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

accesses

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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defining data that

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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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21

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= K)

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END IF. ENDDO. ENDIF. LINK(Q

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

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pool

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return

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pointed

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functions

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are

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23

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memory

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disk

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a

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addresses.

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returns

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key

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stored

ELSE

st

the

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H E A D ( I ) ).

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]

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

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P )s

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

ELSE

),

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=

K)

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ENDIF. ENDIF. [Check

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Of the = 07 THEN

list. DO

PUT

] "not

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STOP

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ENDIF. ENDDO°

Detetions

in

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a

24

retrieval

Locate

an

device

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item

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number

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a

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Structure

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contains

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a

a

bucket

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for

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26

This

atgorithm

auxitiary

variable

bucket

empty,

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variables.

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the

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list

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fitted

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3

function

empty

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filled

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when

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last

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

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i--j * R O V E R .

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ENDIF.

starts DO &5.

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IF

( K = INFO[i THEN

A6 °

we wilt Look at within the bucket

])

DO PUT " f o u n d " .

STOP

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[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

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aitowed

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a

help The

the

being

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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

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summary

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for

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probabiiity The~e

buckets.

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The

of items load

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~

keeping

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occupied

records

need

not

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calculating size

methods

b

N.

an

that

of

the one.

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presented uses

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the

a

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a

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same bucket

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buckets.

=

For

i~j+ROVER,

ENDDO.

I!~

coalescing Assume

the

have

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[ 65]

res~Its. size

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~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

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chaining

to

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with

of

28

P[X

=

In

the

storage

device

address

h(K)

nodes

List

the tend

to

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the

total

total

required

to

List

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the of

k

tota•

t k

where The

mean

per

k

)

LiSt.

be

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be

of

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to

probes

.

of

probes

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÷ _l(k 2

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items

item

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the

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

of

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coalescing

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b,

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seek.

begins.

it the

access

we

snatch

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direct

which

tilt

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where

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=

expected number

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[34]

Length

address

"

Knuth

List

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home

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process

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bucket.

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retrieval

defines

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(k

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of

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the

29

Ce(ae,,l)

1

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* m * !2

Knuth ~ists

b

for

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CN

[34]

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2m

2m

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8e

where

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during

presented

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above

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.05.

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4.3.3.

for

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number

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4.3.4.

The at

deleted. is

List

1).

the

Ci(~,b)

started

maximum

inserted

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K

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for

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4°3.5.

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the

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amount

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of

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by

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Assume

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the

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4.3°6°

a

casej

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Poo~

the buckets

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keys

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do

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The coatescin~

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amount

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(k

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type

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of

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average

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an

-

b

the open

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+

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required

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to

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I }P(k}.

probtem type

of

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addressing

system

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system

organized

is

to

with as

tlnear fo[tows:

a

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47

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49

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(ENEXT(P)

ENDIF. P BS.

~

ENEXT(P),

[Find IF

the (0

ENDIF°

=

0

go

to

next

part.

~

=

SP

1 A

H2. ]

O ~ Cj

=

ENEXT(P), ~)

THEN

go

to

BI0.

B6.

by

PT.

57

IF

(0

=

0)

THEN

go

to

B8.

ENDIF. P E6.

~

Q,

[Last

go

to

B2.

character.

] IF

(CODE(P)

=

THEN

P

" ÷" ) ~

ADATA(P).

ENDIF. IF

"-')

=

(CODE(P)

THEN

go

to

BI0.

ENDIF. IF

(SR

~

1 )

THEN

DO

PU~

"no%

found",

STOP

ENDDOo

END[F. R ~

AVAIL

CT(I)

IF

~

CT(i

(CT(1)

1

) ÷

)

ROV(1))

THEN

CON(i).

ENDIF. --

"-',

ADATA(I~

) ~

ADR,

ANEXT(P)

~

CODE(R)

B7.

[Look

at

IF

=

(0

R,

the

STOP.

next

0)

character.)

Q ~

THEN

go

to

BE.

+

go

to

B2.

in

sibling

ANEXT(P),

END I F . P BSo

~

O,

j

~

j

[Insert

character

INFO(R)

~

IF

Cj,

(CT(i))

1,

ENEXT(P) ROY(i))

~

node,

R,

THEN

CT(i)

]

R ~

AVAIL,

~

CT(I)

÷

1,

CON(i)

ENDIF. j

~

j

1,

+

(Cj

IF

=

P

*- R , THEN

v)

go

to

B6.

