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Access Path Selection

in a Relational Database Management System

P. Griffiths Selinger

M. M. Astrahan

D. D. Chamberlin

R. A. Lorie

T. G. Price

IBM Research Division, San Jose, California 95193

ABSTRACT: In a high level query and data

manipulation language such as SQL, requests

are stated non-procedurally, without refer-

ence to access paths. This paper describes

how System R chooses access paths for both

simple (single relation) and complex que-

ries (such as joins), given a user specifi-

cation of desired data as a boolean

expression of predicates. System R is an

experimental database management system

developed to carry out research on the rela-

tional model of data. System R was designed

and built by members of the IBM San Jose

Research Laboratory.

1. Introduction

System R is an experimental database man-

agement system based on the relational

model of data which has been under develop-

ment at the IBM San Jose Research Laboratory

since 1975 <1>. The software was developed

as a research vehicle in relational data-

base, and is not generally available out-

side the IBM Research Division.

This paper assumes familiarity with rela-

tional data model terminology as described

in Codd <7> and Date <8>. The user interface

in System R is the unified query, data def-

inition, and manipulation language SQL <5>.

Statements in SQL can be issued both from an

on-line casual-user-oriented terminal

interface and from programming languages

such as PL/I and COBOL.

In System R a user need not know how the

tuples are physically stored and what

access paths are available (e.g. which col-

umns have indexes). SQL statements do not

require the user to specify anything about

the access path to be used for tuple

retrieval. Nor does a user specify in what

order joins are to be performed. The System

R optimizer chooses both join order and an

access path for each table in the SQL state-

ment. Of the many possible choices, the

optimizer chooses the one which minimizes

“total access cost” for performing the

entire statement.

This paper will address the issues of

access path selection for queries.

Retrieval for data manipulation (UPDATE,

DELETE) is treated similarly. Section 2

will describe the place of the optimizer in

the processing of a SQL statement, and sec-

tion 3 will describe the storage component

access paths that are available on a single

physically stored table. In section 4 the

optimizer cost formulas are introduced for

single table queries, and section 5 dis-

cusses the joining of two or more tables,

and their corresponding costs. Nested que-

ries (queries in predicates) are covered in

section 6.

2. Processing of an SQL statement

A SQL statement is subjected to four

phases of processing. Depending on the ori-

gin and contents of the statement, these

phases may be separated by arbitrary inter-

vals of time. In System R these arbitrary

time intervals are transparent to the sys-

tem components which process a SQL state-

ment. These mechanisms and a description of

the processing of SQL statements from both

programs and terminals are further dis-

cussed in <2>. Only an overview of those

processing steps that are relevant to

access path selection will be discussed

here.

The four phases of statement processing

are parsing, optimization, code generation,

and execution. Each SQL statement is sent to

the parser, where it is checked for correct

syntax. A query block

is represented by a

SELECT list, a FROM list, and a WHERE tree,

containing, respectively the list of items

to be retrieved, the table(s) referenced,

and the boolean combination of simple pred-

icates specified by the user. A single SQL

statement may have many query blocks

because a predicate may have one operand

which is itself a query.

If the parser returns without any errors

detected, the OPTIMIZER component is

called. The OPTIMIZER accumulates the names

sion to make digital or hard copies is granted provided that copies

are not made or distributed for profit or direct commercial advan-

tage, and that copies show this notice on the first page or initial

screen of a display along with the full citation.

Originally published in the Proceedings of the 1979 ACM SIGMOD

International Conference on the Management of Data.

Digital recreation by Eric A. Brewer, brewer@cs.berke-

ley.edu, October 2002.

of tables and columns referenced in the

query and looks them up in the System R cat-

alogs to verify their existence and to

retrieve information about them.

The catalog lookup portion of the OPTI-

MIZER also obtains statistics about the

referenced relations, and the access paths

available on each of them. These will be

used later in access path selection. After

catalog lookup has obtained the datatype

and length of each column, the OPTIMIZER

rescans the SELECT-list and WHERE-tree to

check for semantic errors and type compati-

bility in both expressions and predicate

comparisons.

