A Comparative Study of Very Large Databases

Lecture Notes in Computer Science Edited by G. Goos and J. Hartmanis 59 Edward Hill, Jr. A Comparative Study of Very L...

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Lecture Notes in Computer Science Edited by G. Goos and J. Hartmanis

59 Edward Hill, Jr.

A Comparative Study of Very Large Data Bases

Springer-Verlag Berlin Heidelberg New York 1978

Editorial Board P. Brinch Hansen D. Gries C. Moler G. Seegm~ller J. Stoer N. Wirth

Author Dr. Edward Hill, Jr. Division of Computer Research and Technology Building 12 A, Room 2041 B National Institute of Health 9 0 0 0 Wisconsin Avenue Bethesda, Maryland 20851/USA

AMS Subject Classifications (1970): 68-02, 68A20, 68A50, 68A99 CR Subject Classifications (1974): 4.33

ISBN 3-540-08653-6 Springer-Verlag Berlin Heidelberg NewYork ISBN 0-387-08653-6 Springer-Verlag New York Heidelberg Berlin This work is subject to copyright. All rights are reserved,whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means,and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Berlin Heidelberg 1978 Printed in Germany Printing and binding: Bettz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210

£R~FACE

This organizing base

to

access

very

storage

average

and number

complete

a

retrieve

items chaining

A

atgorlthm is

storing a

fast

direct

The

on with

and

access

insertion,

operatlons

for

an

Inverted

component

concept.

A

flies.

Aft

structures, the

to

direct

Finally,

compared.

show

access a

inverted

comparison

and

file.

for

Algorithms the New The

method are

analyzed, the

device

white

is

to

components with

number

processing

a

and

on

perform

are

developed

along

stored

generation

average

developed

for

measures

are

and

coalescing

trle

presented flte

to

methods

presented a

the

presented.

with

and

performance

Invo~vlng

on

is

ate

store

hashing

chaining

tree

is

device

to

for

are

direct

concern

probing

inverted

methods

effect

criterion

[tnear

on

storage

device

[a_E~e_~/t~

InvoEvlng

accesses

search

very

immediate

measures

and

methods

storage

access

binary

file.

hybrid

their

direct

performance

deletion

for

of

measures

device.

base

factor

storage

a

for

Information

data

of

methods

called

desired

large

fists

~

of

data

number

access

wlth

presented

linked

an

average

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storage

of

the

performance

retrieving

stored

major

separate

comparison

very

to

direct

a

of

a

the

accesses

retrieval,

the

In

updating, of

a

retrieva[

devices.

presented. and

presents amounts

request.

using

lists

large

facilitate

~etrievat

new

monograph

using is

their of

used

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method

for

data

request,

each

a

is

to

IV

This to The

the

Department

George

monograph of

Washington

is

based

EtectrlcaL University

on

a

D.Sc.

Engineering In

1977e

dissertation and

Computer

submitted Science

at

ACKNOWLEDGEMENTS

[ variety

of

am

indebted

ways

to

the

First

of

art,

who

served

for

encouraging

this

monograph.

as

my

their

and

me

Edward

hours

for

this

to

In

I

am

work

my

career.

owe

has

am

sacrificed

this

great Ao

what

contributed

to

Profo

deserves

has

become

Natlonat

institutes

Computer

Science.

my

Harris

now

of

in

wife,

me

from

indeed so

much

and

Espor

understanding

Ao

Mettzer

K.

the

in

a

monograph.

dear

C.

have

Eugene

to

kept

I

a

Prof.

studies

tope,

who

of

investigate

indebted

their

who

I

Dr.

my

Finally) Gertrude

to

peopte

comptetion

Technology

support

many

advisor.

Thanks Research

to

the

and

and

support

Mettzer

thanks the

Division of

my

C.

topic

of

Hearth,

chitdren during

of

Computer for

Eurica the

and

many

them.

thankful to

aid

for me

my during

parents the

Edward Initlat

and years

of

I.

INTRODUCTION

2.

DATA BASE STRUCTURE

3.

2.1°

Record

2.2.

Data

2.3.

Ava|lable

DIRECT 3°I°

4.

Structure Structure

ACCESS Direct

Space

DEVICES Access

RECORD P R O C E S S I N G 4.1.

Record

4.2.

Chaining

4.3.

Manasement

9

TerminoLogy

9

USING HASHING METHODS

Addressin~ With

TerminoLogy

Separate

Lists

11 11 15

4o2. I.

~etrievat

A1gorithm

[7'

4°2.2.

Retrleval

Time

1/3

4.2.3.

Insertion

Atgorlthm

19

4.2.4.

Insertion

Time

21

4.2.5.

DeLetion

ALgorithm

22

4.2+6.

DeLetion

Time

23

4°2.7°

Storage

Space

Requirements

24

With

Coalescing

Lists

24

Chalning

Vlll

4°3°1.

Retrievat

And

Insertion

Algorithm

4,,4°

4o5°

5°

24

4°3°2°

Retrieval

Time

27

4°3o3.

Insertion

Time

29

4°3.4.

De[etlon

Atgorithm

29

4°3°5°

De[etlon

Time

3O

4°3.6.

Storage

Linear

Space

Requirements

Probing

3O 3O

4.4.1.

Retrieval

Algorithm

31

4.4.2.

Retrlevat

Time

32

4°4.3°

Insertion

Atgorlthm

34

4°4°4°

Insertion

Time

35

4°4°5.

Detetion

Algorithm

36

4.4.6.

Detetion

Time

37

4o4°7°

Storage

Space

Requirements

Summary

37 37

RECORD P R O C E S S I N G U S I N G TREE METHODS

40

5°I.

Tree

40

5.2.

Storing

TREE

5o2.1o

Retrievat

Algorithm

60

5.2.2.

Retrleva[

Time

64

5.2.3.

Insertion

Algorithm

65

5.2.4.

Insertion

Time

69

5,2.5.

Deletion

Algorithm

69

5.2.6°

De[etlon

Time

72

5.2.7.

Storage

Searching

Termlno[ogy And

Binary

Space

Tree

Requirements

52

72

iX

5.3.

5.4.

6.

RECORD 6oi.

6.2.

6.3.

7.

RECORD

Storing

TRIE

5.3.1.

Retr

5.3.2.

73 ALgorithm

73

Retrieval

Time

73

5.3.3.

Insertion

Algorithm

74

5.3.4.

Insertion

Time

75

5.3.5.

Detetion

ALgorithm

75

5.3.6.

Detetion

Time

75

5.3.F.

Storage

levat

Space

Requirements

75 76

Summary

PROCESSING

USING

L~NKED

FILES

79

Files

80

Retrieval

ALgorithm

81

6.1.2.

Retrieva~

T£me

8,2

6.1.3.

Insertion

A~gorithm

83

6.1.4.

Insertion

Time

84

6.1.5.

Deletlon

A~gorithm

84

6.1.6.

Detetion

Time

8,%

6.1.7.

Storage

Space

Storing

Doubte

Linked

6.2.1.

Storage

Storing

Ring

Storing

Linked

6.1.1.

PROCESSING

7.1o

Generation

7.2.

Load

7.3.

