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<!-- doc/src/sgml/ltree.sgml -->
<sect1 id="ltree" xreflabel="ltree">
<title>ltree</title>
<indexterm zone="ltree">
<primary>ltree</primary>
</indexterm>
<para>
This module implements a data type <type>ltree</type> for representing
labels of data stored in a hierarchical tree-like structure.
Extensive facilities for searching through label trees are provided.
</para>
<para>
This module is considered <quote>trusted</quote>, that is, it can be
installed by non-superusers who have <literal>CREATE</literal> privilege
on the current database.
</para>
<sect2>
<title>Definitions</title>
<para>
A <firstterm>label</firstterm> is a sequence of alphanumeric characters
and underscores (for example, in C locale the characters
<literal>A-Za-z0-9_</literal> are allowed).
Labels must be less than 256 characters long.
</para>
<para>
Examples: <literal>42</literal>, <literal>Personal_Services</literal>
</para>
<para>
A <firstterm>label path</firstterm> is a sequence of zero or more
labels separated by dots, for example <literal>L1.L2.L3</literal>, representing
a path from the root of a hierarchical tree to a particular node. The
length of a label path cannot exceed 65535 labels.
</para>
<para>
Example: <literal>Top.Countries.Europe.Russia</literal>
</para>
<para>
The <filename>ltree</filename> module provides several data types:
</para>
<itemizedlist>
<listitem>
<para>
<type>ltree</type> stores a label path.
</para>
</listitem>
<listitem>
<para>
<type>lquery</type> represents a regular-expression-like pattern
for matching <type>ltree</type> values. A simple word matches that
label within a path. A star symbol (<literal>*</literal>) matches zero
or more labels. For example:
<synopsis>
foo <lineannotation>Match the exact label path <literal>foo</literal></lineannotation>
*.foo.* <lineannotation>Match any label path containing the label <literal>foo</literal></lineannotation>
*.foo <lineannotation>Match any label path whose last label is <literal>foo</literal></lineannotation>
</synopsis>
</para>
<para>
Star symbols can also be quantified to restrict how many labels
they can match:
<synopsis>
*{<replaceable>n</replaceable>} <lineannotation>Match exactly <replaceable>n</replaceable> labels</lineannotation>
*{<replaceable>n</replaceable>,} <lineannotation>Match at least <replaceable>n</replaceable> labels</lineannotation>
*{<replaceable>n</replaceable>,<replaceable>m</replaceable>} <lineannotation>Match at least <replaceable>n</replaceable> but not more than <replaceable>m</replaceable> labels</lineannotation>
*{,<replaceable>m</replaceable>} <lineannotation>Match at most <replaceable>m</replaceable> labels &mdash; same as </lineannotation> *{0,<replaceable>m</replaceable>}
</synopsis>
</para>
<para>
There are several modifiers that can be put at the end of a non-star
label in <type>lquery</type> to make it match more than just the exact match:
<synopsis>
@ <lineannotation>Match case-insensitively, for example <literal>a@</literal> matches <literal>A</literal></lineannotation>
* <lineannotation>Match any label with this prefix, for example <literal>foo*</literal> matches <literal>foobar</literal></lineannotation>
% <lineannotation>Match initial underscore-separated words</lineannotation>
</synopsis>
The behavior of <literal>%</literal> is a bit complicated. It tries to match
words rather than the entire label. For example
<literal>foo_bar%</literal> matches <literal>foo_bar_baz</literal> but not
<literal>foo_barbaz</literal>. If combined with <literal>*</literal>, prefix
matching applies to each word separately, for example
<literal>foo_bar%*</literal> matches <literal>foo1_bar2_baz</literal> but
not <literal>foo1_br2_baz</literal>.
</para>
<para>
Also, you can write several possibly-modified labels separated with
<literal>|</literal> (OR) to match any of those labels, and you can put
<literal>!</literal> (NOT) at the start to match any label that doesn't
match any of the alternatives.
</para>
<para>
Here's an annotated example of <type>lquery</type>:
<programlisting>
Top.*{0,2}.sport*@.!football|tennis.Russ*|Spain
a. b. c. d. e.