ENDIF. go

Bg.

to

Bg.

[Stome IF

characters.

(CT(i)

>

] R

ROV(i))

"~ A V A I L , THEN

CT(I

) -- C T ( i )

+

CON(i)

END IF. INFO(R) IF

~

(SR

=

Cj, 0

~

IF

(P

=

0)

P

~

0)

THEN

THEN

ANEXT(P)

PT(i)

-- R

ENDIF, j

~

IF

j

(Cj

+

1,

P ~-- R ,

ffi v )

THEN

go

to

B6.

ENDIF. go HI0,

Definition

%0

B9 o

[Characters

of

CON(i):

found.]

AR

CODE(R)

~

P

~

CT(i

R,

) ~

~

ADATA(P),

÷,

ADATA(P)

ROV(i)

~

ROV(i)

CT(i)

÷

1,

~

STOP.

~

R, + c,

*- A V A I L .

~

R,

I.

58

A

presented Art

typica[

in

rooted

¢igure

pointers

are

5°9o

tree

The

pointers

to

produced

nodes nodes

in

in

this

by the

tree

BUCKET

algorithm

are

and

is

nodes

are

in

not

disk

how

the

BUCKET,

p addresses.

A

modified

internat

disk.

In

B

this

atgorithm a~gorlthm

case

A~ter

ROOT

presented

the

B

rinks

storing

~s

used

are

disk

CAN.

CAND,

tater

witt

to

retrieve

show

records

stored

addresses.

CANDY.

EGG.

[

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

[~Ii!iI11

[21[ii-[i][~Ii!iIi] [!i[:~!Iij--[~Iiiili][:_I~!Ii] ..~

[!I!!~IiJ - [!I! iii] [-_I~1_~3] Figure

5.9.

~sh

Rooted

Symbol

Tree.

on

59

tree

Every in

the

forest

rooted

in

catted

ROOT The

to

store

entry

the

node

is

ROOT.

presented

Qodes tree

of on

The

the

ta~s ETAG

entry.

by

algorithm

An

itLustration

in

figure

symbo~

a direct

introduce

res~ectlve[yo terminating

produced

is

tree

and

placed

~[he A T A G

and 0

ETAG in

in

the

ETAG ANEX~

Figure

be

modified

In

each

Letter

device.

and

ENEXT

field

of

are a

defined

disk

ENEXT the

as

o.ddress

a

po£nter

is

in

within

a

disk

address

track.

track

is

ETAG

5.10.

is

a

pointer

shown

in

figure

=

B,

C}

ATAG

{A,

withi~

track.

ETAG

Organization

ATAG

Of

5.10.

ETAG

A

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fle[ds

word

follows. ~

track.

is

ENEXT

Fire

ATAG

must

=

the a

trees

track.

ENEXT

of

5.9

ANEXT

is

another

organization

binary

=

1

rooted

tree

the

tag8

the

The

binary

two

figure

storage

ANEXT

ETAG

a

of

in

another

ATAG

is

5.9o

access

ATAG

B

in

60

s. 2.1.

R__e_tr_!i_ev_a t__A_t~o_~r_I_t~m The

retrieval

algorithm

B.

The

track

to

other

of

and

zero

track.

the

with

A presented

mean

and

stored

a

on

the

ALgorithm

Bp

of

roots

PT.

A key-to-address

keys

into

bucket

pointed

addresses

to

by

track P,

the

into

main

to

the

-

indicates

*

indefinite

of

another

contains

a

this

case

ADATA

of

part

shows

of

how

retrieve

device.

direct

access

)

are

stored h(K)

functions

nodes

in

is

used

In

function

the £

addresses. the

end

of

the

string.

CODE continuation

iedicatore

to

to

device

buffer. stored

vector

[ink

ANEXT.

defined The

a

is

from

READ(P)

storage

device.

B

typical

Define

tree

storage

atgorlthm

information

symbol

on

tag

data

a

rooted

The

the

the

hash

variables.

memory

address

memory

trees

[ink

the

main

of

operate

a

node

retrieval

transformation

ETAG

is

internal

access

the

remember

an

direct

the

within

to

address

storage

into

retrieval

Cjo

modified

a

In

algorithm

from

in

addresses.

and

the

access

(~tetrievat

The

ATAG

This

a

the

v®

in

B'. is

contains

~

old

algorithm

point

s±orage

of

address

a

Cj

the

to

the

when

contained

direct

on

CODE~

vector

algorithm

reading

containing

occurs

version

al~orlthm

guide

field

access

key

similar

important

Link

direct

the

search

the

the

modified

as

the

is to

An

COndition

special

code

used

tracks.

