Gio Wiederhold: Database Design, 3rd Edition, Appendix 3

© 1995, 1997 (Copyright Notice) by Gio Wiederhold, re-assigned by McGraw-Hill 7 April 1995 from their 1988 copyright.

Appendix C, Draft 1, 25 June 1997.


This Appendix will require the use of a competent HTML browser, that supports TeX formulas, as IBM's techplorer.

Symbols Used

Mathematical Symbols Used

Symbol Definition |
\lceil\; \rceilCEIL, next higher integer. |
\lfloor\;\rfloorFLOOR, next lower integer. |
\approx approximately equal. |
>> much greater than. |
! factorial. |
# number of. |
\log\sb{y}x logarithm base y of x. |
\log{x} natural logarithm of x, base e = 2.71828182846. |
\sum\sb{k}f(k) sum of all f(k) for the integer k's specified}. |
xMODy modulo function, x reduced by y until x< y. |
\jop one of the comparison operators >\ge;=;\ne\;\le\;<. |
\and and, true if both sides are true. |
\or or, true if either side is true. |
| where, precedes a conditional clause. |
\dbinter set intersection. |
\dbunion set union. |
\dbsetdif set difference. |
\dbcross cartesian product. |
\dbselect select tuples from a relation. |
\dbproject project attributes from a relation. |
\dbthetajoin{a = b}join two relations based on equality of the attributes a, b. |
\refto reference connection. |
\ownto ownership connection. |
\subto subset connection. |
\subset subset of. |
\in member of. |
\All for all. |
\becomes becomes. |
{ . . . } enclose a set. |
[ . . . ] enclose a reference. |
\propersubset proper subset. |

Programming and Syntax Symbols As Used

OperationFunction|
a + b addition. |
a - b subtraction. |
a * b multiplication. |
a / b division. |
MOD(a,b) modulo, integer remainder of division. |
a ** b exponentiation, a to the power b. |
a = b depending on context in PL/1, assignment or equality comparison. |
a < b greater than comparison, true if a greater than b. |
a> L{b} greater or equal comparison, true if a greater or equal to b. |
a \AND b and, true if both a, b true, (& in PL/1). |
a \OR b or, true if either a, b true, (| in PL/1). |
\NT c not, true if c false and vice versa. |
s \CAT w catenation, string s connected to string w to form a single new string. |
s | c where, do s if the predicate (conditional) clause c is true. |
R \DBUNION S union of relations R and S. |
R \DBINTER S intersection of relations R and S. |
R \DBCROSS S cross product of relations R and S. |
R \DBSETDIF S difference, remove tuples matching S from R. |
\DBSELECT R.ex select tuples of R according to expression ex. |
\DBPROJECT R.a projection of attributes a of R. |
R.a\DBJOIN S.b Join R and S, on equality of attribute values in a and b. |
R.a\DBOUTERJOIN S.b Outerjoin including all tuples . |
, field separator. |
\kg key and goal fields separator. |
; statement separator. |
. termination of computational section. |
ss, ... section ss may be repeated. |
[ ss ] section ss is optional. |
{ ss|tt}sections ss, tt are alternatives. |
::= is defined by. |
/* Note */ explanatory comments. |
a.b qualification of variable b by a higher-level variable a,\ie, employee.name. |
'Word' character string constant. |
_ (underline) pseudo-alphabetic character without syntactic meaning used for legibility within variable names,|
In COBOL - is used for this function. |

Variables Used in Performance Formulas

SymbolBrief definitionText definition|
A average space required for attribute nameSec. 3-1-3. |
a number of different attributes in a fileSec. 3-1-1. |
a\toprime average number of attributes in a recordSec. 3-1-1, 3-6-3. |
B blocksizeSec. 2-2. |
b blockcountSec. 2-2-2. |
btt block transfer time = B/tEq. 2-13. |
\Bfr blocking factor \approx B/REqs. 2-5, 2-6, 2-7, 2-20. |
C Cost factorsSec. 5-4-6, 5-5-2. |
c computational overhead per record, when not negligibleSec. 2-3-4. |
D space required for dataEq. 5-1, Sec 5-3-3. |
d number of records that have been invalidatedSec. 3-1-3. | %
e = 2.718281828459. |
\sbscr{F} subscript denoting a fetch for a specific recordSec. 3-0-2. |
G space required for an interblock gapSec. 2-2-3. |
h classification variableSec. 5-4-3. |
\sbscr{I} subscript denoting insertion of a recordSec. 3-0-2. |
j number of cylindersSec. 2-2-1. |
K projection listSec. 7-3-2. |
{\tbf K }Kilo or thousand (1024) times. |
k number of tracks per cylinderSec. 2-2-5, Table 2-1. |
L load frequency factors; selection listSec. 5-1; 7-3-3. |
M multiprogramming factorEq. 5-19. |
{\tbf M } Mega or million (1\,048\,576) times. |
m number of available slots for recordsSec. 3-5-1. |
\sbscr{N} subscript denoting getting the next serial recordSec. 3-0-2. |
n number of records in a fileSec. 3-1-3. |
o number of records that overflowSecs. 3-1-3, 3-2-3, 3-3-3, 3-5-3. |
P space required for a pointerSec. 2-3-3. |
p collision cost, also probabilityEqs. 3-73, 3-74, 3-79, Fig. 3-23. |
q production demand by a file applicationEq. 5-2, 5-4 to 5-6. |
R space required for a complete record; relationSec. 3-0-2; 7-1-1. |
\sbscr{RW} subscript indicating rewritingSec. 2-3-6. |
r rotational latency timeEq. 2-3. |
SI storage space for indexEq. 3-52. |
s average seek timeEq. 2-2. |
s\toprime effective seek timeEqs. 2-15, 2-16. |
T the time required for various operations; set of tuplesSec. 3-0-2; 7-3. |
T\sb{sort} the time required to sort a fileEq. 3-11} . |
t transfer rate from a storage unit to processing memorySec. 2-2-5. |
t\toprime bulk transfer rateEqs. 2-17, 2-18, 2-19. |
\sbscr{U} subscript denoting an update of a recordSec. 3-0-2. |
u utilizationEqs. 5-3, 5-7 to 5-18, 5-20. |
uf utilization factorEqs. 6-25, 6-29. |
V average space for value part of an attributeSec. 3-1-3. |
v number of records updatedSec. 3-2-3. |
w wait time in queuesEq. 6-26. |
W wasted space due to gaps per recordEqs. 2-9, 2-10, 2-11, 2-21. |
\sbscr{X} subscript denoting an exhaustive searchSec. 3-0-2. |
x number of levels in an index structure, master levelEq. 3-27, 3-49, 3-97. |
\sbscr{Y} subscript denoting a reorganization of a fileSec. 3-0-2. |
y fanout ratioEq. 3-26, 3-48. |
\sbscr{Z} subscript denoting an update by replacement with a larger recordSec. 3-0-2. |