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Move most /contrib README files into SGML. Some still need conversion or will never be converted.
2007-11-11 00:30:46 +01:00
<sect1 id="ltree">
<title>ltree</title>
<indexterm zone="ltree">
<primary>ltree</primary>
</indexterm>
<para>
<literal>ltree</literal> is a PostgreSQL module that contains implementation
of data types, indexed access methods and queries for data organized as a
tree-like structures.
</para>
<sect2>
<title>Definitions</title>
<para>
A <emphasis>label</emphasis> of a node is a sequence of one or more words
separated by blank character '_' and containing letters and digits ( for
example, [a-zA-Z0-9] for C locale). The length of a label is limited by 256
bytes.
</para>
<para>
Example: 'Countries', 'Personal_Services'
</para>
<para>
A <emphasis>label path</emphasis> of a node is a sequence of one or more
dot-separated labels l1.l2...ln, represents path from root to the node. The
length of a label path is limited by 65Kb, but size <= 2Kb is preferrable.
We consider it's not a strict limitation (maximal size of label path for
DMOZ catalogue - <ulink url="http://www.dmoz.org"></ulink>, is about 240
bytes!)
</para>
<para>
Example: <literal>'Top.Countries.Europe.Russia'</literal>
</para>
<para>
We introduce several datatypes:
</para>
<itemizedlist>
<listitem>
<para>
<literal>ltree</literal> - is a datatype for label path.
</para>
</listitem>
<listitem>
<para>
<literal>ltree[]</literal> - is a datatype for arrays of ltree.
</para>
</listitem>
<listitem>
<para>
<literal>lquery</literal>
- is a path expression that has regular expression in the label path and
used for ltree matching. Star symbol (*) is used to specify any number of
labels (levels) and could be used at the beginning and the end of lquery,
for example, '*.Europe.*'.
</para>
<para>
The following quantifiers are recognized for '*' (like in Perl):
</para>
<itemizedlist>
<listitem>
<para>{n} Match exactly n levels</para>
</listitem>
<listitem>
<para>{n,} Match at least n levels</para>
</listitem>
<listitem>
<para>{n,m} Match at least n but not more than m levels</para>
</listitem>
<listitem>
<para>{,m} Match at maximum m levels (eq. to {0,m})</para>
</listitem>
</itemizedlist>
<para>
It is possible to use several modifiers at the end of a label:
</para>
<itemizedlist>
<listitem>
<para>@ Do case-insensitive label matching</para>
</listitem>
<listitem>
<para>* Do prefix matching for a label</para>
</listitem>
<listitem>
<para>% Don't account word separator '_' in label matching, that is
'Russian%' would match 'Russian_nations', but not 'Russian'
</para>
</listitem>
</itemizedlist>
<para>
<literal>lquery</literal> can contain logical '!' (NOT) at the beginning
of the label and '|' (OR) to specify possible alternatives for label
matching.
</para>
<para>
Example of <literal>lquery</literal>:
</para>
<programlisting>
Top.*{0,2}.sport*@.!football|tennis.Russ*|Spain
a) b) c) d) e)
</programlisting>
<para>
A label path should
</para>
<orderedlist numeration='loweralpha'>
<listitem>
<para>
begin from a node with label 'Top'
</para>
</listitem>
<listitem>
<para>
and following zero or 2 labels until
</para>
</listitem>
<listitem>
<para>
a node with label beginning from case-insensitive prefix 'sport'
</para>
</listitem>
<listitem>
<para>
following node with label not matched 'football' or 'tennis' and
</para>
</listitem>
<listitem>
<para>
end on node with label beginning from 'Russ' or strictly matched
'Spain'.
</para>
</listitem>
</orderedlist>
</listitem>
<listitem>
<para><literal>ltxtquery</literal>
- is a datatype for label searching (like type 'query' for full text
searching, see contrib/tsearch). It's possible to use modifiers @,%,* at
the end of word. The meaning of modifiers are the same as for lquery.
</para>
<para>
Example: <literal>'Europe & Russia*@ & !Transportation'</literal>
</para>
<para>
Search paths contain words 'Europe' and 'Russia*' (case-insensitive) and
not 'Transportation'. Notice, the order of words as they appear in label
path is not important !