A

associated

trees

are

that

contains

internal

tags

indicates

termination

field

a[gorlthm

caLLed

transform

ENEXT.

ADATA.

data maps

the

structure the

track

INFO~

61

INFO

is

the

stored

character,

ANEXT

is

the

address

of

the

next

ENEXT

is

the

address

of

the

sibling.

ADATA

is

the

address

of

data.

PT

is

the

pointer

to

the

0

filial

t~ee

ANEXT

ATAG

ENEXT

[Initiatize.]

GET 0 )

address

in

pointer

a

within

a

disk

address

An

tr~ck,

ffi

the

=

disk

is

ENEXT

(P

a

letter.

track.

another

IF

particular

track.

is

%he

BPl.

s

ffi ANEXT

ETAG

for

is

another

set.

THEN

Cj

j

~

DO

PUT

a

is

pointer

within

track.

I)

i

~

"not

h(Cl)

)

foundW.

P -STOP

PT(i)) ENDDO.

ENDIF. P B'2.

~

I~EAD(P))

[Compare IF

P

--

f(P)°

characters.]

(CODE(P) TBEN

=

IF

(Cj

=

v)

~

f(P)

TttEN

go

to

"÷P)

IF

(ATAG(P) THEN

ffi 0 ) DO

PP

ELSE

P

~

t~EAD(ADATA(P)), ENDDO°

f(ADATA(P))o

ENDIF° ENDIFo IF

(Cj

=

INFO(P))

THEN

go

to

B'7,

ENDIF, B'3.

[Check for IF (CODE(P) THEN

code. ] ffi " * P ) IF

(ATAG(P) THEN

=

0)

DO P

~

P ~ ELSE END I F END[F.

P

~

READ(ADATA( P ) ). f(P)

ENDDOo

f(ADATA(P))°

B'60

62

IF

(CODE(P}

[Is

B'4.

IF

it

a

"-')

=

sibting

(ETAG(P)

=

THEN

or

a

4o

to

fitial

B'5.

set

node?]

0 )

THEN

DO P

ELSE

P

~

~

I~EAD(ENEXT(P)),

P

--

f(P)

ENDDO.

f{ E N E X T ( P ) ) .

ENDIFo to

go

B'2,

[Find

B'5.

IF

the

next

(ETAG(P)

part. ]

ffi 0 )

THEN

DO

Q ~ IF

READ(ENEXT(P)), (Q

~

0)

THEN

Q-

f(Q)

ENDDO.

ENDIFo

ELSE ENDIF. IF (O =

Q ~- f ( E N E X T ( P ) ) .

0

^

Cj

ffi v )

THEN

go

to

B'8.

ENDIF. P ~

[Last

B'6.

IF

gO

Q,

to

B'2.

character.

(CODE(P)

=

THEN

]

" ÷" )

DO

IF

(ATAG(P)

= O)

THEN

P ~

f(P)

P

~

I~EAD(ADATA(P)),

ENDDO.

ENDIF. ELSE

P

~

f(ADATA(P)

{CODE(P)

=

"

")

)o

END IF. IF

THEN

go

to

B'8.

END I F o PUT

"not

IF

STOP.

f o u n d w,

at

[Loom

B'7.

the

(ATAG(P)

next =

THEN

character.

]

0)

DO

0

~

IF

READ{ANEXT(P)), (O

/

O)

THEN

Q-

#(Q)

END I F . ENDDO.

ELSE

O

~

f(ANEXT(P)),

ENDIF. IF

(O

0 )

=

THEN

go

to

go

to

B'5.

ENDIF. P

~

This

than In the

the

the

one

Bayer

B-tree.

particutar

O,

j

~

j

algorithm

presented and This

key

in

1,

+

found.

[Characters

B'S.

] AR

is

by

McCreight

more

and

method a

a

The

ADATA(P)j

efficient

Hayer

requires wage.

B'2. ~

search

in

terms

McCrelght

the

linear

terminate.