Retrleval

List

84

List

85

Files

Space R e q u i r e m e n t s

List

USING Of

Requirements

Time

86

Files

~NVERTED

Inverted

,B5

File

FILES

87 90 94

Algorithm

99

X

8.

7e4u

Retrievat

Time

100

7.5.

Insertion

Aisorlthm

103

7.6.

Insertion

Time

103

7.7.

Deletion

Algorithm

103

7o8.

Deletion

Time

104,

7.9.

Storage

T. lO.

Summary

104

Requirements

105

COMPARISON OF METHODS

106

8.1o

Criterion

106

8.2.

Comparison 8o2.

9.

Space

I,

For

Comparison

108

Load

108

Times

8.2.2.

Retrieval

Times

109

8°2°3.

Insertion

Times

110

8.2.4.

Deletion

8.2.5.

Storage

8.2.6.

Variable

8.2.7o

Fixed

8.2.8°

Hybrid

113

Times Space

Requirements

Length Length Methods

Keys

Keys

113 123 123 123

CONCLUSIONS

124

9.1.

124

Appendix

References

ConcluSions

A.

Glossary

o~

terms

130

134

1

CHAPTER

INTRODUCTION

This methodology

monograph

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CHAPTER

BA~g_~!~¢IU_Eg

DATA

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m~pping h(K)

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have

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Let

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records.

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the

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data

Define

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records of

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= N

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ot

probabitity

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buckets of

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N.

N-k

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the

Poisson Is

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=

m

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to

15

be

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average

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sides

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Taylor

expansion,

find

log

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large

fliO:N,_m) N

any

Ntog

(t

-

_m) N

=

-

m

-

_mz_ 2N

-

°..

N

B(O:N,_m) N FoP

~

fixed

k

=

e -m

and

+ O ( N - I ).

su~fIclentLy

B(k;N,~)

m-(k-1 N N

~avge

N

)(~) N N

Therefore,

B(1;N.m) N

#(2;N,_m) N

and

in

by

general

is

Denote

where

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the

m

is

k

average

of

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=

=

m2 2

e -m

to

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approximation

P( k )

mk

the

average

m

distribution

e -m k!

number

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gives

wilt

transformed

keys

,

be pep

blnomia[

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assigned

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distribution keys

,

k . .e.-.m ~ii k!

probabltlty

Poisson

exactly

me "m

=

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this

=

induction

B(k:N,m) N

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ffi m X B ( O : N , _ m ) N

address.

Chaini~g_~i~b_~n~E~_~!~1~

records

the

fraction for

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of random

the

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buckets.

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distribution

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16

CoLLisions List. are

Each

List

organized

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storage

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bucket,

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first

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all

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figure

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HEAD

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INFO

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pointer

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zero

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BUCKET

pointer

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TAG the b.

Figure

BUCKh~I" a n d

4.1,

OVERFLO~V

NoSe

to node

Structure

Separate

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node.

structure

for

ChaLniu~

ALgorithm°

With

a Lists

direct

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same

end

of

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bucket

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area.

4.1.

NODE

on

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17

Atgovithm

(Retrieval

by

hash

chaining

w~th

separate

Lists.) Assume pointed that

to the

by

that

a

nodes

Link of

a

BUCKET vector

the

is

[inked

variable

OVAIL.

The

variable

P

aEong

key-to-address bucket the

nodes

of

varlabte

Is

I

READ(P)

to

mean

address

P°

f

main

memory

[Hash

the

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data

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and

h(K)

structure

function

of

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that

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the Is

used LINK,

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pointed Link

to

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to

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transform and

the

P°

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INFO

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algorithm.

from

the

disk

operate

[There

contaln~ng into

[Check [Check

a

THEN ENDIF. IF (TAG(P) THEN

DO PUT " n o t

f o u n d m,

ENDDO.

STOP

The

the

internal

key. ] GET K,

STOP

on

Define

addresses°

I~READ(i), i--f(i). key stored at the home address?] IF (LINK(HEAD(t)) ~ O) THEN DO PUT " n o t foundW~ is a List at the home address. ] ELSE P~f(LINK(HEAD(i ))). ENDI F . the ~lst for the current key, ] DO for the end of the List. ] I F ( P ffi 0 )

there

into

va~abLe°

the

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keys

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foLLows

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variables.

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Assume

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NODE,

variable

readln~

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~lnked

storage

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available

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avaiLabLe

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a

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buckets

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moves

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ENDDO.

= ! ) DO P ~ L I N K ( P ) , P~READ(P), P~f(p), IF (OVERFLOW(P) = K) THEN DO PUT " f o u n d " , STOP ENDDO. ELSE DO Q*-Ps P ~ f ( L I N K ( Q ) ) ENDDO.

18

END[F. ENDDO, IF (BUCKET(P)

ELSE

=

K)

THEN

DO PUT ENDDO.

" f o u n d ~,

ELSE

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STOP

P~f(LINK(O))

ENDDO. ENDIF.

ENDIF. ENDDO. 4.2.2.

E@tri~v_~a!_llm~ Johnson

to

address

air tk

=

[33]

defined

items

In

k

( (k

*

!

a

the

totat

number

list

of

k

items

b)(k

-

b

÷

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of

probes

required

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i )),

2 where The

k

)

number

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N

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with

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k=0 The

length

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of

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the

of

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average number

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of

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divided

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1 m

value

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average

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(k2-2kb*k÷h2-b)

÷ _! 2m

the

h

tkP(k)o

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=

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E k=0

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special

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the

number

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b

above

CR(~,I

This

resutt

[27.

47,

was 48.

Introduced 4.2°

)

* m 2

(k

=

I.

Substituting

yields

e-m

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. e.- ~.b k|

.

presented

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[33]

Johnson

chaining

method

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catted

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later

brock

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[17].

Col/meyer

(Insertion

to

OVERFLOW

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Assume

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poiated

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equation

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[inked

the

BUCKET vector bucket avalLabte

is

a

[inked

AVAIL. are

avaitabte

BUCKET ]Linked

storage

is

ttnked

together° poor

pointed

storage in

pool such

Assume to

by

a

way

that the

link

2O variable

OVAIL.

from

avaiLabLe

the

pointer

and

removal

of

area

and

a

node

P

into

variables

moves

along

address bucket

operate

the

nodes

The

algorithm.

Define

of

a

that

[Hash

on

the

maps

track

key.

a

is

the

data

i

to

NODE,

containing

the

of

address main

underfLow The

the

used a

to P,

memory

by

f

Is

List.

Start

address?J

DO a

List

using

this

key.

~=AVAILE i 3, LINK( HEAD( i ) )~R, INFO(f(R})~K, LINK( f( R ) )*-0. NODE( H E A D ( i ) ) ~ N O D E ( H E A D ( I ) ) - 1 , WRITE(R), [There

Is

a

List

STOP

ENDDO.

at the home address. ELSE P ~ f ( L I N K ( H E A D ( i ) ') ) o

ENDI E.

DO

[Check

the

List IF

for the (TAG(P) THEN

current key. ] = 1 ) DO P ~ L I N K ( P ) .

P~READ(P),

P~f(P),

the the

writing

function

addresses.

l~f(l).

Link

from the

a

keys

the in

mean

A

INEO

track

K, t~READ(I),

P.

