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<chapter id="indices">
 <title id="indices-title">Indices</title>

 <para>
  Indices are a common way to enhance database performance.  An index
  allows the database server to find and retrieve specific rows much
  faster than it could do without an index.  But indices also add
  overhead to the database system as a whole, so they should be used
  sensibly.
 </para>


 <sect1 id="indices-intro">
  <title>Introduction</title>

  <para>
   The classical example for the need of an index is if there is a
   table similar to this:
<programlisting>
CREATE TABLE test1 (
    id integer,
    content varchar
);
</programlisting>
   and the application requires a lot of queries of the form
<programlisting>
SELECT content FROM test1 WHERE id = <replaceable>constant</replaceable>;
</programlisting>
   Ordinarily, the system would have to scan the entire
   <structname>test1</structname> table row by row to find all
   matching entries.  If there are a lot of rows in
   <structname>test1</structname> and only a few rows (possibly zero
   or one) returned by the query, then this is clearly an inefficient
   method.  If the system were instructed to maintain an index on the
   <structfield>id</structfield> column, then it could use a more
   efficient method for locating matching rows.  For instance, it
   might only have to walk a few levels deep into a search tree.
  </para>

  <para>
   A similar approach is used in most books of non-fiction:  Terms and
   concepts that are frequently looked up by readers are collected in
   an alphabetic index at the end of the book.  The interested reader
   can scan the index relatively quickly and flip to the appropriate
   page, and would not have to read the entire book to find the
   interesting location.  As it is the task of the author to
   anticipate the items that the readers are most likely to look up,
   it is the task of the database programmer to foresee which indexes
   would be of advantage.
  </para>

  <para>
   The following command would be used to create the index on the
   <structfield>id</structfield> column, as discussed:
<programlisting>
CREATE INDEX test1_id_index ON test1 (id);
</programlisting>
   The name <structname>test1_id_index</structname> can be chosen
   freely, but you should pick something that enables you to remember
   later what the index was for.
  </para>

  <para>
   To remove an index, use the <command>DROP INDEX</command> command.
   Indices can be added and removed from tables at any time.
  </para>

  <para>
   Once the index is created, no further intervention is required: the
   system will use the index when it thinks it would be more efficient
   than a sequential table scan.  But you may have to run the
   <command>VACUUM ANALYZE</command> command regularly to update
   statistics to allow the query planner to make educated decisions.
   Also read <xref linkend="performance-tips"> for information about
   how to find out whether an index is used and when and why the
   planner may choose to <emphasis>not</emphasis> use an index.
  </para>

  <para>
   Indices can also benefit <command>UPDATE</command>s and
   <command>DELETE</command>s with search conditions.  Note that a
   query or data manipulation commands can only use at most one index
   per table.  Indices can also be used in table join methods.  Thus,
   an index defined on a column that is part of a join condition can
   significantly speed up queries with joins.
  </para>

  <para>
   When an index is created, it has to be kept synchronized with the
   table.  This adds overhead to data manipulation operations.
   Therefore indices that are non-essential or do not get used at all
   should be removed.
  </para>
 </sect1>


 <sect1 id="indices-types">
  <title>Index Types</title>

  <para>
   <productname>Postgres</productname> provides several index types:
   B-tree, R-tree, and Hash.  Each index type is more appropriate for
   a particular query type because of the algorithm it uses.  By
   default, the <command>CREATE INDEX</command> command will create a
   B-tree index, which fits the most common situations.  In
   particular, the <productname>Postgres</productname> query optimizer
   will consider using a B-tree index whenever an indexed column is
   involved in a comparison using one of these operators:

   <simplelist type="inline">
    <member><literal>&lt;</literal></member>
    <member><literal>&lt;=</literal></member>
    <member><literal>=</literal></member>
    <member><literal>&gt;=</literal></member>
    <member><literal>&gt;</literal></member>
   </simplelist>
  </para>