</programlisting>
This query will match any label path that:
</para>
<orderedlist numeration="loweralpha">
<listitem>
<para>
begins with the label <literal>Top</literal>
</para>
</listitem>
<listitem>
<para>
and next has zero to two labels before
</para>
</listitem>
<listitem>
<para>
a label beginning with the case-insensitive prefix <literal>sport</literal>
</para>
</listitem>
<listitem>
<para>
then a label not matching <literal>football</literal> nor
<literal>tennis</literal>
</para>
</listitem>
<listitem>
<para>
and then ends with a label beginning with <literal>Russ</literal> or
exactly matching <literal>Spain</literal>.
</para>
</listitem>
</orderedlist>
</listitem>
<listitem>
<para><type>ltxtquery</type> represents a full-text-search-like
pattern for matching <type>ltree</type> values. An
<type>ltxtquery</type> value contains words, possibly with the
modifiers <literal>@</literal>, <literal>*</literal>, <literal>%</literal> at the end;
the modifiers have the same meanings as in <type>lquery</type>.
Words can be combined with <literal>&amp;</literal> (AND),
<literal>|</literal> (OR), <literal>!</literal> (NOT), and parentheses.
The key difference from
<type>lquery</type> is that <type>ltxtquery</type> matches words without
regard to their position in the label path.
</para>
<para>
Here's an example <type>ltxtquery</type>:
<programlisting>
Europe &amp; Russia*@ &amp; !Transportation
</programlisting>
This will match paths that contain the label <literal>Europe</literal> and
any label beginning with <literal>Russia</literal> (case-insensitive),
but not paths containing the label <literal>Transportation</literal>.
The location of these words within the path is not important.
Also, when <literal>%</literal> is used, the word can be matched to any
underscore-separated word within a label, regardless of position.
</para>
</listitem>
</itemizedlist>
<para>
Note: <type>ltxtquery</type> allows whitespace between symbols, but
<type>ltree</type> and <type>lquery</type> do not.
</para>
</sect2>
<sect2>
<title>Operators and Functions</title>
<para>
Type <type>ltree</type> has the usual comparison operators
<literal>=</literal>, <literal>&lt;&gt;</literal>,
<literal>&lt;</literal>, <literal>&gt;</literal>, <literal>&lt;=</literal>, <literal>&gt;=</literal>.
Comparison sorts in the order of a tree traversal, with the children
of a node sorted by label text. In addition, the specialized
operators shown in <xref linkend="ltree-op-table"/> are available.
</para>
<table id="ltree-op-table">
<title><type>ltree</type> Operators</title>
<tgroup cols="3">
<thead>
<row>
<entry>Operator</entry>
<entry>Returns</entry>
<entry>Description</entry>
</row>
</thead>
<tbody>
<row>
<entry><type>ltree</type> <literal>@&gt;</literal> <type>ltree</type></entry>
<entry><type>boolean</type></entry>
<entry>is left argument an ancestor of right (or equal)?</entry>
</row>
<row>
<entry><type>ltree</type> <literal>&lt;@</literal> <type>ltree</type></entry>
<entry><type>boolean</type></entry>
<entry>is left argument a descendant of right (or equal)?</entry>
</row>
<row>
<entry><type>ltree</type> <literal>~</literal> <type>lquery</type></entry>
<entry><type>boolean</type></entry>
<entry>does <type>ltree</type> match <type>lquery</type>?</entry>
</row>
<row>
<entry><type>lquery</type> <literal>~</literal> <type>ltree</type></entry>
<entry><type>boolean</type></entry>
<entry>does <type>ltree</type> match <type>lquery</type>?</entry>
</row>
<row>
<entry><type>ltree</type> <literal>?</literal> <type>lquery[]</type></entry>
<entry><type>boolean</type></entry>
<entry>does <type>ltree</type> match any <type>lquery</type> in array?</entry>
</row>
<row>
<entry><type>lquery[]</type> <literal>?</literal> <type>ltree</type></entry>
<entry><type>boolean</type></entry>
<entry>does <type>ltree</type> match any <type>lquery</type> in array?</entry>
</row>
<row>
<entry><type>ltree</type> <literal>@</literal> <type>ltxtquery</type></entry>
<entry><type>boolean</type></entry>
<entry>does <type>ltree</type> match <type>ltxtquery</type>?</entry>
</row>
<row>