Finally the OPTIMIZER performs access

path selection. It first determines the

evaluation order among the query blocks in

the statement. Then for each query block,

the relations in the FROM list are pro-

cessed. If there is more than one relation

in a block, permutations of the join order

and of the method of joining are evaluated.

The access paths that minimize total cost

for the block are chosen from a tree of

alternate path choices. This minimum cost

solution is represented by a structural

modification of the parse tree. The result

is an execution plan in the Access Specifi-

cation Language (ASL) <10>.

After a plan is chosen for each query

block and represented in the parse tree, the

CODE GENERATOR is called. The CODE GENERA-

TOR is a table-driven program which trans-

lates ASL trees into machine language code

to execute the plan chosen by the OPTIMIZER.

In doing this it uses a relatively small

number of code templates, one for each type

of join method (including no join). Query

blocks for nested queries are treated as

“subroutines” which return values to the

predicates in which they occur. The CODE

GENERATOR is further described in <9>.

During code generation, the parse tree is

replaced by executable machine code and its

associated data structures. Either control

is immediately transferred to this code or

the code is stored away in the database for

later execution, depending on the origin of

the statement (program or terminal). In

either case, when the code is ultimately

executed, it calls upon the System R inter-

nal storage system (RSS) via the storage

system interface (RSI) to scan each of the

physically stored relations in the query.

These scans are along the access paths cho-

sen by the OPTIMIZER. The RSI commands that

may be used by generated code are described

in the next section.

3. The Research Storage System

The Research Storage System (RSS) is the

storage subsystem of System R. It is respon-

sible for maintaining physical storage of

relations, access paths on these relations,

locking (in a multi-user environment), and

logging and recovery facilities. The RSS

presents a tuple-oriented interface (RSI)

to its users. Although the RSS may be used

independently of System R, we are concerned

here with its use for executing the code

generated by the processing of SQL state-

ments in System R, as described in the pre-

vious section. For a complete description

of the RSS, see <1>.

Relations are stored in the RSS as a col-

lection of tuples whose columns are physi-

cally contiguous. These tuples are stored

on 4K byte pages; no tuple spans a page.

Pages are organized into logical units

called segments. Segments may contain one

or more relations, but no relation may span

a segment. Tuples from two or more relations

may occur on the same page. Each tuple is

tagged with the identification of the rela-

tion to which it belongs.

The primary way of accessing tuples in a

relation is via an RSS scan. A scan returns

a tuple at a time along a given access path.

OPEN, NEXT, and CLOSE are the principal com-

mands on a scan.

Two types of scans are currently avail-

able for SQL statements. The first type is a

segment scan to find all the tuples of a

given relation. A series of NEXTs on a seg-

ment scan simply examines all pages of the

segment which contain tuples, from any

relation, and returns those tuples belong-

ing to the given relation.

The second type of scan is an index scan.

An index may be created by a System R user

on one or more columns of a relation, and a

relation may have any number (including

zero) of indexes on it. These indexes are

stored on separate pages from those con-

taining the relation tuples. Indexes are

implemented as B-trees <3>, whose leaves

are pages containing sets of (key, identi-

fiers of tuples which contain that key).

Therefore a series of NEXTs on an index scan

does a sequential read along the leaf pages

of the index, obtaining the tuple identifi-

ers matching a key, and using them to find

and return the data tuples to the user in

key value order. Index leaf pages are

chained together so that NEXTs need not ref-

erence any upper level pages of the index.

In a segment scan, all the non-empty

pages of a segment will be touched, regard-

less of whether there are any tuples from

the desired relation on them. However, each

page is touched only once. When an entire

relation is examined via an index scan, each

page of the index is touched only once, but

a data page may be examined more than once

if it has two tuples on it which are not

“close” in the index ordering. If the tuples

are inserted into segment pages in the index

ordering, and if this physical proximity

corresponding to index key value is main-

tained, we say that the index is clustered

A clustered index has the property that not

only each index page, but also each data

page containing a tuple from that relation

will be touched only once in a scan on that

index.

