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<chapter id="indexes">
 <title id="indexes-title">Indexes</title>

 <indexterm zone="indexes">
  <primary>indexes</primary>
 </indexterm>

 <para>
  Indexes 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 indexes also add
  overhead to the database system as a whole, so they should be used
  sensibly.
 </para>


 <sect1 id="indexes-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.
   Indexes can be added to 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>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>
   Indexes can benefit <command>UPDATE</command>s and
   <command>DELETE</command>s with search conditions.  Indexes can also be
   used in join queries.  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, the system has to keep it synchronized with the
   table.  This adds overhead to data manipulation operations.
   Therefore indexes that are non-essential or do not get used at all
   should be removed.  Note that a
   query or data manipulation command can use at most one index
   per table.
  </para>
 </sect1>


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

  <para>
   <productname>PostgreSQL</productname> provides several index types:
   B-tree, R-tree, GiST, and Hash.  Each index type is more appropriate for
   a particular query type because of the algorithm it uses.
   <indexterm>
    <primary>indexes</primary>
    <secondary>B-tree</secondary>
   </indexterm>
   <indexterm>
    <primary>B-tree</primary>
    <see>indexes</see>
   </indexterm>
   By
   default, the <command>CREATE INDEX</command> command will create a
   B-tree index, which fits the most common situations.  In
   particular, the <productname>PostgreSQL</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>
   <indexterm>
    <primary>indexes</primary>
    <secondary>R-tree</secondary>
   </indexterm>
   <indexterm>
    <primary>R-tree</primary>
    <see>indexes</see>
   </indexterm>
   R-tree indexes are especially suited for spatial 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>PostgreSQL</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>
   <indexterm>
    <primary>indexes</primary>
    <secondary>hash</secondary>
   </indexterm>
   <indexterm>
    <primary>hash</primary>
    <see>indexes</see>
   </indexterm>
   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>
     Testing has shown PostgreSQL's hash indexes to be similar or slower
     than B-tree indexes, and the index size and build time for hash
     indexes is much worse. Hash indexes also suffer poor performance
     under high concurrency. For these reasons, hash index use is
     discouraged.
    </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="indexes-multicolumn">
  <title>Multicolumn Indexes</title>

  <indexterm zone="indexes-multicolumn">
   <primary>indexes</primary>
   <secondary>multicolumn</secondary>
  </indexterm>

  <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 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 and GiST implementations support multicolumn
   indexes.  Up to 32 columns may be specified.  (This limit can be
   altered when building <productname>PostgreSQL</productname>; see the
   file <filename>pg_config.h</filename>.)
  </para>

  <para>
   The query optimizer can use a multicolumn 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>
   Multicolumn 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>
   Multicolumn indexes 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="indexes-unique">
  <title>Unique Indexes</title>

  <indexterm zone="indexes-unique">
   <primary>indexes</primary>
   <secondary>unique</secondary>
  </indexterm>

  <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>
   Currently, only B-tree indexes 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
   indexes 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 multicolumn 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.
  </para>

  <note>
   <para>
    The preferred way to add a unique constraint to a table is
    <literal>ALTER TABLE ... ADD CONSTRAINT</literal>.  The use of
    indexes to enforce unique constraints could be considered an
    implementation detail that should not be accessed directly.
   </para>
  </note>
 </sect1>


 <sect1 id="indexes-functional">
  <title>Functional Indexes</title>

  <indexterm zone="indexes-functional">
   <primary>indexes</primary>
   <secondary>on functions</secondary>
  </indexterm>

  <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 indexes 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> function:
<programlisting>
SELECT * FROM test1 WHERE lower(col1) = 'value';
</programlisting>
   This query can use an index, if one has been
   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 indexes are always single-column (namely, the function
   result) even if the function uses more than one input field; there
   cannot be multicolumn indexes that contain function calls.
  </para>

  <tip>
   <para>
    The restrictions mentioned in the previous paragraph can easily be
    worked around by defining a custom function to use in the index
    definition that computes any desired result internally.
   </para>
  </tip>
 </sect1>