<entry><type>ltxtquery</type> <literal>@</literal> <type>ltree</type></entry>
<entry><type>boolean</type></entry>
<entry>does <type>ltree</type> match <type>ltxtquery</type>?</entry>
</row>
<row>
<entry><type>ltree</type> <literal>||</literal> <type>ltree</type></entry>
<entry><type>ltree</type></entry>
<entry>concatenate <type>ltree</type> paths</entry>
</row>
<row>
<entry><type>ltree</type> <literal>||</literal> <type>text</type></entry>
<entry><type>ltree</type></entry>
<entry>convert text to <type>ltree</type> and concatenate</entry>
</row>
<row>
<entry><type>text</type> <literal>||</literal> <type>ltree</type></entry>
<entry><type>ltree</type></entry>
<entry>convert text to <type>ltree</type> and concatenate</entry>
</row>
<row>
<entry><type>ltree[]</type> <literal>@&gt;</literal> <type>ltree</type></entry>
<entry><type>boolean</type></entry>
<entry>does array contain an ancestor of <type>ltree</type>?</entry>
</row>
<row>
<entry><type>ltree</type> <literal>&lt;@</literal> <type>ltree[]</type></entry>
<entry><type>boolean</type></entry>
<entry>does array contain an ancestor of <type>ltree</type>?</entry>
</row>
<row>
<entry><type>ltree[]</type> <literal>&lt;@</literal> <type>ltree</type></entry>
<entry><type>boolean</type></entry>
<entry>does array contain a descendant of <type>ltree</type>?</entry>
</row>
<row>
<entry><type>ltree</type> <literal>@&gt;</literal> <type>ltree[]</type></entry>
<entry><type>boolean</type></entry>
<entry>does array contain a descendant of <type>ltree</type>?</entry>
</row>
<row>
<entry><type>ltree[]</type> <literal>~</literal> <type>lquery</type></entry>
<entry><type>boolean</type></entry>
<entry>does array contain any path matching <type>lquery</type>?</entry>
</row>
<row>
<entry><type>lquery</type> <literal>~</literal> <type>ltree[]</type></entry>
<entry><type>boolean</type></entry>
<entry>does array contain any path matching <type>lquery</type>?</entry>
</row>
<row>
<entry><type>ltree[]</type> <literal>?</literal> <type>lquery[]</type></entry>
<entry><type>boolean</type></entry>
<entry>does <type>ltree</type> array contain any path matching any <type>lquery</type>?</entry>
</row>
<row>
<entry><type>lquery[]</type> <literal>?</literal> <type>ltree[]</type></entry>
<entry><type>boolean</type></entry>
<entry>does <type>ltree</type> array contain any path matching any <type>lquery</type>?</entry>
</row>
<row>
<entry><type>ltree[]</type> <literal>@</literal> <type>ltxtquery</type></entry>
<entry><type>boolean</type></entry>
<entry>does array contain any path matching <type>ltxtquery</type>?</entry>
</row>
<row>
<entry><type>ltxtquery</type> <literal>@</literal> <type>ltree[]</type></entry>
<entry><type>boolean</type></entry>
<entry>does array contain any path matching <type>ltxtquery</type>?</entry>
</row>
<row>
<entry><type>ltree[]</type> <literal>?@&gt;</literal> <type>ltree</type></entry>
<entry><type>ltree</type></entry>
<entry>first array entry that is an ancestor of <type>ltree</type>; NULL if none</entry>
</row>
<row>
<entry><type>ltree[]</type> <literal>?&lt;@</literal> <type>ltree</type></entry>
<entry><type>ltree</type></entry>
<entry>first array entry that is a descendant of <type>ltree</type>; NULL if none</entry>
</row>
<row>
<entry><type>ltree[]</type> <literal>?~</literal> <type>lquery</type></entry>
<entry><type>ltree</type></entry>
<entry>first array entry that matches <type>lquery</type>; NULL if none</entry>
</row>
<row>
<entry><type>ltree[]</type> <literal>?@</literal> <type>ltxtquery</type></entry>
<entry><type>ltree</type></entry>
<entry>first array entry that matches <type>ltxtquery</type>; NULL if none</entry>
</row>
</tbody>
</tgroup>
</table>
<para>
The operators <literal>&lt;@</literal>, <literal>@&gt;</literal>,
<literal>@</literal> and <literal>~</literal> have analogues
<literal>^&lt;@</literal>, <literal>^@&gt;</literal>, <literal>^@</literal>,
<literal>^~</literal>, which are the same except they do not use
indexes. These are useful only for testing purposes.
</para>
<para>
The available functions are shown in <xref linkend="ltree-func-table"/>.