TAG ~nd

to

AVAIL

overflow

transform

WRITE(P)

tnterna~

the

Q foLLows

LINK,

reading

Define

key stored at the home I F ( L I N K ( H E A D ( I ) ) ffi 0 )

no

used

the

in

the

the

variables.

vari~bte

mean

he

and

auxiliary

to

into

Link

node

of

to

pointer

pointed

an

P°

pool

structure

is

a

management

variable

is

of

~

THEN [There

the

h(K)

address disk

i~h(K), there

of

~ ~re

and

functions

addresses

GET [Is

List

READ(P)

the

track

the

OVAIL

Q and

remova~

R~OVAIL

of

the

the

final

sto~age

The

variable

contaln£ng

the

Define

transformation

v~r£abtes.

disk

and

be

avaiLabLe

P, the

addresses.

on

the

managemant

The

variable

pool

to

conditions.

from

final

conditions°

R~AVAIL[i]

storage

underfLow

the

key-to-

Define

21

IF

(OVERFLOW(P)

= K)

THEN

DO

PUT "found", STOP ENDDO.

ELSE

DO Q ~ P . P~(LINK(O))

ENDDO.

ENDXF. ENDDO. IF

ELSE

(BUCKET(P) = K) THEN DO P U T " f o u n d * , STOP ENDDO. ELSE DO Q , , - P , P - - f ( L I N K ( O ) ) ENDDO.

ENDIF. [Check

for

the

ENDIF. end IF

[The the

key LAst.

is

(P

not

of

the

tist.]

= 0) T H E N DO the fist.

In

Insert

the

key

into

] IF

(NODE(HEAD(I)) THEN

DC

= 0 ) R~OYAI L, TAG( ~( R ) )~-1.

TAG( O )--1 ENDDOo ELSE

DO ; / ~ A V A I L E i ] , NODE( H E A D ( 1 ) ) ~ N O D E ( H E A D ( i ) )- I ENDDO.

END IF. ENDDO. ENDIF. LINK(Q

)oR.

L I N K ( f ( R ) ) ~ 0 ,, I N F O ( 2 ( R ) )--K,, WRITE(f'I(0)

)s, W R I T E ( R ) .

STOP ENDDO. 4.2.4.

I_ns_~£t ifln_I£m_e item

An operation. about

its

tnse

r ted o

If

chain

item

ls

in

associated

inserted

item

presence.

The the

the

~S

is

If

the

the item

time

file.

with

in

the

insertion

by

The

the

home

first

structure Is

ls item

performing

not

that is

address

in

tame £n

in

a

retrleval

~

notification

the

structure

required the

the

bucket

over,

to d

tow

Is it

glven Is

determine or

Lt

area.

is

If on

The

a

22

average an

number

of

insertion

operation

Ci(a.b)

The

=

unsuccessfut

to

accesses

the

direct

access

storage

device

during

is

1

+

search

~ k)b was

(k

-

b)P(k)

presented

by

k>b

Knuth

[34]

as

kZ

!

where

CN

is

the

unsuccessfu[

average

search,

number

This

insertion

time.

4.2.5,

~te!ifi~_A!g~Ki~bm

Algorithm

(Deietlon

by

of

file

unsuccessfui

hash

chaining

in

accesses

search

wlth

an

is

defined

%o

the

be

separate

tists.) that

Assume pointed that

to

the

by

a

nodes

OVERFLOW

is

vamiab%e

OVAIL.

the

pointer vetu~n

and

a

avaitabte

the

moves

Linked

a

node

finai

atong

the

nodes

variable

of i

is

the an

Linked

poor a n d

to

the

conditions. the

available

of

variables list

and

the P

and

the

The data

pool

h(K)

structure

he

the

OVAIL~P

storage

poor

pointer [ink

is

Q

LINK)

pointed

to

used

in

and

in

of

a

of

the

be

the

by

the

the

[ink

node

to

AVAIL

area

overftow The

varlab[e

the

keys

A

transform and

the

way

overftow

the

P.

TAG

a

that

by

variables.

to

such

to

to

follows

used

pool

Assume

return

Define

are

in

pointed

NODE,

variable

[inked

management

varlabie

functions

auxiliary

0

is

together.

finn[

OVAIL

storage

avaitabte

BUCKET

storage

transformation

addresses.

[inked

AVAIL[i]~P

management

the

are

avallab[e

to

The

a

AVAIL.

bucket

Define

key-to-address bucket

the

overflow

conditions. P

vector

storage

and of

[ink of

is

BUCKET

INFO

Link

overate

variabZe.

algorithm.

Let

into on

The LOC

23

be

a

to

mean

P.

function the

containing

reading

an

the

main

to

mean

track

Po

from

the f

memory

is

of

the

variable.

Define

disk

containing

of

track

writing a

a

function

a that

on

maps

the the

READ(P) address

disk

track

addresses

addresses.

K,

ioh(K), there

a

address

key. ] GET

[Is

the

of

address

internal

[}{ash

returns

WHITE(P)

Define

into

that

a

i--f(i). home address?] (LINK(HEAD( i )) = 0 ) THEN DO P U T " n o t found", STOP

key

IF

i--READ(i),

stored

ELSE

st

the

O~LOC(

ENDDO.

H E A D ( I ) ).

ENDIF. [There

is

a

list

at

the

home

address.

]

P ~ f ( L I N K ( H E A D ( i ) ) ).

DO [Check

the

list IF

fop the (TAG.(P) THEN

current key.] = 1 ) DO P ~ L I N K ( P ) , IF

P--READ(P),

P~f(P),

( OVERFLOW( P ) = K) THEN

DO L I N K ( Q ) ~ L I N K (

P )s

OVA[L~f-I(P), WRITE(LINK(Q) STOP DO Q ~ P ,

ELSE

),

ENDDO.

P~f(LINK(Q)) ENDDO. ENDIP. ENDDO.

ELSE

IF

(BUCKET(P) THEN

=

K)

DO L I N ~

Q)~LINK(P).

AVAIL[ i ] = P , WRITE(LINK(Q)), ELSE

STOP ENDDO. DO Q ~ P , P~f(LINK(Q)) ENDDO.

ENDIF. ENDIF. [Check

for

%he end IF (P

Of the = 07 THEN

list. DO

PUT

] "not

found",

STOP

ENDDO.

ENDIF. ENDDO°

Detetions

in

this

structuee

are

performed

by

initiating

a

24

retrieval

Locate

an

device

is

operation.

item

The

is

number

of

accesses

to

the

required

to

CR(~,b)o

The

average

the

same

The

amount

is

average

number as

that

of for

accesses ihe

retrieval

direct

access

operation.

storage

This

average

CD(~.b).