  <para>
   R-tree indices are especially suited for spacial data.  To create
   an R-tree index, use a command of the form
<synopsis>
CREATE INDEX <replaceable>name</replaceable> ON <replaceable>table</replaceable> USING RTREE (<replaceable>column</replaceable>);
</synopsis>
   The <productname>Postgres</productname> query optimizer will
   consider using an R-tree index whenever an indexed column is
   involved in a comparison using one of these operators:

   <simplelist type="inline">
    <member><literal>&lt;&lt;</literal></member>
    <member><literal>&amp;&lt;</literal></member>
    <member><literal>&amp;&gt;</literal></member>
    <member><literal>&gt;&gt;</literal></member>
    <member><literal>@</literal></member>
    <member><literal>~=</literal></member>
    <member><literal>&amp;&amp;</literal></member>
   </simplelist>
   (Refer to <xref linkend="functions-geometry"> about the meaning of
   these operators.)
  </para>

  <para>
   The query optimizer will consider using a hash index whenever an
   indexed column is involved in a comparison using the
   <literal>=</literal> operator.  The following command is used to
   create a hash index:
<synopsis>
CREATE INDEX <replaceable>name</replaceable> ON <replaceable>table</replaceable> USING HASH (<replaceable>column</replaceable>);
</synopsis>
   <note>
    <para>
     Because of the limited utility of hash indices, a B-tree index
     should generally be preferred over a hash index.  We do not have
     sufficient evidence that hash indices are actually faster than
     B-trees even for <literal>=</literal> comparisons.  Moreover,
     hash indices require coarser locks; see <xref
     linkend="locking-indices">.
    </para>
   </note>  
  </para>

  <para>
   The B-tree index is an implementation of Lehman-Yao
   high-concurrency B-trees.  The R-tree index method implements
   standard R-trees using Guttman's quadratic split algorithm.  The
   hash index is an implementation of Litwin's linear hashing.  We
   mention the algorithms used solely to indicate that all of these
   access methods are fully dynamic and do not have to be optimized
   periodically (as is the case with, for example, static hash access
   methods).
  </para>
 </sect1>


 <sect1 id="indices-multicolumn">
  <title>Multi-Column Indices</title>

  <para>
   An index can be defined on more than one column.  For example, if
   you have a table of this form:
<programlisting>
CREATE TABLE test2 (
  major int,
  minor int,
  name varchar
);
</programlisting>
   (Say, you keep you your <filename class="directory">/dev</filename>
   directory in a database...) and you frequently make queries like
<programlisting>
SELECT name FROM test2 WHERE major = <replaceable>constant</replaceable> AND minor = <replaceable>constant</replaceable>;
</programlisting>
   then it may be appropriate to define an index on the columns
   <structfield>major</structfield> and
   <structfield>minor</structfield> together, e.g.,
<programlisting>
CREATE INDEX test2_mm_idx ON test2 (major, minor);
</programlisting>
  </para>

  <para>
   Currently, only the B-tree implementation supports multi-column
   indices.  Up to 16 columns may be specified.  (This limit can be
   altered when building <productname>Postgres</productname>; see the
   file <filename>config.h</filename>.)
  </para>

  <para>
   The query optimizer can use a multi-column index for queries that
   involve the first <parameter>n</parameter> consecutive columns in
   the index (when used with appropriate operators), up to the total
   number of columns specified in the index definition.  For example,
   an index on <literal>(a, b, c)</literal> can be used in queries
   involving all of <literal>a</literal>, <literal>b</literal>, and
   <literal>c</literal>, or in queries involving both
   <literal>a</literal> and <literal>b</literal>, or in queries
   involving only <literal>a</literal>, but not in other combinations.
   (In a query involving <literal>a</literal> and <literal>c</literal>
   the optimizer might choose to use the index for
   <literal>a</literal> only and treat <literal>c</literal> like an
   ordinary unindexed column.)
  </para>