 <sect1 id="indexes-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 indexes 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_method,
       opc.opcname AS ops_name
    FROM pg_am am, pg_opclass opc
    WHERE opc.opcamid = am.oid
    ORDER BY acc_method, ops_name;
    </programlisting>

    It can be extended to show all the operators included in each class:
    <programlisting>
SELECT am.amname AS acc_method,
       opc.opcname AS ops_name,
       opr.oprname AS ops_comp
    FROM pg_am am, pg_opclass opc, pg_amop amop, pg_operator opr
    WHERE opc.opcamid = am.oid AND
          amop.amopclaid = opc.oid AND
          amop.amopopr = opr.oid
    ORDER BY acc_method, ops_name, ops_comp;
    </programlisting>
  </para>
 </sect1>


 <sect1 id="indexes-partial">
  <title>Partial Indexes</title>

  <indexterm zone="indexes-partial">
   <primary>indexes</primary>
   <secondary>partial</secondary>
  </indexterm>

  <para>
   A <firstterm>partial index</firstterm> is an index built over a
   subset of a table; the subset is defined by a conditional
   expression (called the <firstterm>predicate</firstterm> of the
   partial index).  The index contains entries for only those table
   rows that satisfy the predicate.
  </para>

  <para>
   A major motivation for partial indexes is to avoid indexing common
   values.  Since a query searching for a common value (one that
   accounts for more than a few percent of all the table rows) will not
   use the index anyway, there is no point in keeping those rows in the
   index at all.  This reduces the size of the index, which will speed
   up queries that do use the index.  It will also speed up many table
   update operations because the index does not need to be
   updated in all cases.  <xref linkend="indexes-partial-ex1"> shows a
   possible application of this idea.
  </para>

  <example id="indexes-partial-ex1">
   <title>Setting up a Partial Index to Exclude Common Values</title>

   <para>
    Suppose you are storing web server access logs in a database.
    Most accesses originate from the IP range of your organization but
    some are from elsewhere (say, employees on dial-up connections).
    If your searches by IP are primarily for outside accesses,
    you probably do not need to index the IP range that corresponds to your
    organization's subnet.
   </para>

   <para>
    Assume a table like this:
<programlisting>
CREATE TABLE access_log (
    url varchar,
    client_ip inet,
    ...
);
</programlisting>
   </para>

   <para>
    To create a partial index that suits our example, use a command
    such as this:
<programlisting>
CREATE INDEX access_log_client_ip_ix ON access_log (client_ip)
    WHERE NOT (client_ip > inet '192.168.100.0' AND client_ip < inet '192.168.100.255');
</programlisting>
   </para>

   <para>
    A typical query that can use this index would be:
<programlisting>
SELECT * FROM access_log WHERE url = '/index.html' AND client_ip = inet '212.78.10.32';
</programlisting>
    A query that cannot use this index is:
<programlisting>
SELECT * FROM access_log WHERE client_ip = inet '192.168.100.23';
</programlisting>
   </para>

   <para>
    Observe that this kind of partial index requires that the common
    values be predetermined.  If the distribution of values is
    inherent (due to the nature of the application) and static (not
    changing over time), this is not difficult, but if the common values are
    merely due to the coincidental data load this can require a lot of
    maintenance work.
   </para>
  </example>

  <para>
   Another possibility is to exclude values from the index that the
   typical query workload is not interested in; this is shown in <xref
   linkend="indexes-partial-ex2">.  This results in the same
   advantages as listed above, but it prevents the
   <quote>uninteresting</quote> values from being accessed via that
   index at all, even if an index scan might be profitable in that
   case.  Obviously, setting up partial indexes for this kind of
   scenario will require a lot of care and experimentation.
  </para>

  <example id="indexes-partial-ex2">
   <title>Setting up a Partial Index to Exclude Uninteresting Values</title>

