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

  <para>
   Indexes are commonly used to enhance database
   performance. They should be defined on table columns (or class
   attributes) that are used as qualifications in repetitive queries.
   Inappropriate use will result in slower performance, since update
   and insertion times are increased in the presence of indices.
  </para>

  <para>
   Indexes may also be used to enforce uniqueness of a table's primary key.
   When an index is declared UNIQUE, multiple table rows with identical
   index entries won't be allowed.
   For this purpose, the goal is ensuring data consistency, not improving
   performance, so the above caution about inappropriate use doesn't apply.
  </para>

  <para>
   Two forms of indices may be defined:

   <itemizedlist>
    <listitem>
     <para>
      For a <firstterm>value index</firstterm>,
      the key fields for the
      index are specified as column names; multiple columns
      can be specified if the index access method supports
      multi-column indexes.
     </para>
    </listitem>

    <listitem>
     <para>
      For a <firstterm>functional index</firstterm>, an index is defined
      on the result of a function applied
      to one or more attributes of a single class.
      This is a single-column index (namely, the function result)
      even if the function uses more than one input field.
      Functional indices can be used to obtain fast access to data
      based on operators that would normally require some
      transformation to apply them to the base data.
     </para>
    </listitem>
   </itemizedlist>
  </para>

  <para>
   Postgres provides btree, rtree and hash access methods for
   indices.  The btree access method is an implementation of
   Lehman-Yao high-concurrency btrees.  The rtree access method
   implements standard rtrees using Guttman's quadratic split algorithm.
   The hash access method 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>

  <para>
   The <productname>Postgres</productname>
   query optimizer will consider using a btree index whenever
   an indexed attribute is involved in a comparison using one of:

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

  <para>
   The <productname>Postgres</productname>
   query optimizer will consider using an rtree index whenever
   an indexed attribute is involved in a comparison using one of:

   <simplelist type="inline">
    <member>&lt;&lt;</member>
    <member>&amp;&lt;</member>
    <member>&amp;&gt;</member>
    <member>&gt;&gt;</member>
    <member>@</member>
    <member>~=</member>
    <member>&amp;&amp;</member>
   </simplelist>
  </para>

  <para>
   The <productname>Postgres</productname>
   query optimizer will consider using a hash index whenever
   an indexed attribute is involved in a comparison using
   the <literal>=</literal> operator.
  </para>

  <para>
   Currently, only the btree access method supports multi-column
   indexes. Up to 16 keys may be specified by default (this limit
   can be altered when building Postgres).
  </para>

  <para>
   An <firstterm>operator class</firstterm> can be specified for each
   column of an index.  The operator class identifies the operators to
   be used by the index for that column.  For example, a btree 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 field's
   datatype is usually sufficient.  The main point of having operator classes
   is that for some datatypes, there could be more than one meaningful
   ordering.  For example, we might want to sort a complex-number datatype
   either by absolute value or by real part.  We could do this by defining
   two operator classes for the datatype 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 rtree indices on the
      <literal>box</literal> datatype.
      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>

  <para>
   Use <command>DROP INDEX</command> to remove an index.
  </para>

  <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>
    <programlisting>
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?
    </programlisting>
   </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 "Life Science", 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 "Life Science" to "Biology", 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 updateable, 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 implementational 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
    <programlisting>
CREATE MEMSTORE ON &lt;table&gt; COLUMNS &lt;cols&gt;
    </programlisting>
    (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>

   <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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