Reys

search

for

are of

length

of

Large

ordered the

for

search

Keys this

data

speed

bases.

in

pages

to

find

search

is

of a

63

2k ÷ 1. 2

the

They

for

page

search

suggested

targe

tength

keys

when

Cannot

of

the

sotve

the

binary

sequentiat

input

of

6,,

sequence

is

15.

from

The

using

consider

5.

there

used.

a

a~ocatton

is

binary

A binary

so~ved

5.11

12.

a

Remember,

probtem

track

o~

keys.

search

figure

{i0,, The

sets

use

Log22k,

the

In

the

te~t

in

search

is

~s

a

price

Bayer

track

2,,

13}.

to

right.

track

1

track

2

track

3

B"

size The

of fi~e

faster o£

and

atgorithm

method. 9.

search

ordering

McCreight

three used

to is

® 5ollo

Sequentiat

Binary

tree

Allocation,

a the

method

economic~tty.

=

Figure

with

ittustrate

64

In transitions

this in

a

Muntz number a

of

direct

that

the

search

and

access

path

number

retrieval

first

any

search

tree.

store

of

keys

in

the

tree

is

search

to

number

of

track

tree

be

node

direct

N.

average

sequentially

involved

that

ks

A

the

buckets

The

numbe~

storage

device ks

Of

with of

in

approximation

new

t~acks

d

on

assumption

interrogated

approximation two

first

in

stored

access

This

stored

tree

tree

reference,

the

approximate

an

average

each

the

about

the

This

presented.

assumptions

a

binary

track

new

is

Consider

presented

tracks

references

average

[50]

device.

a

the

15/8.

a

two

operation

without

number

for

requires Of

is

stora~e

the

method

Uz~a[is

references

after

search

a~locatlon

during

a

binary

b.

buckets

to

developed

the

size

a

Let

the

needed

to

•

.hooe

ks

The

function

tree

f(x)

those

nodes

Assume

the

and

is

keys

of

the

generate that

equ&[Ly

dynamically tree

as is

not

exoeedod

sequentiat[y

to

buckets

are

oteoer

stored

f-l(x)

within

constructed structure

=a.est

to

keys

determined

the

addresses

reference,

[ikeiy the

in

b

are by

k

to

nodes

buckets

other

in

arrive.

The

the

order

buckets

other

for

is

Therefore, in

the

buckets,

tree

received.

using

which

the

the

Meys

the

average

arrive, The path

lenMth

with

N

to

internal

average an

internat

Internai

nodes,

or

there

or

external

external are

N!

path

node,

sequences

length

is

binary

in

a

in

the

tree,

search

tree

HibhaPd

65

derived The

formulas

internal

[29]

for

path

the

average

Length

for

a

internal

and

binary

search

in

tree

external tree

path

Lengths.

defined

by

Hibbard

is

L(N)

where

N is

average So,

=

the

number

internal

[og21

is

records

k

assigned the

path

Load

k

nodes

the

be

bucket

factor.

coot

has

into

accessed. m

and

= ab#

number

of

by

b

buckets

the equal

to

one.

1.4Log2(1.64).

buckets.

average

where

is

Length

one

k

The

~(N)

path

approximately

divided

is

The

the

The

value

are

must

each

,

Length.

N records

buckets to

of

assigned

The

is

lo4-[og2(N)

To

access

number

of

is

the

bucket

is

represented

the

N

records

size

and

cz

as

= ~.N. m

Therefore storage

device

the

durin@

CR(~.b)

=

a

mean

numbeP

of

retrieval

1.4[oga(~N

accesses

to

the

direct

access

is

+

.64)

.

ra 5. 2 . 3 .

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

ALgorithm

B'"

(Insertion on

Assume

pointed from

the

pointer in used

a

to

by

Link

direct

that

AVAIL.

avaiLabLe and

to

a

storage

transform

catted the

a

hash

access

BUCKET

Define

underfto~

vector

in

is

conditions.

keys

storage

a

Large

R~AVAIL pool

PTo

~'ooted

and

to the The

symbol

tree

device.

)

storage

be

the

bucket

disk

of

management of

A key-to-address into

of

removal

final roots

pool

stored

addresses.

the

transformation The

a node of

trees

tracks

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

main the

from

nodes

variables. the

subtree,

of

~EAD(P)

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.