   <para>
    If you have a table that contains both billed and unbilled orders,
    where the unbilled orders take up a small fraction of the total
    table and yet those are the most-accessed rows, you can improve
    performance by creating an index on just the unbilled rows.  The
    command to create the index would look like this:
<programlisting>
CREATE INDEX orders_unbilled_index ON orders (order_nr)
    WHERE billed is not true;
</programlisting>
   </para>

   <para>
    A possible query to use this index would be
<programlisting>
SELECT * FROM orders WHERE billed is not true AND order_nr < 10000;
</programlisting>
    However, the index can also be used in queries that do not involve
    <structfield>order_nr</> at all, e.g.,
<programlisting>
SELECT * FROM orders WHERE billed is not true AND amount > 5000.00;
</programlisting>
    This is not as efficient as a partial index on the
    <structfield>amount</> column would be, since the system has to
    scan the entire index.  Yet, if there are relatively few unbilled
    orders, using this partial index just to find the unbilled orders
    could be a win.
   </para>

   <para>
    Note that this query cannot use this index:
<programlisting>
SELECT * FROM orders WHERE order_nr = 3501;
</programlisting>
    The order 3501 may be among the billed or among the unbilled
    orders.
   </para>
  </example>

  <para>
   <xref linkend="indexes-partial-ex2"> also illustrates that the
   indexed column and the column used in the predicate do not need to
   match.  <productname>PostgreSQL</productname> supports partial
   indexes with arbitrary predicates, so long as only columns of the
   table being indexed are involved.  However, keep in mind that the
   predicate must match the conditions used in the queries that
   are supposed to benefit from the index.  To be precise, a partial
   index can be used in a query only if the system can recognize that
   the query's WHERE condition mathematically <firstterm>implies</>
   the index's predicate.
   <productname>PostgreSQL</productname> does not have a sophisticated
   theorem prover that can recognize mathematically equivalent
   predicates that are written in different forms.  (Not
   only is such a general theorem prover extremely difficult to
   create, it would probably be too slow to be of any real use.)
   The system can recognize simple inequality implications, for example
   <quote>x &lt; 1</quote> implies <quote>x &lt; 2</quote>; otherwise
   the predicate condition must exactly match the query's WHERE condition
   or the index will not be recognized to be usable.
  </para>

  <para>
   A third possible use for partial indexes does not require the
   index to be used in queries at all.  The idea here is to create
   a unique index over a subset of a table, as in <xref
   linkend="indexes-partial-ex3">.  This enforces uniqueness
   among the rows that satisfy the index predicate, without constraining
   those that do not.
  </para>

  <example id="indexes-partial-ex3">
   <title>Setting up a Partial Unique Index</title>

   <para>
    Suppose that we have a table describing test outcomes.  We wish
    to ensure that there is only one <quote>successful</> entry for
    a given subject and target combination, but there might be any number of
    <quote>unsuccessful</> entries.  Here is one way to do it:
<programlisting>
CREATE TABLE tests (subject text,
                    target text,
                    success bool,
                    ...);
CREATE UNIQUE INDEX tests_success_constraint ON tests (subject, target)
    WHERE success;
</programlisting>
    This is a particularly efficient way of doing it when there are few
    successful trials and many unsuccessful ones.
   </para>
  </example>

  <para>
   Finally, a partial index can also be used to override the system's
   query plan choices.  It may occur that data sets with peculiar
   distributions will cause the system to use an index when it really
   should not.  In that case the index can be set up so that it is not
   available for the offending query.  Normally,
   <productname>PostgreSQL</> makes reasonable choices about index
   usage (e.g., it avoids them when retrieving common values, so the
   earlier example really only saves index size, it is not required to
   avoid index usage), and grossly incorrect plan choices are cause
   for a bug report.
  </para>

  <para>
   Keep in mind that setting up a partial index indicates that you
   know at least as much as the query planner knows, in particular you
   know when an index might be profitable.  Forming this knowledge
   requires experience and understanding of how indexes in
   <productname>PostgreSQL</> work.  In most cases, the advantage of a
   partial index over a regular index will not be much.
  </para>