Assume

that

a

word

Hence, Pool

[55]

and

new

it

bucket

bucket

tables that

to

device. coatesclng

ALgorithm

70],

memory.

aLLows

by hold

ihe a

buckets

key

and

requirement

is

a

hd

words.

pointer.

presented

by

van

der

~s

(k

-

by

storing

the

when

the

enters

~34. in

~

b)P(k).

the

a

convenient

A is

to a

within

(DoubLe algorithm

address

record is

of

An

are

information

chaining

This

system.

tables

new

the

processes

the is

a

chain

technique

Our

ALgorithm

A

home

current

This

first

WiLLiams

d

to

storage

~c

generated

~g~_~Rg_t_!g~. when

enough

average by

required

k) b

un¢iLted

this

+

storage

Large

denoted

Lists any

Is

the

ffi b d

~c

0¢

he

to

Large placed

convenient

way

free and

slot

address

are

each

record

onLY

due

to

the

problem

catted

Knuth

we

desire

an

on

a

direct

access

to

solve

the

of

Linking

home

solve

so

a

occupied

algorithm,

way

in

once and using

algorithm storage

problem

using

buckets.

chained

scatter

searches

a

t~bLe double

search

and

chained

List

insertion) o~

buckets,

25

o~

size

b

the

bucket

key

is

are

taken

Looking

is

not

placed

current

.re

of

node other

node

two

wlth

a

tilled

is of

by

Each

fields.

whose

key

fields

respectively.

An

List

a.

are

Node

given

to

BUCKET[i

].

for

empty

a

s

Structure

figure

Of

0

Link

the

and node

in

to

by

AVAIL.

pointer

a

node.

Node

Figure

Structure

4,2.

Of

Coalescing

Node

Structure.

The

of

ROVER. of

they

occupied

and node

RLIIqK[ ROVER] structure

buckets

nodes

An

first

List List

~tnd

LINK[i],

Bucket.

A

The

occupied.

field

the

caLLed

( b,

and

fuLL, New

LINK

b.

is H.

a

( i

Ducker

by

4o2.

A

the

bucket to

by

and

LLINK[~OVER~

in

the

distinguishable

of

not

pointed

catted

ittustratlon

is

space

is

has

is

pointed

BUCKET

INFO[i],

bucket

K

If

pointed

types,

field

If

header

available

unit

key

K.

inserted.

o~

denoted

a

key

K is

distinguishable

contains

coalescing

List

basic

are

given

llst

being

The buckets

a

a

bucket

a

fuLL,

on

from

the

for

the

possible and

t~s¢

26

This

atgorithm

auxitiary

variable

bucket

empty,

is

variables.

of

the

BUCKET[

Alp

Aa. A3.

test

is

The 3]

is

use

used,

to

R=~OVER*b.

of

node

currently

respectively. and

use

The

b~cket

R

makes

are

list

occupied

fitted

a[[

3

function

empty

and

SS

filled

bucket

are

pointed

to

coalesce

in

the

range

h(K)°

spaces;

variables

by

within R

when

GS

and

to

j 3

An

are the

SS

J

last

and

each

[Are there any tuft buckets?] IF (R ROVER .,~ R L I N K [ G S ] ~ THEN

DO

ELSE

i--j * R O V E R .

ENDIF. [ Is t h e r e a IF ( BUCKET[ THEN

t--j÷ROVE~, A4 ENDDO.

ENDIF.

starts DO &5.

A7 o

which

here).

[Compareo

]

IF

( K = INFO[i THEN

A6 °

we wilt Look at within the bucket

])

DO PUT " f o u n d " .

STOP

ENDDOo

ENDIF. [Advance to next.] IF (LINK[i] ~ O) THEN i~LINK[ i ] ELSE go to AT. ENDIF. ENDDO.

[Find

empty node°] (The search was unsuccessfut want %o f i n d an empty position in the bucket). Decrease R one or more times untit finding a value

and

we

GS

ROVER.

[istT] i ] is empty ) DO M a r k B U C K E T [ i ] a s a n o c c u p i e d node, with INFO[ i ~K and L I N K [ i ] ~ 0 , STOP ENDDO.

(The BUCKET[i] is occupied~ the tlst of occupied nodes

node

bucket,

0)

ROVER--RLINK[GS], R--ROVER+b, @o to

the link

[ Initiatize pointers. ] IF (H = O) THEN DO R O V E R ~ A V A I L , A V A I L - - R L I N K [ A V A I L ] , GS~I~OVER*b, R L I N K [ G S ] ~ O , SS*-H, R L I N K [ H ] ~ R O V E R , R*-GS, L L I N K [ R O V E R ] ~ S S . S S ~ R ENDDO. ENDIF. [Hash.] j~h(K}+l. (Now i ( j (b.)

=

A4o

hash

find

last

aitowed

fo:

a

help The

the

being

of

27

such IF

that

(R

=

BUCKET[F] ROVEN

THEN

^

IF

is

empty,

RLINK[GS]

(AVAIL

=

THEN

=

0)

O) DO P U T " o v e r Z i o w " , STOP ENDDO. DO [~OVER~AVA I L , AVAIL~RLINK[AVAIL], R~ROVER +b, GS~R, RLINK[ R ]~0, RL I N K [ S S ] - - R O V E R .

ELSE

LHNK[ ~ V E R ]-ss. SS--R,

go

to

i--j *ROVER, A4 ENDDO.

ENDIF. ENDIF. IF (R

=

ROVER

THEN

^

RLINK[GS]

to

go

moved

lists after

4.3.2.

are they

using

Duhne

in A

for

[34]

a

new

a

A4

avaiLabLe

coalescing

been

lists

method

in

coalesce,

inserted

so into

results

[isis

summary

an

to

presented

of is

for

a

for

bucket

addressing presented

here

equal

d

probabiiity The~e

buckets.

are

N

The

of items load

m__s

where

d d

~

~

keeping

that

occupied

records

need

not

be

buckets.

calculating size

methods

b

N.

an

that

of

the one.

Severance

presented uses

retrieval

the

a

general

a

record

and

same bucket

List.

buckets.

=

For

i~j+ROVER,

ENDDO.

I!~

coalescing Assume

the

have

coalescing

[ 65]

res~Its. size

aLLowed

~e~rievat

Knuth time

0)

ENDIF. L I N K [ i ]~R, i--R, [ Insert new key. ] Mark BUCKET[i] as node, with I N F O [ i ] ~ K a n d L I N K [ i ]--0

AS.

Several

~

DO R O V E R ' - R L I N K [ G S ] , R~ROVER+b, GS~R,

m constant

we

have.

assigning stored factor

by is

chaining

to

any

with

of

28

P[X

=

In

the

storage

device

address

h(K)

nodes

List

the tend

to

be to

the

total

total

required

to

List

List

the of

k

tota•

t k

where The

mean

per

k

)

LiSt.

be

address

the

a

the

bucket,

are

aLLowed

Length

due

to

short.

Items

due

to

to

k

exactly, list

must

that

the

coalescing

is

number

or occupied The

be

of

smaLL

to

probes

.

of

probes

required

to

address

aLL

÷ _l(k 2

-

b)(k

-

b

÷

I )

items

item

addressed

in

a

'~ i _ k _ - - ~ 2

value

of

of

probes

This

the

number

per

list

of

probes

divided

by

per

the

mean

numbem

yields N

)

=

~

tkP(k)

.

k=O N kP( k ) k=0 average

of

coalesce.

coalescing

The

b,

CS(=,b

The

seek.

begins.

it the

access

we

snatch

that

Assume

direct

which

tilt

lists

at[

concluded

the

record

where

fiLL

on

as

=

expected number

to

record

when

number

items

each

[34]

Length

address

"

Knuth

List

£ k___- __b_) 2 Define

home

partiaLLy

short

e -m

LikeLy

the

may

--~T-

process

equaLLy

bucket.

contribution

keep

is

mk

=

retrieval

defines

A

over£tow

ffi P ( k }

k)

of

number

CR(~C,,b)

=

accesses

1

÷

The

special

N

1 2m

case

is

~

(k2-2kb*k~'b2-blL~x__blk_e_-~b

k)b

b

k!

