow=
s 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 writte=
n in SQL-89 as

SELECT DISTINCT pilot=20
FROM PilotSkills AS PS1
WHERE NOT EXISTS=20
(SELECT *
FROM Hangar
WHERE NOT EXISTS=20
(SELECT *
FROM PilotSkills AS PS2
WHERE (PS1.pilot =3D PS2.pilot)
AND (PS2.plane =3D Hangar.plane)));

The quickest way to explain what is happening in this query is to imagine a=
n old World War II movie where a cocky pilot has just walked into the hanga=
r, looked over the fleet, and announced, "There ain't no plane in this hang=
ar that I can't fly!" We are finding the pilots for whom there does not exi=
st 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 que=
ry optimizer choose the column to use when looking for the index.=20

This query for relational division was made popular by Chris Date in his te=
xtbooks, but it is not the only method nor always the fastest. Another vers=
ion 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.=20

SELECT PS1.pilot=20
FROM PilotSkills AS PS1, Hangar AS H1
WHERE PS1.plane =3D H1.plane
GROUP BY PS1.pilot=20
HAVING COUNT(PS1.plane) =3D (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.=20

In the sixth edition of his book, INTRODUCTION TO DATABASE SYSTEMS (Addison=
-Wesley; 1995 ;ISBN 0-201-82458-2), Chris Date defined another operator (DI=
VIDEBY ... PER) which produces the same results as my query, but with more =
complexity.=20

Exact Division

The second kind of relational division is exact relational division. The di=
vidend table must match exactly to the values of the divisor without any ex=
tra values.=20

SELECT PS1.pilot=20
FROM PilotSkills AS PS1
LEFT OUTER JOIN
Hangar AS H1
ON PS1.plane =3D H1.plane
GROUP BY PS1.pilot=20
HAVING COUNT(PS1.plane) =3D (SELECT COUNT(plane) FROM Hangar)
AND COUNT(H1.plane) =3D (SELECT COUNT(plane) FROM Hangar);
=20
This says that a pilot must have the same number of certificates as there p=
lanes in the hangar and these certificates all match to a plane in the hang=
ar, not something else. The "something else" is shown by a created NULL fro=
m 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) =3D COUNT(H1.plane)=20

because it does not work; it will tell you that the hangar has (n) planes i=
n 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=20

The nested EXISTS() predicates version of relational division was made popu=
lar by Chris Date's textbooks, while the author is associated with populari=
zing the COUNT(*) version of relational division. The Winter 1996 edition o=
f DB2 ON-LINE MAGAZINE (http://www.db2mag.com/96011ar:htm) had an article e=
ntitled "Powerful SQL:Beyond the Basics" by Sheryl Larsen which gave the re=
sults of testing both methods. Her conclusion for DB2 was that the nested E=
XISTS() version is better when the quotient has less than 25% of the divide=
nd table's rows and the COUNT(*) version is better when the quotient is mor=
e than 25% of the dividend table.=20

-- end of forwarded message --

  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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