  <para>
   More information about partial indexes can be found in <xref
   linkend="STON89b">, <xref linkend="OLSON93">, and <xref
   linkend="SESHADRI95">.
  </para>
 </sect1>

 <sect1 id="indexes-examine">
  <title>Examining Index Usage</title>

  <para>
   Although indexes in <productname>PostgreSQL</> do not need
   maintenance and tuning, it is still important to check
   which indexes are actually used by the real-life query workload.
   Examining index usage is done with the <command>EXPLAIN</> command;
   its application for this purpose is illustrated in <xref
   linkend="using-explain">.
  </para>

  <para>
   It is difficult to formulate a general procedure for determining
   which indexes to set up.  There are a number of typical cases that
   have been shown in the examples throughout the previous sections.
   A good deal of experimentation will be necessary in most cases.
   The rest of this section gives some tips for that.
  </para>

  <itemizedlist>
   <listitem>
    <para>
     Always run <command>ANALYZE</command> first.  This command
     collects statistics about the distribution of the values in the
     table.  This information is required to guess the number of rows
     returned by a query, which is needed by the planner to assign
     realistic costs to each possible query plan.  In absence of any
     real statistics, some default values are assumed, which are
     almost certain to be inaccurate.  Examining an application's
     index usage without having run <command>ANALYZE</command> is
     therefore a lost cause.
    </para>
   </listitem>

   <listitem>
    <para>
     Use real data for experimentation.  Using test data for setting
     up indexes will tell you what indexes you need for the test data,
     but that is all.
    </para>

    <para>
     It is especially fatal to use proportionally reduced data sets.
     While selecting 1000 out of 100000 rows could be a candidate for
     an index, selecting 1 out of 100 rows will hardly be, because the
     100 rows will probably fit within a single disk page, and there
     is no plan that can beat sequentially fetching 1 disk page.
    </para>

    <para>
     Also be careful when making up test data, which is often
     unavoidable when the application is not in production use yet.
     Values that are very similar, completely random, or inserted in
     sorted order will skew the statistics away from the distribution
     that real data would have.
    </para>
   </listitem>

   <listitem>
    <para>
     When indexes are not used, it can be useful for testing to force
     their use.  There are run-time parameters that can turn off
     various plan types (described in the &cite-admin;).
     For instance, turning off sequential scans
     (<varname>enable_seqscan</>) and nested-loop joins
     (<varname>enable_nestloop</>), which are the most basic plans,
     will force the system to use a different plan.  If the system
     still chooses a sequential scan or nested-loop join then there is
     probably a more fundamental problem for why the index is not
     used, for example, the query condition does not match the index.
     (What kind of query can use what kind of index is explained in
     the previous sections.)
    </para>
   </listitem>

   <listitem>
    <para>
     If forcing index usage does use the index, then there are two
     possibilities: Either the system is right and using the index is
     indeed not appropriate, or the cost estimates of the query plans
     are not reflecting reality.  So you should time your query with
     and without indexes.  The <command>EXPLAIN ANALYZE</command>
     command can be useful here.
    </para>
   </listitem>

   <listitem>
    <para>
     If it turns out that the cost estimates are wrong, there are,
     again, two possibilities.  The total cost is computed from the
     per-row costs of each plan node times the selectivity estimate of
     the plan node.  The costs of the plan nodes can be tuned with
     run-time parameters (described in the &cite-admin;).
     An inaccurate selectivity estimate is due to
     insufficient statistics.  It may be possible to help this by
     tuning the statistics-gathering parameters (see <command>ALTER
     TABLE</command> reference).
    </para>

    <para>
     If you do not succeed in adjusting the costs to be more
     appropriate, then you may have to resort to forcing index usage
     explicitly.  You may also want to contact the
     <productname>PostgreSQL</> developers to examine the issue.
    </para>
   </listitem>
  </itemizedlist>
 </sect1>
</chapter>

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