÷

I 2m

; k> b

=

I,

yletds

(k

-

b)P(k)

of

is items

the

29

Ce(ae,,l)

1

=

* m * !2

Knuth ~ists

b

for

=

CN

[34]

presented

!_

e-m

2m

2m

result

a

+ _!

I

(e2~

I

-

-

2~)

*

8e

where

CN

toad

is

the

factor.

I¢

,

with

separate

of

new

wlth

accesses

result

a

during

presented

maximum

absolute

a

retrieval

above

for

b

error

of

.05.

and

ffi 1

~

is

the

approximates

.1

for

_~ ~
b

amount

way

*

to

and open

d

E k>b

(k

resotve use

type

(k

-

of

storage

denoted

structurej

bd

links) An

I

average

list

~t

=

an

-

b

the open

addressing

+

by

*

required

~[,

to

store

~

I }P(k}.

probtem type

of

co[tisions

addressing

system

is

system

organized

is

to

with as

tlnear fo[tows:

a

31

there

is

a

set

sequence;

for

positions

is

inserted in

sequence the

the

open

position

is

used.

K,

using

for

made

g

addressing. and

is

every

Peterson

If

time [54]

with

K as

with

open

probe

is

K is

is

normally

probe

already is

sequence

key

the

position

List,

its

using

probe

memory

key

position

occupied,

encountered

determined

since

the

same

method

and

called

by

K,

the

sequence

of

processed.

introduced

this

obtained

estimates

and

simulation

different

with

Linear

types

it of

results

open addressing

for

the

mean

time.

A"

AL~or~i~hm

(Retrieval

hashing

A key-to-address keys

into

retrieve that

a

bucket

key

contains

from the

reading

of

a

the

address

of

the

READ(P).

the

a

node

first that

Location

i and

function

k

of

that

of

a a

disk

F

is the

the

auxitiary

maps

track.

of

a

address

track

P

address

P.

track

that

of

the

a

that

used into

by

to

transform

is

used

[ink

Assume has

to that

been Location

L

is

to

variable

READ(P)

first

containing

variables addresses

be

Define

Assume track

used

INFO[ i]

Let

the

Last

is

function

directory.

the

probing) h(K)

bucket.

Location

of

are

The

containing

containin~

Last

variables

addresses.

track

Assume

track

first

transformation

address

the

a

an

possible

List

first

the

K is

the

a

of

record

several

ALgorithm

is

the

in

List

record

on

the

K determines

discussed

Retrieval

of

a

the

If

not

key

Peterson

4.4.1.

the

the

position K.

that

K,

Initially

by

is

search

whenever

first

is

every

key

determined

conclusion

systems,

which

acceptable

inspected

searching

probes

by

retrieved.

second

while

rules

each

or

stored

of

the

mean r

set

is by

of

the

address

the

directory.

The

the

algorithm,

f

internal

main

memory

32 addresses.

[itash

the

the

key

address.

and

read

the

track

GET K. L~h( K ). i ~ R E A D ( I ) , k~i, DO Key with current

[Compare

~F ~ I S F O [ i ]

ENDIF. the next

to

i--i

-

iF

key.

]

K)

DO PUT " f o u n d " , STOP ENDDO° I F ( [NFO[ i ] empty ) THEN DO PUT * n o t found** STOP I~NDDO. ENDIF° TM

position. I,

(f-1(1)

ffi k )

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46

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ittustration

5.5. -I,

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4,

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flIii!Ll Jill!fill Iii[!!i[i] Figure

5.5.

Binary

Search

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47

Efficient by

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fire

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[15]o

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,-4

49

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51

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58

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in

rooted

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disk.

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[~Iiiili] [!IiiIi] [~Ii!iIi]

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5.9.

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59

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61

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62

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P

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P

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[Characters

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5.11

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figure

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Figure

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ittustrate

64

In transitions

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of

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the

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access

path

number

retrieval

first

any

search

tree.

store

of

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to

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of

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sequentially

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ks

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approximate

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[50]

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a

the

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a

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operation

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a

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size

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function

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and

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generate that

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dynamically tree

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are

oteoer

stored

f-l(x)

within

constructed structure

=a.est

to

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determined

the

addresses

reference,

[ikeiy the

in

b

are by

k

to

nodes

buckets

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in

arrive.

The

the

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Therefore, in

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using

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the

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nodes,

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path

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HibhaPd

65

derived The

formulas

internal

[29]

for

path

the

average

Length

for

a

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and

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search

in

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external tree

path

Lengths.

defined

by

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=

the

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[og21

is

records

k

assigned the

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k

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the

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has

into

accessed. m

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= ab#

number

of

by

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the equal

to

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buckets.

average

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one

k

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~(N)

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value

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,

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of

assigned

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the

N

records

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= ~.N. m

Therefore storage

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CR(~.b)

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a

mean

numbeP

of

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.

ra 5. 2 . 3 .

!_ns_~e_r t i_ea_Al_~o_x!_t_~_m

ALgorithm

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(Insertion on

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pointed from

the

pointer in used

a

to

by

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direct

that

AVAIL.

avaiLabLe and

to

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catted the

a

hash

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BUCKET

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conditions.

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to the The

symbol

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)

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of

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pool

stored

addresses.

the

transformation The

a node of

trees

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the

are

AVAIL

stored h(K)

functions

Is

66

ANEXT,

ENEXT,

defined link

in

reading the

P

a

that

used

the

is

main

P.

into

an

the

move

and

an

Internal

of

a

track

Define

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from

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of

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fo

device

iS

tree

the mean

Define

access

storage

track the

WRITE(P) device

P.

indicates

the

Of

end

the

string.

CODE ÷

indefinite

continuation

indicator.

INFO

is

the

stored

ANEXT

is

the

address

of

the

next

ENEXT

is

the

address

of

the

slblin@.

ADATA

is

the

address

of

data.

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is

the

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to

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CT

is

the

number

~OV

is

the

upper

a

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is

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of

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length

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to

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a

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character.

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The

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to

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to

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into

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of

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data

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initial

addresses

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ADATA,

67

ENEXT

is

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[ Initialize.] (P

=

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address

GET THEN

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j

~

go

to

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1,

i ~

h(Cl),

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ENDIF. P

B''2.

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P

~

f(P)o

characters.~

IF

(C 0

=

v)

THEN

to

go

BP'6°

ENDIF. IF

(CODEfP) THEN

=

t+.)

IF

(ATAG( P ) = THEN

0)

DO

P

~

READ(ADATA(P)),

P

~

f(P)

ENDDOo

END I F . ELSE

P

~

f(ADATA(P))0

ENDIF. IF

(Cj

=

INFO(P))

THEN

go

to

B''7.

ENDIF°

B''3.

[ Check IF

for

code

.]

= "+') IF (ATAG(P)= THEN

(CODE(P) THEN

O) DO

P

~

READ(ADATA(P))~

P

~

f(P)

ENDDO.

E N D IF. ELSE

P

~

f(ADATA(P)

).