</para>
</listitem>
</itemizedlist>
</sect2>
<sect2>
<title>Operations</title>
<para>
The following operations are defined for type ltree:
</para>
<itemizedlist>
<listitem>
<para>
<literal><,>,<=,>=,=, <></literal>
- Have their usual meanings. Comparison is doing in the order of direct
tree traversing, children of a node are sorted lexicographic.
</para>
</listitem>
<listitem>
<para>
<literal>ltree @> ltree</literal>
- returns TRUE if left argument is an ancestor of right argument (or
equal).
</para>
</listitem>
<listitem>
<para>
<literal>ltree <@ ltree </literal>
- returns TRUE if left argument is a descendant of right argument (or
equal).
</para>
</listitem>
<listitem>
<para>
<literal>ltree ~ lquery, lquery ~ ltree</literal>
- return TRUE if node represented by ltree satisfies lquery.
</para>
</listitem>
<listitem>
<para>
<literal>ltree ? lquery[], lquery ? ltree[]</literal>
- return TRUE if node represented by ltree satisfies at least one lquery
from array.
</para>
</listitem>
<listitem>
<para>
<literal>ltree @ ltxtquery, ltxtquery @ ltree</literal>
- return TRUE if node represented by ltree satisfies ltxtquery.
</para>
</listitem>
<listitem>
<para>
<literal>ltree || ltree, ltree || text, text || ltree</literal>
- return concatenated ltree.
</para>
</listitem>
</itemizedlist>
<para>
Operations for arrays of ltree (<literal>ltree[]</literal>):
</para>
<itemizedlist>
<listitem>
<para>
<literal>ltree[] @> ltree, ltree <@ ltree[]</literal>
- returns TRUE if array ltree[] contains an ancestor of ltree.
</para>
</listitem>
<listitem>
<para>
<literal>ltree @> ltree[], ltree[] <@ ltree</literal>
- returns TRUE if array ltree[] contains a descendant of ltree.
</para>
</listitem>
<listitem>
<para>
<literal>ltree[] ~ lquery, lquery ~ ltree[]</literal>
- returns TRUE if array ltree[] contains label paths matched lquery.
</para>
</listitem>
<listitem>
<para>
<literal>ltree[] ? lquery[], lquery[] ? ltree[]</literal>
- returns TRUE if array ltree[] contains label paths matched atleaset one
lquery from array.
</para>
</listitem>
<listitem>
<para>
<literal>ltree[] @ ltxtquery, ltxtquery @ ltree[]</literal>
- returns TRUE if array ltree[] contains label paths matched ltxtquery
(full text search).
</para>
</listitem>
<listitem>
<para>
<literal>ltree[] ?@> ltree, ltree ?<@ ltree[], ltree[] ?~ lquery, ltree[] ?@ ltxtquery</literal>
- returns first element of array ltree[] satisfies corresponding condition
and NULL in vice versa.
</para>
</listitem>
</itemizedlist>
</sect2>
<sect2>
<title>Remark</title>
<para>
Operations <literal>&lt;@</literal>, <literal>@&gt;</literal>, <literal>@</literal> and
<literal>~</literal> have analogues - <literal>^&lt;@, ^@&gt;, ^@, ^~,</literal> which don't use
indices!
</para>
</sect2>
<sect2>
<title>Indices</title>
<para>
Various indices could be created to speed up execution of operations:
</para>
<itemizedlist>
<listitem>
<para>
B-tree index over ltree: <literal>&lt;, &lt;=, =, &gt;=, &gt;</literal>
</para>
</listitem>
<listitem>
<para>
GiST index over ltree: <literal>&lt;, &lt;=, =, &gt;=, &gt;, @&gt;, &lt;@, @, ~, ?</literal>
</para>
<para>
Example:
</para>
<programlisting>
CREATE INDEX path_gist_idx ON test USING GIST (path);
</programlisting>
</listitem>
<listitem>
<para>GiST index over ltree[]:
<literal>ltree[]<@ ltree, ltree @> ltree[], @, ~, ?.</literal>
</para>
<para>
Example:
</para>
<programlisting>
CREATE INDEX path_gist_idx ON test USING GIST (array_path);
</programlisting>
<para>
Notices: This index is lossy.