PT

is

the

pointer

to

the

CT

is

the

number

~OV

is

the

upper

a

list

is

the

of

is

length

on

to

by

inserted of 0

a

filial

tree

node,

limit

pointed

indicator C

character.

in the

FT

the

particular

list

number

the

list°

before

ANEXT

is

a

nodes

the

is

a

in

a contKnu~%ion. disk

address

track.

track.

to

continuation

= ANEXT

letter.

pointed

of a

another ATAG

a

before

in

fist

for

set.

pointer

within

in

by

PT.

a

and

containing

buffer.

direct

a

A O

root.

f maps

storage

memory

on

link

function

access

on

the

the

The

addresses.

operate

tree

alon@

P.

direct

by

the

move of

ETAG

to

a£ong

to

value

the

address

ATAG

pointed

used

from

writing

contain

to

memory

%rack

address mean

is

varlab[e

into

CODE,

structure

vaiue

of

INFO,

data

£ink

initial

addresses

to

the

variable

temporai'y its

ADATA,

67

ENEXT

is

another ETAG

[ Initialize.] (P

=

O)

address

GET THEN

C,

j

~

go

to

is

a

pointer

within

1,

i ~

h(Cl),

P ~

PT(i),

B'P9.

ENDIF. P

B''2.

~

READ(P),

[Comoare

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

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69

5.2.4.

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72

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73

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82

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K-[NFO[ i ] . [Advance

to

the IF

next

record.

(TAG(

i ) =

THEN

]

1 ) DO

I~LINK(1),

i~f( i ) ELSE ENDIF [Check

for

the

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o of

end

IF

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( i

the

=

0 )

tist.

]

THEN

STCP.

END I F . ENDDO.

that

Assume The

contribution

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to

the

totat

CR(~.b)

=

search

retrievat

is

time

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section

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1

*

tb(o()

*

t2b(¢)

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t3b(a{)

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--*

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(k tnb(~)

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a

retrieve

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record.

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in

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ptaced

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=

I

number

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of

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accesses

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-

separate

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83

The storage

average

number

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device

CR(0c,b)

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ALgorithm

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The

with

in

section

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4.2.3

structure

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the

for

the

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a

probe

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file

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the

access

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.

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of

)

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algorithm

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in

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remove

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containing

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K~INFO(

f ( ( READ( P ) ) )

IF

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K~ ) DO

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I.

as

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84

6, 1 . 4 ,

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key

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created is

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The device

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is

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device

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in

section

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in

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7

CHAP~E~

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[38]

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88

A useful p(j,0

distribution

)

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in

[.34]

Knuth

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where,

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rule.

distribution.

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For

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In

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30.

57,

data

as

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figure

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89

[!I~[!!!I!!!Ii!!I!!]ii!!Iiiiii

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Figure

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91

Define

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of file

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set

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92

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in

the

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bucket.

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the

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and

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figure

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2] Inverted

Fi~e.

to record

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a.

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93

el.

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I.j,k_

C4.

~

r~O,

O,

(D

file

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]

processed?] g o to C 1 0 E N D D O . Is

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(k

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)

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on

direct

access

ENDI F.

CIO,

go to C6, [Write a[[ updated storage device. ] IF

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THEN

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ell.

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been written?] go to C 1 2 .

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go to C 1 . IF ( r = 0 ) THEN

STOP.

ENDIF. END[F.

C13.

[Atlocate R ~- A V A I L ,

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buffel"

for

thls

item.]

94

IF

(r

1)

=

TREN

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Ij-1

ENDDO. ENDIF.

qj

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IF

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i--O.

z,

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r--O.

O)

THEN

DO

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ENDDO.

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wj C14.

-

1,

go

[Process

to

position.] (P

IF

C5.

chain

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P-Ij,k.l,

=

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THEN

R ~ AVAIL,

DO

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WRITE q j

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6,

wj

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DO WRITE q j wj

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0

ENDIF.

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buffers

÷ I, to C5.

ENDIF.

(wj_ 1 = I)

IF

THEN

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I3-1"

ENDDO.

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qj-I

"

D,

READ D

Ij_l,

I F ( D = O) THEN DO r ~ l , ENDIF. j~j - 1. go to C5.

When of

time

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files

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Assume readiness

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file the

the

go

exists,

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load

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the time

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small

amount

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95

are

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Under

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Assume J

to

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8

CHAPTER

~MEA~!~N__QE_METHOD~

Consider records,

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chaining

flies wlth

are

the

direct

average

chaining

percent

assuming

List.

the

with

fuLL

Trio

aLL

number

Links.

TREE

access

separate

coalescing

reautrement probing,

the

number

insertion,

search

percent

fewer

both

are

than

deletion

with

and

1500.

than

to

retrievaL,

and

I00

with

than

two

a

average

~or

8,5

figure

probing.