THEN

go

E N D I F. IF

= "-')

(CODE(P)

to

B''5°

END[ F.

B''4.

[ Is IF

it

a

sibling

(ETAG(P)

=

or

a

(ilia[

set

node?]

0)

THEN

DO

ELSE

ENDDO. P ~ f(ENEXT(P)

P

~

READ(ENEXT(P)),

P

).

ENDIF.

go B''5.

to

[Find IF

B''2. the next

( ETAG(P} THEN

part.

=

0 )

DO

Q IF

-

] READ(ENEXT(P)

(0

~

THEN

END IF.

),

0) O

ENDiF°

ELSE

in

track,

the

IF

disk

TM

ENEXT

B~Sl.

a

track.

ENDDO. O ~ f(ENEXT(P)

)o

~

f( O }

~

f(P)

68

IF

(O

ENDIF. P ~ 0,

B''6.

= 0

^

go

Cj

to

= v

THEN

go

to

BP'8.

B''2.

[Last character.] CT(1)~CT(i ) * I, IF (CT(i) > ROV(i) ENDIF. CODE( f ( R ) )~-"- " , ADATA( f ( R ) ) ~ A D R ,

R:AVAIL, )

THEN

CON(i

),

ANEXT( P ) ~ R j

B''7.

p,.f-l(p)~ W R I T E ( P )~ STOP. [Look at the IF

(ATAG(P)

THEN

P ~

Q,

j

[Characters

B''9.

[Store

~

character°

]

O)

DO

Q ~ READ(ANEXT(P)), IF (O ~ 0) THEN END I F . ENDDO° O ~ f(ANEXT(P)),

ELSE ENDIF. IF (O = O) ENDIF, SlJS.

next =

j

THEN

go

to

+ I, found,

go

"to B ' ' 2 .

characters.

ADATA(P),

terminate,

] t~-AVAIL,

CT(i )*-CT(i) * 1, IF (CT(i| > ROV(I)) E N D I F. INFO(f(R))*-Cj,

IF

(P

THEN

CON(i),

~

THEN

O)

ANEXT(P)~R

ENDIF. PT( E )~R + I, P~f(R), IF (Cj = V) THEN

.j~j

go

to

B~6.

ENDIF. go to BPsg,

CON( I ):

f(O)

B°'5.

~

]AR

O ~

CODE( f ( R ) ) ~ ÷ , P~f(R), CT( i )~T(i

ADATA(P)~R,

ROV(i)~ROV(i) ) +

1,

÷ c,

R~-AVAIL.

69

5.2.4.

I nsertioD_Ti~e The

one

more

key

was

number

than

the

inserted

to

accesses operation

of

number into

the

comparisons of

the

direct

comparisons

t~ee,

= CR(G,b)

Algorithm

B'''

(De[etlon on

Assume

pointed

to

and

to

ANEXT, defined [ink

in

its

addresses

the to

that

is

into

is

needed average

during

an

of

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contains

a

P,

to

from

into

writing an

move to

va~ue

memory

internal

of

a

track P.

storage

%o b e

pool

exactly

when

that

number

of

insertion

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of

along move o~

on

by

The

access

the

The

node the

AVAIL

are

stored h(K)

the

tree the

[ink

nodes

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on

variabteSo

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functions

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Define

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of

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the

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P.

the

disk

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management

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device.

fina[

pointed

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and

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pool

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rink

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a key

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conditions.

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temporary

Define

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find

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5.2.5.

the

to

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to

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Q

a

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Define

access

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WRITE(P) device

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70

indicates

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end

o~

the

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CODE +

indefinite

continuation

indicator.

[NFO

is

the

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Bucket Size Figure 7.3.

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8

CHAPTER

~MEA~!~N__QE_METHOD~

Consider records,

I000

summarize invotved object the

words

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generate

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107

I.

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108

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A comparison

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109

time

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flles

the

the

fewer

~or

separate For

accesses

require

analyzed

Lists,

percent

more

fuLL

accesses

chaining

and to

with

the

bucket

insert coalescing

a

size

record Lists,

128

Linear

probing,

requires

more

inserting

a

chaining risked

record,

for

are

the

sizes

The

average

file

number

with

number

bucket

of

of

accesses

coatesclng

tistsj

bucket

sizes,

record

than

the An

binary

inverted

bucket

size

greater

record

than

chaining

tlsts,

tinear

required bucket

by sizes

the

greater

delete

a

case

the

with and

inverted

greater the

than

record

contesting

the

search

than

a

tlsts, fire

file

furL.

the

inverted

the

average

chaining

wlth

method.

For

accesses

to

aLL

insert

a

trie.

tess

the

than

Linked

the

in

lists~

fewer

percent

tO0

percent

accesses

to

chaining

with

method.

Fewer

trie

to

delete

fuLL

and

futt

and

delete

a

the

coatescing accesses

a

are

record

for

bucket

sizes

accesses

to

2. are

50

percent

inverted

chaining

llnear

tess

buckets

requires

than

Fewer

file

50

record

IS

the

the

linked

and

six.

inverted

are

separate

and

separate the

ten

requires

with

five

buckets

nine

a

tree

fire

than

than

ilsts, binary

fire

than

probing

When are

search

an

insert

and

flte

in

than

Lists

approximatety

buckets

with

probing

inverted

thRn

When

accesses

Coatescing

the

than

chalnin~

fewer

tree

2.

where to

search

sizes.

bucket

with

record

than

greater

linear

the

a

accesses

for

art

binary

requires

greater

case

sizes

file

insert

The

for

chaining

greater

the

trie.

case

sizes to

Consider

this

fists,

required

the

inverted

bucket

bucket

and

in

separate

files

with

file

accesses

with

accesses trie

linked

with

~robing, tree

flie

requires

separate Linked

requires

more

fewer

ilsts,

files

the

and

accesses

chaining the to

with

trle. delete

In

this

a

record. The storage

for

the

storage fate,

regulrement inverted

list

for and

the the

inverted

fire

includes

index.

When

the

bucket

129

size every

is g r e a t e r method

and

the

presented particular

in

choice

operations this

large

seiecting processing

this

method

requires

tess

storage

than

of which on

monograph

that

method

is best

data.

indicate

The where

depends

on

performance one

method

the

type

of

measures is

good

for

a

operation.

This very

I0000,

presented,

The data

than

data the

anatysis

is

bases.

The

Correct

very

large

important

approach

data

structure

dRta

bases,

to

designers

taken and

wilt

search

of

aid

systems the

algorithms

using

designe~ for

in

APPENDIX

The

foliowlng

notation

A

Is

used

consistently

or

link

vector

throughout: SYMBOL

MEANING The

AVAIL

A

Load

Link

to

factor.

variable

that

points

BUCKET.

h

The

bucket

size.

BUCKET

An

B(k~N,!) d

Binomial

probability

CC

ChaLnin~

with

coalesclng

CS

Chaining

with

separate

C D ( ~, h )

Average

number

available

pool®

storage

distribution,

Lists. ~ists,

of

accesses

in

a

of

~ccesses

in

~n

of

accesses

in

a

deletion

operation.

CI(~,b)

Average

number

insertion

opemation.