</para>
</listitem>
</itemizedlist>
</sect2>
<sect2>
<title>Functions</title>
<itemizedlist>
<listitem>
<para>
<literal>ltree subltree(ltree, start, end)</literal>
returns subpath of ltree from start (inclusive) until the end.
</para>
<programlisting>
# select subltree('Top.Child1.Child2',1,2);
subltree
--------
Child1
</programlisting>
</listitem>
<listitem>
<para>
<literal>ltree subpath(ltree, OFFSET,LEN)</literal> and
<literal>ltree subpath(ltree, OFFSET)</literal>
returns subpath of ltree from OFFSET (inclusive) with length LEN.
If OFFSET is negative returns subpath starts that far from the end
of the path. If LENGTH is omitted, returns everything to the end
of the path. If LENGTH is negative, leaves that many labels off
the end of the path.
</para>
<programlisting>
# select subpath('Top.Child1.Child2',1,2);
subpath
-------
Child1.Child2
# select subpath('Top.Child1.Child2',-2,1);
subpath
---------
Child1
</programlisting>
</listitem>
<listitem>
<para>
<literal>int4 nlevel(ltree)</literal> - returns level of the node.
</para>
<programlisting>
# select nlevel('Top.Child1.Child2');
nlevel
--------
3
</programlisting>
<para>
Note, that arguments start, end, OFFSET, LEN have meaning of level of the
node !
</para>
</listitem>
<listitem>
<para>
<literal>int4 index(ltree,ltree)</literal> and
<literal>int4 index(ltree,ltree,OFFSET)</literal>
returns number of level of the first occurence of second argument in first
one beginning from OFFSET. if OFFSET is negative, than search begins from |
OFFSET| levels from the end of the path.
</para>
<programlisting>
SELECT index('0.1.2.3.5.4.5.6.8.5.6.8','5.6',3);
index
-------
6
SELECT index('0.1.2.3.5.4.5.6.8.5.6.8','5.6',-4);
index
-------
9
</programlisting>
</listitem>
<listitem>
<para>
<literal>ltree text2ltree(text)</literal> and
<literal>text ltree2text(text)</literal> cast functions for ltree and text.
</para>
</listitem>
<listitem>
<para>
<literal>ltree lca(ltree,ltree,...) (up to 8 arguments)</literal> and
<literal>ltree lca(ltree[])</literal> Returns Lowest Common Ancestor (lca).
</para>
<programlisting>
# select lca('1.2.2.3','1.2.3.4.5.6');
lca
-----
1.2
# select lca('{la.2.3,1.2.3.4.5.6}') is null;
?column?
----------
f
</programlisting>
</listitem>
</itemizedlist>
</sect2>
<sect2>
<title>Installation</title>
<programlisting>
cd contrib/ltree
make
make install
make installcheck
</programlisting>
</sect2>
<sect2>
<title>Example</title>
<programlisting>
createdb ltreetest
psql ltreetest < /usr/local/pgsql/share/contrib/ltree.sql
psql ltreetest < ltreetest.sql
</programlisting>
<para>
Now, we have a database ltreetest populated with a data describing hierarchy
shown below:
</para>
<programlisting>
TOP
/ | \
Science Hobbies Collections
/ | \
Astronomy Amateurs_Astronomy Pictures
/ \ |
Astrophysics Cosmology Astronomy
/ | \
Galaxies Stars Astronauts
</programlisting>
<para>
Inheritance:
</para>
<programlisting>
ltreetest=# select path from test where path <@ 'Top.Science';
path
------------------------------------
Top.Science
Top.Science.Astronomy
Top.Science.Astronomy.Astrophysics
Top.Science.Astronomy.Cosmology
(4 rows)
</programlisting>
<para>
Matching:
</para>
<programlisting>
ltreetest=# 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=# select path from test where path ~ '*.!pictures@.*.Astronomy.*';
path
------------------------------------
Top.Science.Astronomy
Top.Science.Astronomy.Astrophysics
Top.Science.Astronomy.Cosmology
(3 rows)
</programlisting>
<para>
Full text search:
</para>
<programlisting>
ltreetest=# select path from test where path @ 'Astro*% & !pictures@';
path
------------------------------------
Top.Science.Astronomy
Top.Science.Astronomy.Astrophysics
Top.Science.Astronomy.Cosmology
Top.Hobbies.Amateurs_Astronomy
(4 rows)
ltreetest=# select path from test where path @ 'Astro* & !pictures@';
path
------------------------------------
Top.Science.Astronomy
Top.Science.Astronomy.Astrophysics
Top.Science.Astronomy.Cosmology
(3 rows)
</programlisting>
<para>
Using Functions:
</para>
<programlisting>
ltreetest=# select subpath(path,0,2)||'Space'||subpath(path,2) from test where path <@ 'Top.Science.Astronomy';
?column?