An index scan need not scan the entire

relation. Starting and stopping key values

may be specified in order to scan only those

tuples which have a key in a range of index

values. Both index and segment scans may

optionally take a set of predicates, called

search arguments (or SARGS), which are

applied to a tuple before it is returned to

the RSI caller. If the tuple satisfies the

predicates, it is returned; otherwise the

scan continues until it either finds a tuple

which satisfies the SARGS or exhausts the

segment or the specified index value range.

This reduces cost by eliminating the over-

head of making RSI calls for tuples which

can be efficiently rejected within the RSS.

Not all predicates are of the form that can

become SARGS. A sargable predicate

is one of

the form (or which can be put into the form)

“column comparison-operator value”. SARGS

are expressed as a boolean expression of

such predicates in disjunctive normal form.

4. Costs for single relation access paths

In the next several sections we will

describe the process of choosing a plan for

evaluating a query. We will first describe

the simplest case, accessing a single rela-

tion, and show how it extends and general-

izes to 2-way joins of relations, n-way

joins, and finally multiple query blocks

(nested queries).

The OPTIMIZER examines both the predi-

cates in the query and the access paths

available on the relations referenced by

the query, and formu1ates a cost prediction

for each access plan, using the following

cost formula:

COST = PAGE FETCHES + W * (RSI CALLS).

This cost is a weighted measure of I/O

(pages fetched) and CPU utilization

(instructions executed). W is an adjustable

weighting factor between I/O and CPU. RSI

CALLS is the predicted number of tuples

returned from the RSS. Since most of System

R’s CPU time is spent in the RSS, the number

of RSI calls is a good approximation for CPU

utilization. Thus the choice of a minimum

cost path to process a query attempts to

minimize total resources required.

During execution of the type-compatibil-

ity and semantic checking portion of the

OPTIMIZER, each query block’s WHERE tree of

predicates is examined. The WHERE tree is

considered to be in conjunctive normal

form, and every conjunct is called a boolean

factor. Boolean factors are notable because

every tuple returned to the user must sat-

isfy every boolean factor. An index is said

to match a boolean factor if the boolean

factor is a sargable predicate whose refer-

enced column is the index key; e.g., an

index on SALARY matches the predicate ‘SAL-

ARY = 20000’. More precisely, we say that a

predicate or set of predicates matches

index access path when the predicates are

sargable and the columns mentioned in the

predicate(s) are an initial substring of

the set of columns of the index key. For

example, a NAME, LOCATION index matches

NAME = 'SMITH' AND LOCATION = 'SAN JOSE'. If

an index matches a boolean factor, an access

using that index is an efficient way to sat-

isfy the boolean factor. Sargable boolean

factors can also be efficiently satisfied

if they are expressed as search arguments.

Note that a boolean factor may be an entire

tree of predicates headed by an OR.

During catalog lookup, the OPTIMIZER

retrieves statistics on the relations in

the query and on the access paths available

on each relation. The statistics kept are

the following:

For each relation T,

- NCARD(T), the cardinality of relation T.

- TCARD(T), the number of pages in the seg-

ment that hold tuples of relation T.

- P(T), the fraction of data pages in the

segment that hold tuples of relation T.

P(T) = TCARD(T) / (no. of non-empty

pages in the segment).

For each index I on relation T,

- ICARD(I),

number of distinct keys in index

- NINDX(I), the number of pages in index I.

These statistics are maintained in the

System R catalogs, and come from several

sources. Initial relation loading and index

creation initialize these statistics. They

are then updated periodically by an UPDATE

STATISTICS command, which can be run by any

user. System R does not update these statis-

tics at every INSERT, DELETE, or UPDATE

because of the extra database operations

and the locking bottleneck this would cre-

ate at the system catalogs. Dynamic updat-

ing of statistics would tend to serialize

accesses that modify the relation contents.

Using these statistics, the OPTIMIZER

assigns a selectivity factor

'F' for each

boolean factor in the predicate list. This

selectivity factor very roughly corresponds

to the expected fraction of tuples which

will satisfy the predicate. TABLE 1 gives

the selectivity factors for different kinds

of predicates. We assume that a lack of sta-

tistics implies that the relation is small,

so an arbitrary factor is chosen.

Query cardinality (QCARD) is the product

of the cardinalities of every relation in

the query block’s FROM list times the prod-

uct of all the selectivity factors of that

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