Average

numbem

operationo

C 6 ( ~. b. x . y )

The

expected

value

of

the

mixture

retPievat

131

MEANING

SY MBO L

probabiilty Deletion

opema~iOOo

~etrieva[

operation.

The

DL

A

E(X)

The

f

A

number

double

of

buckets,

[inked

expected

function

into

H.

operation.

Insertion

d

F( C S : C C °

dlstribu%ion.

file.

value that

internal

Comparison

of

the

variable track

transforms

maln

memory

X. addresses

addresses.

operator.

(N,d,~))

g(j)

A

frequency

of

the

items

in

V(x)

Gamma

function.

h

The

h(K)

A key-to-address

transformation.

R( N , s )

The

number

K

A

LL

Linked

file.

LP

Linear

probing.

Lt(

m,

b)

a

function

height

Nth

of

file.

or

the

teve[

harmonic

of

a

of

tree.

order

s.

key.

Average

load

ra

The

avera@e

N

The

number

n

Average

OVAIL

occurrence

a

key.

A

[ink

time

number of

number

variable

for

of

a

file.

records

assigned

to

a

bucket.

~ecords, of

dl@its

that

or

points

characters

to

possible

OVEI~FLOW.

in

I32

SYMBOL

MEANING

OVERFLOW

An

overflow

Mean

m,b)

an

p( J,e

avaiLabLe

number

o£

inverted

when

$

=

Zipfian

approximately

READ( P )

Read

a

Read

the

main

memory

READ

P

s

Ss(n,b)

Total

T

A

WR [ T E ( P )

Write

a

WRITE

Write

the

e

=

0

and

when

e

~

L~g_a~ tog .20

.

the

P

into

P.

address

the

internal

an

inverted

s.

for

file.

track

containing

record s

in into

the

the the

address

internal

P.

main starting

~ocation

P.

storage

seoarate

requirement

for

chaining

fists.

Average

storage

requirement

for

a

Average

storage

requirement

for

chaining

for

a

coalescing

Average

Linked ~p

Uniform

when

required

buffer

Average

with wt~

at

buffer

storage

address

with

~t

iS

trie.

at

~f

of

List.

memory

tdc

buckets

that

containing

record

A ring

the

distribution.

track

RL

P s

80-20

probability

A

in

distribution

1~

Pfk)

items

pooL.

file.

A probability

)

storage

Storage

storage

Linked

Lists. requirement

double

file. requirement

for

Linear

probing.

flee.

133

MEANING

SYMBOL

us

~t

Storage

requirement

Average

number

of

nodes

Average

number

of

digits

in

used

Uniform z

NODE

OPERATORS

position

a

tree.

required

or

of

a

to

store

a

characters trie.

rute.

80-20

e

each

for

distribution.

Zipf's

Law.

Assign

a

value

Assign

a

[ink

manage

the

to

a

variabte.

variabte

avaitable

a

value

storage

and pool.

MEANING

ADATA

Address

of

the

data°

ANEXT

Address

of

the

next

ATAG

A

CODE

Code

ENEXT

Address

ETAG

A

GET

Read

i,put®

HEAD

List

head.

[NFO

Stored

NODE

Count

of

PUT

Write

output.

TAG

Bit

tag

indicating indicating

tag

of

the

[ndicatlng

filial

the the

set.

state state

of of

an a

ANEXT

node.

sibling. the

state

of

an

ENEXT

key.

tag

the

to

node.

bucket

indicate

size.

a

bucket

node

state.

node.

trLe.

REFERENCES

1,

Abd-Atta,

A.M.

and

2°

Ackerman,

A,F,

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17.3

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C.

~The

16,1

(Jan.

3.

~o

Bayer, Large pp.

5.

R°

J.R°

Bert,

Indexes",

~The

E.

of

Size

On " ,

164° Hash-Coded

Tabtes~,

*tCrganization

and

A ~ _ ~ E ~ & ~ ,

Binary ~

Quadratic

Secondary

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and 13,11

F.H°

Management

9.

Tabtes

~fi~L_A~,

1

Maintenance

of

(1972)

B-Trees: _

~

~

G

Data A

.

Structure 1

and

(1972)

Quotient

CLustering

Method:

~,

b

~gL-A~,

Hash

13j2

Code

(Feb.

1970)

107--100.

C~.~wa &~M, 8.

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Atgorithmsn,

Etiminating

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Bert,

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McCreight,

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Maintenance

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Search

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1973)

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Fire

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Binary 18,9

Search {Sew°

Trees

Used

1975 ) pp°

~or

B09-S17o

135

10.

BLoom, Data

11.

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Broom,

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H=Ao

Coffman, Hashing

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A.C.

Storage". 19.

de

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20.

ta

an.

7,3

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Eve,

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IBM_SX.S~s

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1970)

1970)

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FiLe

1964)

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13=8

422-426°

105-109o

to B e s t - M a t c h

Binary

Sheme~,

ACM,

Briandais,

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Using 427--A36.

Retrieval

for

9onfemenc~

Scattee

481-482o

Using

Variable

Length

295-298.

Dodd.

G.G.

~X~X~. 21,

Comm

With

Scatter

Addressing

WRandomized

TabLe

pp®

of

pp°

230-236°

Organization

"Fut~

1973)

A C M Nat~o_nna~

Coding

1970)

1973) p p .

~£mm_A~M,

and

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Large

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Functions",

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Day,

E,G.

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Time

and

Approaches

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Jr.,

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Affecting

-

(JuLy

Retrieval

Organization

W°A.

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Techniques",

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the

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Trade-offs

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W.

and

T i ~ e s n,

~Space/Time

R°P.

Jo~n~, 14.

Techniques

Retrlevat

ALLowabLe 12.

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"ELements

1,~ W.

(June

1969)

Data pp.

Management

volume

Finket,

and

I,

John

BentLey,

Systems',

Computing

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A~_~s!r_~o~__qc~ion_~£_~o~i!i~

A~li£~_t~on_ss, R.A.

of

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Theor_/f_&ndiXs Sons, Trees

Inc,

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for

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Ghosh,

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J_~__ACM,

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M.E.

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C_~mm ACM.

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Random

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",

569-579.

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~Note

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Index pp.

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1963)

Storage

Schema",

297-319.

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"Some

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to

AppLications pp.

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Hsiao.

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Comm

ACM.

(1962)

Combinatorial

Properties

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Sorting

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IBM c o r p . .

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Key~ ~.

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Computer

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Information

SIAM

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67-73.

Search-Trees ~L. A ~ . _

Math..

514-532.

Int£o~uc~on

N.

System

13,2

AtphabeticaL

1971 ) p p .

IBM c o r p .

",

Certain

12-28.

Retrieval

PLains,

33.

of

(1974)

!n~orm_~t_i£~ . 4

205-207.

Hibbard,

21,4

Acts

C om_m ACM,

Acces~

and

HeLLerman. H.

(Jan.

31.

Senko.

I_nf~otmatica,

with

30.

Memory",

(Oct.

C.C.

Keys".

513-517°

Random

16,4

Gottieb~

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GeneraLization

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LBM S T ~ t e m ~ 28.

"A

=Trie

S.P.

SeLection

Acts

Composite

197~ ) p p .

(A~g.

26.

on

Indlrect

~Qmm_~.