  <para>
   Multi-column indexes can only be used if the clauses involving the
   indexed columns are joined with <literal>AND</literal>.  For instance,
<programlisting>
SELECT name FROM test2 WHERE major = <replaceable>constant</replaceable> OR minor = <replaceable>constant</replaceable>;
</programlisting>
   cannot make use of the index <structname>test2_mm_idx</structname>
   defined above to look up both columns.  (It can be used to look up
   only the <structfield>major</structfield> column, however.)
  </para>

  <para>
   Multi-column indices should be used sparingly.  Most of the time,
   an index on a single column is sufficient and saves space and time.
   Indexes with more than three columns are almost certainly
   inappropriate.
  </para>
 </sect1>


 <sect1 id="indices-unique">
  <title>Unique Indices</title>

  <para>
   Indexes may also be used to enforce uniqueness of a column's value,
   or the uniqueness of the combined values of more than one column.
<synopsis>
CREATE UNIQUE INDEX <replaceable>name</replaceable> ON <replaceable>table</replaceable> (<replaceable>column</replaceable> <optional>, ...</optional>);
</synopsis>
   Only B-tree indices can be declared unique.
  </para>

  <para>
   When an index is declared unique, multiple table rows with equal
   indexed values will not be allowed.  NULL values are not considered
   equal.
  </para>

  <para>
   <productname>PostgreSQL</productname> automatically creates unique
   indices when a table is declared with a unique constraint or a
   primary key, on the columns that make up the primary key or unique
   columns (a multi-column index, if appropriate), to enforce that
   constraint.  A unique index can be added to a table at any later
   time, to add a unique constraint.  (But a primary key cannot be
   added after table creation.)
  </para>
 </sect1>


 <sect1 id="indices-functional">
  <title>Functional Indices</title>

  <para>
   For a <firstterm>functional index</firstterm>, an index is defined
   on the result of a function applied to one or more columns of a
   single table.  Functional indices can be used to obtain fast access
   to data based on the result of function calls.
  </para>

  <para>
   For example, a common way to do case-insensitive comparisons is to
   use the <function>lower</function>:
<programlisting>
SELECT * FROM test1 WHERE lower(col1) = 'value';
</programlisting>
   In order for that query to be able to use an index, it has to be
   defined on the result of the <literal>lower(column)</literal>
   operation:
<programlisting>
CREATE INDEX test1_lower_col1_idx ON test1 (lower(col1));
</programlisting>
  </para>

  <para>
   The function in the index definition can take more than one
   argument, but they must be table columns, not constants.
   Functional indices are always single-column (namely, the function
   result) even if the function uses more than one input field; there
   cannot be multi-column indices that contain function calls.
  </para>

  <tip>
   <para>
    The restrictions mentioned in the previous paragraph can easily be
    worked around by defining custom functions to use in the index
    definition that call the desired function(s) internally.
   </para>
  </tip>
 </sect1>


 <sect1 id="indices-opclass">
  <title>Operator Classes</title>

  <para>
   An index definition may specify an <firstterm>operator
   class</firstterm> for each column of an index.
<synopsis>
CREATE INDEX <replaceable>name</replaceable> ON <replaceable>table</replaceable> (<replaceable>column</replaceable> <replaceable>opclass</replaceable> <optional>, ...</optional>);
</synopsis>
   The operator class identifies the operators to be used by the index
   for that column.  For example, a B-tree index on four-byte integers
   would use the <literal>int4_ops</literal> class; this operator
   class includes comparison functions for four-byte integers.  In
   practice the default operator class for the column's data type is
   usually sufficient.  The main point of having operator classes is
   that for some data types, there could be more than one meaningful
   ordering.  For example, we might want to sort a complex-number data
   type either by absolute value or by real part.  We could do this by
   defining two operator classes for the data type and then selecting
   the proper class when making an index.  There are also some
   operator classes with special purposes:

   <itemizedlist>
    <listitem>
     <para>
      The operator classes <literal>box_ops</literal> and
      <literal>bigbox_ops</literal> both support R-tree indices on the
      <literal>box</literal> data type.  The difference between them is
      that <literal>bigbox_ops</literal> scales box coordinates down,
      to avoid floating point exceptions from doing multiplication,
      addition, and subtraction on very large floating point
      coordinates.  If the field on which your rectangles lie is about
      20 000 units square or larger, you should use
      <literal>bigbox_ops</literal>.
     </para>
    </listitem>
   </itemizedlist>
  </para>