</para>
<table id="ltree-func-table">
<title><type>ltree</type> Functions</title>
<tgroup cols="5">
<thead>
<row>
<entry>Function</entry>
<entry>Return Type</entry>
<entry>Description</entry>
<entry>Example</entry>
<entry>Result</entry>
</row>
</thead>
<tbody>
<row>
<entry><function>subltree(ltree, int start, int end)</function><indexterm><primary>subltree</primary></indexterm></entry>
<entry><type>ltree</type></entry>
<entry>subpath of <type>ltree</type> from position <parameter>start</parameter> to
position <parameter>end</parameter>-1 (counting from 0)</entry>
<entry><literal>subltree('Top.Child1.Child2',1,2)</literal></entry>
<entry><literal>Child1</literal></entry>
</row>
<row>
<entry><function>subpath(ltree, int offset, int len)</function><indexterm><primary>subpath</primary></indexterm></entry>
<entry><type>ltree</type></entry>
<entry>subpath of <type>ltree</type> starting at position
<parameter>offset</parameter>, length <parameter>len</parameter>.
If <parameter>offset</parameter> is negative, subpath starts that far from the
end of the path. If <parameter>len</parameter> is negative, leaves that many
labels off the end of the path.</entry>
<entry><literal>subpath('Top.Child1.Child2',0,2)</literal></entry>
<entry><literal>Top.Child1</literal></entry>
</row>
<row>
<entry><function>subpath(ltree, int offset)</function></entry>
<entry><type>ltree</type></entry>
<entry>subpath of <type>ltree</type> starting at position
<parameter>offset</parameter>, extending to end of path.
If <parameter>offset</parameter> is negative, subpath starts that far from the
end of the path.</entry>
<entry><literal>subpath('Top.Child1.Child2',1)</literal></entry>
<entry><literal>Child1.Child2</literal></entry>
</row>
<row>
<entry><function>nlevel(ltree)</function><indexterm><primary>nlevel</primary></indexterm></entry>
<entry><type>integer</type></entry>
<entry>number of labels in path</entry>
<entry><literal>nlevel('Top.Child1.Child2')</literal></entry>
<entry><literal>3</literal></entry>
</row>
<row>
<entry><function>index(ltree a, ltree b)</function><indexterm><primary>index</primary></indexterm></entry>
<entry><type>integer</type></entry>
<entry>position of first occurrence of <parameter>b</parameter> in
<parameter>a</parameter>; -1 if not found</entry>
<entry><literal>index('0.1.2.3.5.4.5.6.8.5.6.8','5.6')</literal></entry>
<entry><literal>6</literal></entry>
</row>
<row>
<entry><function>index(ltree a, ltree b, int offset)</function></entry>
<entry><type>integer</type></entry>
<entry>position of first occurrence of <parameter>b</parameter> in
<parameter>a</parameter>, searching starting at <parameter>offset</parameter>;
negative <parameter>offset</parameter> means start <parameter>-offset</parameter>
labels from the end of the path</entry>
<entry><literal>index('0.1.2.3.5.4.5.6.8.5.6.8','5.6',-4)</literal></entry>
<entry><literal>9</literal></entry>
</row>
<row>
<entry><function>text2ltree(text)</function><indexterm><primary>text2ltree</primary></indexterm></entry>
<entry><type>ltree</type></entry>
<entry>cast <type>text</type> to <type>ltree</type></entry>
<entry><literal></literal></entry>
<entry><literal></literal></entry>
</row>
<row>
<entry><function>ltree2text(ltree)</function><indexterm><primary>ltree2text</primary></indexterm></entry>
<entry><type>text</type></entry>
<entry>cast <type>ltree</type> to <type>text</type></entry>
<entry><literal></literal></entry>
<entry><literal></literal></entry>
</row>
<row>
<entry><function>lca(ltree, ltree, ...)</function><indexterm><primary>lca</primary></indexterm></entry>
<entry><type>ltree</type></entry>
<entry>longest common ancestor of paths
(up to 8 arguments supported)</entry>
<entry><literal>lca('1.2.3','1.2.3.4.5.6')</literal></entry>
<entry><literal>1.2</literal></entry>
</row>
<row>
<entry><function>lca(ltree[])</function></entry>