! g _ ! B M S~te~__3Z_70 _ D l r e ~ t

1974,

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Chaining 4.5

Access

(May

Method 1951 ) pp.

for

Addressing

218-222.

on

I37

~nd

Se~h~ng~

Addison-Wesley,

F~nt~_&~£P~th~s, 36.

3Z.

Knuth,

D.E.

(1971)

PP.

LandaueP,

38.

39°

W.I.

"The

41.

Lowe.

T.C°

Usage

on

(Oct.

1968)

1963)

"The

Direct

F.

V.Y.,

Data

Management

Lum,

V°Y.,

43.

996°

Lum~

~emm_~M, 44.

Mau~e~. £emm_A~M,

45°

A

Mau~e~.

of

File

and

InfoPma__~i~a,

and

13,11

[

in

up_u_~texa,

CharaetemistEcs J._ACM,

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15,4

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Ig6S)

Lewis,

E.

M.

"Analysis

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~esults

Fundamental ~ _ ~ M ~

~ash op.

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T~ansfo~m

Large

"Addltionat

PP.

a Complex

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Ret~ieva[

ToG.

of

1971 ) pp.

A

Scatter

10~5--|047.

Simulation

Files",

1970)

Improved

pp.

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14,4 ( A p r i l

Techniques:

"An

M.

Search

Performance

P.S.T°

(Nov.

and

1972)

Dodd,

"Multi-Attribute

WoD.

Base

Linear

by

Me%hod

~ _ ~ M ,

Existing

II,I

Utilization

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Senko,

Fundamental

Yuen,

W°D°

its

and

Data

(Dec.

15,12

P.S.T°

Transform

V°Y.

&eta

863-871.

Increment

H.

Yuen,

and

p.

PP.

Access

Lum,

Large

Trees",

!EE~_TE~nn=_~!e~ron,_~em

Influence

Ling.

Flies",

on

228-606°

535-548.

Formatted

Address

Tree

"Weighted

Lum,

V.Y.

Balanced

Access

pp.

Techniques:

42.

Search

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Tables" • ~emm_A~M.

40.

Binary

PP.

14-25o

(Dec.

Luccio)

389-700.

Addison-~esLey,

"Optimum

Information EC-12,5

pp~

Existin~

228-239°

on

Key-to-

Performance 15,11

Combined

(NOV.

Study IQ72)

Indexes",

660-665° Code

for

ScatteP

Storage",

35--38° "Mash

Table

Methods",

~P-~-~i~g

138

S~e~S,

47.

Mclimoy.

Method

M.D.

Mo~is.

~.

51.

pp.

and

Binary

J,

55.

£emm_~AfM,

CQmm_&~_M.

II, I

Algorithm

to

Retrleve

~._AC_M.

15,4

(Oct.

1968)

Trees

and

R. in

Storage

"Dynamic a

Two-Leve£

Reingotd,

E.M.

Memory ",

~Binary

SiAM_~._~sm~s~iag,

Allocation P£o___qc~edi_~

Search

2,1

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and

File

Trees

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1973)

33-43,

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C~tin_~_S~EX~X~ 53.

Storage

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R,

Bounded

52.

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Z4-88.

38-44.

D.R,

Nie~ergett,

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MUff%Z, for

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1968)

Morrison,

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"A

Inc.~

101.

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5-19,

pp.

Holden-Day,

(Jan. 49°

1975)

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w° 48.

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"Random

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Search {Sept.

Access

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F~Lo

£~e£~iBM~

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130-145.

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Initial

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56.

van

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~es~_~x~!!a~_Mg~s!ing_~_qtur~_~e~

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Mechanisms:

Co m~tiQ~_S__uurvey~,

Duhne.

Kddress~n~ A[sorithms"

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A Survey

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R.

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64.

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"AnaLysis

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1963) D.

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Residue

Retrleva~

1976)

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The

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1970)

R.L.

Method", 62.

S¢orage

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"The

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Com_j~ti_nng, 5 , 1 60,

A.

27-38.

HaLt,

58.

J°

Tainiter,

M.

E.H.

~Use

of

Tree

6,5 (May 1 9 6 3 ) pp.

"Address[n~

for

Structures

for

Processin~

272-279°

Random-Access

Stomate

w~%h

I40

MuLtipLe 68,

69.

Bucket

Capacities"j

Uttman.

J.D.

"A

~a~_A~M.

19,3

(JuLy

Wedekind,

H.

non

B~eM~/g_ement, 70.

WiLliams,

Lan~age 71.

Zipf, Hafner

Note

F.A,

1972) The

pp.

(1963)

Efficiency

Ppo

of

307-315.

Hashing

Functioos~j

pp.569-575. of

Access

Paths

in

a

Data

Base

385-397. Identi~iers

~o@~_ACM,

HM~_B~h~_vi2£

PubLishing

the

SeLection

"HandLing

Processors'.

G.K.

on

~¢_A~M,

Company,

2,6

as

(June

Internal

1959)

~ n f l TT~ P r i ~ A p L ~ _ ~ o f

(1965).

SymboLs

pp. Least

in

21-24o Effort,

A Comparative Study of Very Large Databases

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Plural Policing: A Comparative Study

A Comparative Lexical Study of Quranic Arabic

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Politics and Ethnicity: A Comparative Study (Perspectives in Comparative Politics)

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Restitution at the Crossroads: A Comparative Study

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Understanding Early Civilizations: A Comparative Study

Jung and Searles: A Comparative Study

Primary School Teacher Deployment: A Comparative Study

The Struggle Against Corruption: A Comparative Study

Probation Round the World: A Comparative Study

Economic anthropology: A study in comparative economics

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Religious Worlds: The Comparative Study of Religion

Managed Evolution: A Strategy for Very Large Information Systems

Team Killers: A Comparative Study of Collaborative Criminals

Beyond Sacred Violence: A Comparative Study of Sacrifice

The Presidentialization of Politics: A Comparative Study of Modern Democracies (Comparative Politics)

Oriental Despotism: a Comparative Study of Total Power

A Comparative Study of Very Large Databases

29th Conference on Very Large Databases, 2003

Plural Policing: A Comparative Study

A Comparative Lexical Study of Quranic Arabic

A Comparative Lexical Study of Quranic Arabic

A Comparative Study of Human Reproduction

Design of Very Large Scale Integration Systems

Computational Aspects of Very Large Scale Integration

Politics and Ethnicity: A Comparative Study (Perspectives in Comparative Politics)

Politics and Ethnicity: A Comparative Study

Restitution at the Crossroads: A Comparative Study

Slavery and Social Death: A Comparative Study

Understanding Early Civilizations: A Comparative Study

Jung and Searles: A Comparative Study

Primary School Teacher Deployment: A Comparative Study

The Struggle Against Corruption: A Comparative Study

Probation Round the World: A Comparative Study

Economic anthropology: A study in comparative economics

Natural language processing using very large corpora

Very Large Scale Integration.. Fundamentals and Applications

Very Large Floating Structures (Spon Research)

The Comparative Study of Electoral Systems

Religious Worlds: The Comparative Study of Religion

Managed Evolution: A Strategy for Very Large Information Systems

Team Killers: A Comparative Study of Collaborative Criminals

Beyond Sacred Violence: A Comparative Study of Sacrifice

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