------------------------------------------
Top.Science.Space.Astronomy
Top.Science.Space.Astronomy.Astrophysics
Top.Science.Space.Astronomy.Cosmology
(3 rows)
We could create SQL-function:
CREATE FUNCTION ins_label(ltree, int4, text) RETURNS ltree
AS 'select subpath($1,0,$2) || $3 || subpath($1,$2);'
LANGUAGE SQL IMMUTABLE;
</programlisting>
<para>
and previous select could be rewritten as:
</para>
<programlisting>
ltreetest=# select ins_label(path,2,'Space') from test where path <@ 'Top.Science.Astronomy';
ins_label
------------------------------------------
Top.Science.Space.Astronomy
Top.Science.Space.Astronomy.Astrophysics
Top.Science.Space.Astronomy.Cosmology
(3 rows)
</programlisting>
<para>
Or with another arguments:
</para>
<programlisting>
CREATE FUNCTION ins_label(ltree, ltree, text) RETURNS ltree
AS 'select subpath($1,0,nlevel($2)) || $3 || subpath($1,nlevel($2));'
LANGUAGE SQL IMMUTABLE;
ltreetest=# select ins_label(path,'Top.Science'::ltree,'Space') from test where path <@ 'Top.Science.Astronomy';
ins_label
------------------------------------------
Top.Science.Space.Astronomy
Top.Science.Space.Astronomy.Astrophysics
Top.Science.Space.Astronomy.Cosmology
(3 rows)
</programlisting>
</sect2>
<sect2>
<title>Additional data</title>
<para>
To get more feeling from our ltree module you could download
dmozltree-eng.sql.gz (about 3Mb tar.gz archive containing 300,274 nodes),
available from
<ulink url="http://www.sai.msu.su/~megera/postgres/gist/ltree/"></ulink>
dmozltree-eng.sql.gz, which is DMOZ catalogue, prepared for use with ltree.
Setup your test database (dmoz), load ltree module and issue command:
</para>
<programlisting>
zcat dmozltree-eng.sql.gz| psql dmoz
</programlisting>
<para>
Data will be loaded into database dmoz and all indices will be created.
</para>
</sect2>
<sect2>
<title>Benchmarks</title>
<para>
All runs were performed on my IBM ThinkPad T21 (256 MB RAM, 750Mhz) using DMOZ
data, containing 300,274 nodes (see above for download link). We used some
basic queries typical for walking through catalog.
</para>
<sect3>
<title>Queries</title>
<itemizedlist>
<listitem>
<para>
Q0: Count all rows (sort of base time for comparison)
</para>
<programlisting>
select count(*) from dmoz;
count
--------
300274
(1 row)
</programlisting>
</listitem>
<listitem>
<para>
Q1: Get direct children (without inheritance)
</para>
<programlisting>
select path from dmoz where path ~ 'Top.Adult.Arts.Animation.*{1}';
path
-----------------------------------
Top.Adult.Arts.Animation.Cartoons
Top.Adult.Arts.Animation.Anime
(2 rows)
</programlisting>
</listitem>
<listitem>
<para>
Q2: The same as Q1 but with counting of successors
</para>
<programlisting>
select path as parentpath , (select count(*)-1 from dmoz where path <@
p.path) as count from dmoz p where path ~ 'Top.Adult.Arts.Animation.*{1}';
parentpath | count
-----------------------------------+-------
Top.Adult.Arts.Animation.Cartoons | 2
Top.Adult.Arts.Animation.Anime | 61
(2 rows)
</programlisting>
</listitem>
<listitem>
<para>
Q3: Get all parents
</para>
<programlisting>
select path from dmoz where path @> 'Top.Adult.Arts.Animation' order by
path asc;
path
--------------------------
Top
Top.Adult
Top.Adult.Arts
Top.Adult.Arts.Animation
(4 rows)
</programlisting>
</listitem>
<listitem>
<para>
Q4: Get all parents with counting of children
</para>
<programlisting>
select path, (select count(*)-1 from dmoz where path <@ p.path) as count
from dmoz p where path @> 'Top.Adult.Arts.Animation' order by path asc;
path | count
--------------------------+--------
Top | 300273
Top.Adult | 4913