<entry><type>ltree</type></entry>
<entry>longest common ancestor of paths in array</entry>
<entry><literal>lca(array['1.2.3'::ltree,'1.2.3.4'])</literal></entry>
<entry><literal>1.2</literal></entry>
</row>
</tbody>
</tgroup>
</table>
</sect2>
<sect2>
<title>Indexes</title>
<para>
<filename>ltree</filename> supports several types of indexes that can speed
up the indicated operators:
</para>
<itemizedlist>
<listitem>
<para>
B-tree index over <type>ltree</type>:
<literal>&lt;</literal>, <literal>&lt;=</literal>, <literal>=</literal>,
<literal>&gt;=</literal>, <literal>&gt;</literal>
</para>
</listitem>
<listitem>
<para>
GiST index over <type>ltree</type> (<literal>gist_ltree_ops</literal>
opclass):
<literal>&lt;</literal>, <literal>&lt;=</literal>, <literal>=</literal>,
<literal>&gt;=</literal>, <literal>&gt;</literal>,
<literal>@&gt;</literal>, <literal>&lt;@</literal>,
<literal>@</literal>, <literal>~</literal>, <literal>?</literal>
</para>
<para>
<literal>gist_ltree_ops</literal> GiST opclass approximates set of
path labels as a bitmap signature. Optional integer parameter
<literal>siglen</literal> of <literal>gist_ltree_ops</literal> determines
signature length in bytes. Default signature length is 8 bytes.
Valid values of signature length are between 1 and 2024 bytes. Longer
signatures leads to more precise search (scan less fraction of index, scan
less heap pages), but larger index.
</para>
<para>
Example of creating such an index with a default signature length of 8 bytes:
</para>
<programlisting>
CREATE INDEX path_gist_idx ON test USING GIST (path);
</programlisting>
<para>
Example of creating such an index with a signature length of 100 bytes:
</para>
<programlisting>
CREATE INDEX path_gist_idx ON test USING GIST (path gist_ltree_ops(siglen=100));
</programlisting>
</listitem>
<listitem>
<para>
GiST index over <type>ltree[]</type> (<literal>gist__ltree_ops</literal>
opclass):
<literal>ltree[] &lt;@ ltree</literal>, <literal>ltree @&gt; ltree[]</literal>,
<literal>@</literal>, <literal>~</literal>, <literal>?</literal>
</para>
<para>
<literal>gist__ltree_ops</literal> GiST opclass works similar to
<literal>gist_ltree_ops</literal> and also takes signature length as
a parameter. Default value of <literal>siglen</literal> in
<literal>gist__ltree_ops</literal> is 28 bytes.
</para>
<para>
Example of creating such an index with a default signature length of 28 bytes:
</para>
<programlisting>
CREATE INDEX path_gist_idx ON test USING GIST (array_path);
</programlisting>
<para>
Example of creating such an index with a signature length of 100 bytes:
</para>
<programlisting>
CREATE INDEX path_gist_idx ON test USING GIST (array_path gist__ltree_ops(siglen=100));
</programlisting>
<para>
Note: This index type is lossy.
</para>
</listitem>
</itemizedlist>
</sect2>
<sect2>
<title>Example</title>
<para>
This example uses the following data (also available in file
<filename>contrib/ltree/ltreetest.sql</filename> in the source distribution):
</para>
<programlisting>
CREATE TABLE test (path ltree);
INSERT INTO test VALUES ('Top');
INSERT INTO test VALUES ('Top.Science');
INSERT INTO test VALUES ('Top.Science.Astronomy');
INSERT INTO test VALUES ('Top.Science.Astronomy.Astrophysics');
INSERT INTO test VALUES ('Top.Science.Astronomy.Cosmology');
INSERT INTO test VALUES ('Top.Hobbies');
INSERT INTO test VALUES ('Top.Hobbies.Amateurs_Astronomy');
INSERT INTO test VALUES ('Top.Collections');
INSERT INTO test VALUES ('Top.Collections.Pictures');
INSERT INTO test VALUES ('Top.Collections.Pictures.Astronomy');
INSERT INTO test VALUES ('Top.Collections.Pictures.Astronomy.Stars');
INSERT INTO test VALUES ('Top.Collections.Pictures.Astronomy.Galaxies');
INSERT INTO test VALUES ('Top.Collections.Pictures.Astronomy.Astronauts');
CREATE INDEX path_gist_idx ON test USING GIST (path);