  <para>
   The following query shows all defined operator classes:
<programlisting>
SELECT am.amname AS acc_name,
       opc.opcname AS ops_name,
       opr.oprname AS ops_comp
    FROM pg_am am, pg_amop amop,
         pg_opclass opc, pg_operator opr
    WHERE amop.amopid = am.oid AND
          amop.amopclaid = opc.oid AND
          amop.amopopr = opr.oid
    ORDER BY acc_name, ops_name, ops_comp;
</programlisting>
  </para>
 </sect1>


  <sect1 id="keys">
   <title id="keys-title">Keys</title>

   <para>
    <note>
     <title>Author</title>
     <para>
      Written by Herouth Maoz (<email>herouth@oumail.openu.ac.il</email>).
      This originally appeared on the User's Mailing List on 1998-03-02
      in response to the question:
      "What is the difference between PRIMARY KEY and UNIQUE constraints?".
     </para>
    </note>
   </para>

   <para>
<literallayout>
Subject: Re: [QUESTIONS] PRIMARY KEY | UNIQUE

        What's the difference between:

              PRIMARY KEY(fields,...) and
              UNIQUE (fields,...)

       - Is this an alias?
       - If PRIMARY KEY is already unique, then why
         is there another kind of key named UNIQUE?
</literallayout>
   </para>

   <para>
    A primary key is the field(s) used to identify a specific row. For example,
    Social Security numbers identifying a person.
   </para>

   <para>
    A simply UNIQUE combination of fields has nothing to do with identifying
    the row. It's simply an integrity constraint. For example, I have
    collections of links. Each collection is identified by a unique number,
    which is the primary key. This key is used in relations.
   </para>

   <para>
    However, my application requires that each collection will also have a
    unique name. Why? So that a human being who wants to modify a collection
    will be able to identify it. It's much harder to know, if you have two
    collections named <quote>Life Science</quote>, the the one tagged 24433 is the one you
    need, and the one tagged 29882 is not.
   </para>

   <para>
    So, the user selects the collection by its name. We therefore make sure,
    within the database, that names are unique. However, no other table in the
    database relates to the collections table by the collection Name. That
    would be very inefficient.
   </para>

   <para>
    Moreover, despite being unique, the collection name does not actually
    define the collection! For example, if somebody decided to change the name
    of the collection from <quote>Life Science</quote> to <quote>Biology</quote>, it will still be the
    same collection, only with a different name. As long as the name is unique,
    that's OK.
   </para>

   <para>
    So:

    <itemizedlist>
     <listitem>
      <para>
       Primary key:
       <itemizedlist spacing="compact" mark="bullet">
	<listitem>
	 <para>
	  Is used for identifying the row and relating to it.
	 </para>
	</listitem>
	<listitem>
	 <para>
	  Is impossible (or hard) to update.
	 </para>
	</listitem>
	<listitem>
	 <para>
	  Should not allow NULLs.
	 </para>
	</listitem>
       </itemizedlist>
      </para>
     </listitem>

     <listitem>
      <para>
       Unique field(s):
       <itemizedlist spacing="compact" mark="bullet">
	<listitem>
	 <para>
	  Are used as an alternative access to the row.
	 </para>
	</listitem>
	<listitem>
	 <para>
	  Are updatable, so long as they are kept unique.
	 </para>
	</listitem>
	<listitem>
	 <para>
	  NULLs are acceptable.
	 </para>
	</listitem>
       </itemizedlist>
      </para>
     </listitem>
    </itemizedlist>
   </para>