Top.Adult.Arts | 339
Top.Adult.Arts.Animation | 65
(4 rows)
</programlisting>
</listitem>
<listitem>
<para>
Q5: Get all children with levels
</para>
<programlisting>
select path, nlevel(path) - nlevel('Top.Adult.Arts.Animation') as level
from dmoz where path ~ 'Top.Adult.Arts.Animation.*{1,2}' order by path asc;
path | level
------------------------------------------------+-------
Top.Adult.Arts.Animation.Anime | 1
Top.Adult.Arts.Animation.Anime.Fan_Works | 2
Top.Adult.Arts.Animation.Anime.Games | 2
Top.Adult.Arts.Animation.Anime.Genres | 2
Top.Adult.Arts.Animation.Anime.Image_Galleries | 2
Top.Adult.Arts.Animation.Anime.Multimedia | 2
Top.Adult.Arts.Animation.Anime.Resources | 2
Top.Adult.Arts.Animation.Anime.Titles | 2
Top.Adult.Arts.Animation.Cartoons | 1
Top.Adult.Arts.Animation.Cartoons.AVS | 2
Top.Adult.Arts.Animation.Cartoons.Members | 2
(11 rows)
</programlisting>
</listitem>
</itemizedlist>
</sect3>
<sect3>
<title>Timings</title>
<programlisting>
+---------------------------------------------+
|Query|Rows|Time (ms) index|Time (ms) no index|
|-----+----+---------------+------------------|
| Q0| 1| NA| 1453.44|
|-----+----+---------------+------------------|
| Q1| 2| 0.49| 1001.54|
|-----+----+---------------+------------------|
| Q2| 2| 1.48| 3009.39|
|-----+----+---------------+------------------|
| Q3| 4| 0.55| 906.98|
|-----+----+---------------+------------------|
| Q4| 4| 24385.07| 4951.91|
|-----+----+---------------+------------------|
| Q5| 11| 0.85| 1003.23|
+---------------------------------------------+
</programlisting>
<para>
Timings without indices were obtained using operations which doesn't use
indices (see above)
</para>
</sect3>
<sect3>
<title>Remarks</title>
<para>
We didn't run full-scale tests, also we didn't present (yet) data for
operations with arrays of ltree (ltree[]) and full text searching. We'll
appreciate your input. So far, below some (rather obvious) results:
</para>
<itemizedlist>
<listitem>
<para>
Indices does help execution of queries
</para>
</listitem>
<listitem>
<para>
Q4 performs bad because one needs to read almost all data from the HDD
</para>
</listitem>
</itemizedlist>
</sect3>
</sect2>
<sect2>
<title>Some Backgrounds</title>
<para>
The approach we use for ltree is much like one we used in our other GiST based
contrib modules (intarray, tsearch, tree, btree_gist, rtree_gist). Theoretical
background is available in papers referenced from our GiST development page
(<ulink url="http://www.sai.msu.su/~megera/postgres/gist"></ulink>).
</para>
<para>
A hierarchical data structure (tree) is a set of nodes. Each node has a
signature (LPS) of a fixed size, which is a hashed label path of that node.
Traversing a tree we could *certainly* prune branches if
</para>
<programlisting>
LQS (bitwise AND) LPS != LQS
</programlisting>
<para>
where LQS is a signature of lquery or ltxtquery, obtained in the same way as
LPS.
</para>
<programlisting>
ltree[]:
</programlisting>
<para>
For array of ltree LPS is a bitwise OR-ed signatures of *ALL* children
reachable from that node. Signatures are stored in RD-tree, implemented using
GiST, which provides indexed access.
</para>
<programlisting>
ltree:
</programlisting>
<para>
For ltree we store LPS in a B-tree, implemented using GiST. Each node entry is
represented by (left_bound, signature, right_bound), so that we could speedup
operations <literal><, <=, =, >=, ></literal> using left_bound, right_bound and prune branches of
a tree using signature.
</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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