CREATE INDEX path_idx ON test USING BTREE (path);
</programlisting>
<para>
Now, we have a table <structname>test</structname> populated with data describing
the hierarchy shown below:
</para>
<literallayout class="monospaced">
Top
/ | \
Science Hobbies Collections
/ | \
Astronomy Amateurs_Astronomy Pictures
/ \ |
Astrophysics Cosmology Astronomy
/ | \
Galaxies Stars Astronauts
</literallayout>
<para>
We can do inheritance:
<screen>
ltreetest=&gt; SELECT path FROM test WHERE path &lt;@ 'Top.Science';
path
------------------------------------
Top.Science
Top.Science.Astronomy
Top.Science.Astronomy.Astrophysics
Top.Science.Astronomy.Cosmology
(4 rows)
</screen>
</para>
<para>
Here are some examples of path matching:
<screen>
ltreetest=&gt; SELECT path FROM test WHERE path ~ '*.Astronomy.*';
path
-----------------------------------------------
Top.Science.Astronomy
Top.Science.Astronomy.Astrophysics
Top.Science.Astronomy.Cosmology
Top.Collections.Pictures.Astronomy
Top.Collections.Pictures.Astronomy.Stars
Top.Collections.Pictures.Astronomy.Galaxies
Top.Collections.Pictures.Astronomy.Astronauts
(7 rows)
ltreetest=&gt; SELECT path FROM test WHERE path ~ '*.!pictures@.*.Astronomy.*';
path
------------------------------------
Top.Science.Astronomy
Top.Science.Astronomy.Astrophysics
Top.Science.Astronomy.Cosmology
(3 rows)
</screen>
</para>
<para>
Here are some examples of full text search:
<screen>
ltreetest=&gt; SELECT path FROM test WHERE path @ 'Astro*% &amp; !pictures@';
path
------------------------------------
Top.Science.Astronomy
Top.Science.Astronomy.Astrophysics
Top.Science.Astronomy.Cosmology
Top.Hobbies.Amateurs_Astronomy
(4 rows)
ltreetest=&gt; SELECT path FROM test WHERE path @ 'Astro* &amp; !pictures@';
path
------------------------------------
Top.Science.Astronomy
Top.Science.Astronomy.Astrophysics
Top.Science.Astronomy.Cosmology
(3 rows)
</screen>
</para>
<para>
Path construction using functions:
<screen>
ltreetest=&gt; SELECT subpath(path,0,2)||'Space'||subpath(path,2) FROM test WHERE path &lt;@ 'Top.Science.Astronomy';
?column?
------------------------------------------
Top.Science.Space.Astronomy
Top.Science.Space.Astronomy.Astrophysics
Top.Science.Space.Astronomy.Cosmology
(3 rows)
</screen>
</para>
<para>
We could simplify this by creating a SQL function that inserts a label
at a specified position in a path:
<screen>
CREATE FUNCTION ins_label(ltree, int, text) RETURNS ltree
AS 'select subpath($1,0,$2) || $3 || subpath($1,$2);'
LANGUAGE SQL IMMUTABLE;
ltreetest=&gt; SELECT ins_label(path,2,'Space') FROM test WHERE path &lt;@ 'Top.Science.Astronomy';
ins_label
------------------------------------------
Top.Science.Space.Astronomy
Top.Science.Space.Astronomy.Astrophysics
Top.Science.Space.Astronomy.Cosmology
(3 rows)
</screen>
</para>
</sect2>
<sect2>
<title>Transforms</title>
<para>
Additional extensions are available that implement transforms for
the <type>ltree</type> type for PL/Python. The extensions are
called <literal>ltree_plpythonu</literal>, <literal>ltree_plpython2u</literal>,
and <literal>ltree_plpython3u</literal>
(see <xref linkend="plpython-python23"/> for the PL/Python naming
convention). If you install these transforms and specify them when
creating a function, <type>ltree</type> values are mapped to Python lists.
(The reverse is currently not supported, however.)
</para>
</sect2>
<sect2>
<title>Authors</title>
<para>
All work was done by Teodor Sigaev (<email>teodor@stack.net</email>) and
Oleg Bartunov (<email>oleg@sai.msu.su</email>). See
<ulink url="http://www.sai.msu.su/~megera/postgres/gist/"></ulink> for
additional information. Authors would like to thank Eugeny Rodichev for
helpful discussions. Comments and bug reports are welcome.
</para>
</sect2>
</sect1>
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