Lists

chaining

a

greater

chaining

the

device

binary

requires

buckets

Linear

The probing

track

8.4,

figure

required

is

retrieva[

and

storage

record

TREE Tale

than

require

accesses

For

accesses

the

tvle

magnitude

sequential

between

storage

a

greater

When

a

separate

and

fewer

the

the

8.3,

figure

for

greater

Lists

requires

chaining

for

buckets

with

a~proximateLy

hold

of

Lists

chaining

separate

and

number

percent

approximately

tree.

access

accesses

When

The

using

relationship

direct

device

coalescing

than

the

ooeration. and

is

records

8.2,

figure

required

percent

with

the

average

accesses

deletion

8.I, indicate

to

T~IE.

of

delete

method. Figure

and

and

presented

Separate

Lists

as

a

hybrid

method.

of

the

ALgorlthms

Linear have

of to

127

been In

presented air

than

and

cases,

the

chaining

with

Linear

probing.

fewer

[inked

than

When

I00.

binary

tree

search

buckets

accesses

than

the

The with

separate

for

binary

tLnks

a

that

binary

than

the

search binary

ALgorithms flte.

Assume

average

number

gerater

than

using for

the

%he a

of four

with

probing

number

blnary

is

2,

than

the

the

accesses

search

tree the

inverted

chainLng

the

with

and

50 than

Lists)

is a

than

to

accesses

than

1500.

the

When

fewer

and

hold

files

than

a

Linear record

require

storage

an

probing.

or

the

100

average

method,

in

number

a

trie. inverted

bucket

number coatesclng

two

The

percent

with

the

the

for

with

and

more

than

analyzed

chaining

of

size

full, accesses lists,

retrievaL,

of

accesses

for

%tie, are

100

requires

separate

up

storage

to

percent the

require

files

require

record

file

less

sizes

Linear

chaining

[inked

always

buckets file

bess

hybrid

using a

flies

and

trie,

enough

and

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Linked

Lists

presented

accesses

trie.

the

more

bess

buckets is

the

[inked

retrieve

the

files

and

searched to

separate

of

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is

file,

and

tree

been

accesses and

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Linked

fewer

coalescing

Large

of

approximately

require

with

search

index

inverted

chalning

linear

the

and

deletion.

coalescing

bucket

to

and

number

fuLL

Linked

tree

is

and

require

the

tree.

have

for

up

flies

a word

tree

percent

sizes

search

chaining

the

trie

fuLL

Lists,

deletion

files

bucket

greater with

100

tlnked

percent

a

search

the

Linked

Assume

storage

than

insertion

chaining

and

are

hybrid

probing. for

buckets

50

are

Lists,

binary

The

retrlevat, require

retrleval

accesses

approxlmate[y

the

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

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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,

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A.M.

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C.

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(Jan.

3.

~o

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R°

J.R°

Bert,

Indexes",

~The

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Size

On " ,

164° Hash-Coded

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*tCrganization

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Binary ~

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Secondary

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~fi~L_A~,

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Search {Sew°

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1975 ) pp°

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BLoom, Data

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105-109o

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ACM,

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Retrieval

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9onfemenc~

Scattee

481-482o

Using

Variable

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Comm

With

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Addressing

WRandomized

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Organization

"Fut~

1973)

A C M Nat~o_nna~

Coding

1970)

1973) p p .

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Large

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Functions",

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Time

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Retrieval

Organization

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Techniques",

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Proceedings

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the

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Trade-offs

Trade-offs

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W.

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T i ~ e s n,

~Space/Time

R°P.

Jo~n~, 14.

Techniques

Retrlevat

ALLowabLe 12.

"Some

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"ELements

1,~ W.

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Management

volume

Finket,

and

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John

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A~_~s!r_~o~__qc~ion_~£_~o~i!i~

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Inc,

( 1950).

a Data

Str~cture

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C.C.

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C_~mm ACM.

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PP.

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Hsiao.

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Sorting

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~o~m_~,

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IBM c o r p . .

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for 1970)

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~

pp. 29.

GeneraLization

and

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,

94pp.

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,

and

15,4

Formatted

(Jan°

Ig6S)

Lewis,

E.

M.

"Analysis

Modeting",

Study

on

~esults

Fundamental ~ _ ~ M ~

~ash op.

with

T~ansfo~m

Large

"Addltionat

PP.

a Complex

"Key-to-Address

Ret~ieva[

ToG.

of

1971 ) pp.

A

Scatter

10~5--|047.

Simulation

Files",

1970)

Improved

pp.

for

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

Organization",

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

retriever",

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

(March

and

File

Trees

of

1973)

33-43,

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Trees 1974)

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