   <para>
    As for why no non-unique keys are defined explicitly in standard
    <acronym>SQL</acronym> syntax? Well, you
    must understand that indices are implementation-dependent.
    <acronym>SQL</acronym> does not
    define the implementation, merely the relations between data in the
    database. <productname>Postgres</productname> does allow
    non-unique indices, but indices
    used to enforce <acronym>SQL</acronym> keys are always unique.
   </para>

   <para>
    Thus, you may query a table by any combination of its columns, despite the
    fact that you don't have an index on these columns. The indexes are merely
    an implementation aid that each <acronym>RDBMS</acronym> offers
    you, in order to cause
    commonly used queries to be done more efficiently.
    Some <acronym>RDBMS</acronym> may give you
    additional measures, such as keeping a key stored in main memory. They will
    have a special command, for example
<synopsis>
CREATE MEMSTORE ON <replaceable>table</replaceable> COLUMNS <replaceable>cols</replaceable>
</synopsis>
    (This is not an existing command, just an example.)
   </para>

   <para>
    In fact, when you create a primary key or a unique combination of fields,
    nowhere in the <acronym>SQL</acronym> specification does it say
    that an index is created, nor that
    the retrieval of data by the key is going to be more efficient than a
    sequential scan!
   </para>

   <para>
    So, if you want to use a combination of fields that is not unique as a
    secondary key, you really don't have to specify anything - just start
    retrieving by that combination! However, if you want to make the retrieval
    efficient, you'll have to resort to the means your
    <acronym>RDBMS</acronym> provider gives you
    - be it an index, my imaginary MEMSTORE command, or an intelligent
    <acronym>RDBMS</acronym>
    that creates indices without your knowledge based on the fact that you have
    sent it many queries based on a specific combination of keys... (It learns
    from experience).
   </para>
  </sect1>


  <sect1 id="partial-index">
   <title id="partial-index-title">Partial Indices</title>

   <note>
    <title>Author</title>
    <para>
     This is from a reply to a question on the email list
     by Paul M. Aoki (<email>aoki@CS.Berkeley.EDU</email>)
     on 1998-08-11.
<!--
  Paul M. Aoki         | University of California at Berkeley
  aoki@CS.Berkeley.EDU | Dept. of EECS, Computer Science Division #1776
                       | Berkeley, CA 94720-1776
-->
    </para>
   </note>

   <note>
    <title>Note</title>
    <para>
     Partial indices are not currently supported by
     <productname>PostgreSQL</productname>, but they were once supported
     by its predecessor <productname>Postgres</productname>, and much
     of the code is still there.  We hope to revive support for this
     feature someday.
    </para>
   </note>

   <para>
    A <firstterm>partial index</firstterm>
    is an index built over a subset of a table; the subset is defined by
    a predicate.  <productname>Postgres</productname>
    supported partial indices with arbitrary
    predicates.  I believe IBM's <productname>DB2</productname>
    for AS/400 supports partial indices
    using single-clause predicates.
   </para>

   <para>
    The main motivation for partial indices is this:
    if all of the queries you ask that can
    profitably use an index fall into a certain range, why build an index
    over the whole table and suffer the associated space/time costs?

    (There are other reasons too; see 
    <xref endterm="STON89b" linkend="STON89b-full"> for details.)
   </para>

   <para>
    The machinery to build, update and query partial indices isn't too
    bad.  The hairy parts are index selection (which indices do I build?)
    and query optimization (which indices do I use?); i.e., the parts
    that involve deciding what predicate(s) match the workload/query in
    some useful way.  For those who are into database theory, the problems
    are basically analogous to the corresponding materialized view
    problems, albeit with different cost parameters and formulae.  These
    are, in the general case, hard problems for the standard ordinal 
    <acronym>SQL</acronym>
    types; they're super-hard problems with black-box extension types,
    because the selectivity estimation technology is so crude.
   </para>

   <para>
    Check <xref endterm="STON89b" linkend="STON89b-full">,
    <xref endterm="OLSON93" linkend="OLSON93-full">,
    and
    <xref endterm="SESHADRI95" linkend="SESHADRI95-full">
    for more information.
   </para>
  </sect1>
 </chapter>

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