├── .gitignore
├── LICENSE.md
├── README.md
├── generate-btree-graph.sh
├── generate-demo-graphs.sh
├── graphviz-query.sql
├── leaf-page-split.dot
├── lehman-yao-orthodox-btree-suffix-short.dot
├── lehman-yao-orthodox-btree-suffix.dot
├── lehman-yao-orthodox-btree.dot
├── optimized-leaf-page-split-1.dot
├── optimized-leaf-page-split-2.dot
├── optimized-leaf-page-split-3.dot
├── pg_query_internals.sql
├── postgres-real-btree.dot
├── unoptimized-leaf-page-split-1.dot
├── unoptimized-leaf-page-split-2.dot
└── unoptimized-leaf-page-split-3.dot


/.gitignore:
--------------------------------------------------------------------------------
1 | *.svg
2 | *.pdf
3 | *.swp
4 | 


--------------------------------------------------------------------------------
/LICENSE.md:
--------------------------------------------------------------------------------
 1 | Copyright (c) 2016, Peter Geoghegan
 2 | 
 3 | Permission to use, copy, modify, and distribute this software and its
 4 | documentation for any purpose, without fee, and without a written agreement
 5 | is hereby granted, provided that the above copyright notice and this
 6 | paragraph and the following two paragraphs appear in all copies.
 7 | 
 8 | IN NO EVENT SHALL THE UNIVERSITY OF CALIFORNIA BE LIABLE TO ANY PARTY FOR
 9 | DIRECT, INDIRECT, SPECIAL, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, INCLUDING
10 | LOST PROFITS, ARISING OUT OF THE USE OF THIS SOFTWARE AND ITS
11 | DOCUMENTATION, EVEN IF THE UNIVERSITY OF CALIFORNIA HAS BEEN ADVISED OF THE
12 | POSSIBILITY OF SUCH DAMAGE.
13 | 
14 | THE UNIVERSITY OF CALIFORNIA SPECIFICALLY DISCLAIMS ANY WARRANTIES,
15 | INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY
16 | AND FITNESS FOR A PARTICULAR PURPOSE.  THE SOFTWARE PROVIDED HEREUNDER IS
17 | ON AN "AS IS" BASIS, AND THE UNIVERSITY OF CALIFORNIA HAS NO OBLIGATIONS TO
18 | PROVIDE MAINTENANCE, SUPPORT, UPDATES, ENHANCEMENTS, OR MODIFICATIONS.
19 | 


--------------------------------------------------------------------------------
/README.md:
--------------------------------------------------------------------------------
 1 | # pg_query_internals: Query PostgreSQL internals using SQL
 2 | 
 3 | Current version: 0.2
 4 | 
 5 | Author: Peter Geoghegan [`<pg@bowt.ie>`](mailto:pg@bowt.ie)
 6 | 
 7 | License: <a href="https://opensource.org/licenses/postgresql">PostgreSQL license</a>
 8 | 
 9 | Minimum supported version: PostgreSQL 9.5 (most things work on earlier versions, though)
10 | 
11 | Requires: <a href="https://www.postgresql.org/docs/current/static/pageinspect.html">contrib/pageinspect</a>,
12 | <a href="https://www.postgresql.org/docs/current/static/pgbuffercache.html">contrib/pg_buffercache</a>
13 | 
14 | ## Overview
15 | 
16 | `pg_query_internals` is a collection of SQL queries that are useful for
17 | inspecting the state of a PostgreSQL database.  SQL queries for querying the
18 | contents of the buffer cache are provided, as well as for querying the
19 | structure of a given B-Tree index, and how the index is cached.
20 | 
21 | These queries are published for educational purposes only; they are not
22 | designed for production use.  These queries may have some hard-coded
23 | assumptions about the underlying data being queried, although that is generally
24 | directly noted in comments.  While the queries may be useful as a starting
25 | point for certain types of low-level investigations, they are generally not
26 | usable as instrumentation to find issues in production systems.
27 | 
28 | In short, the SQL queries are written for those with a specific interest in
29 | PostgreSQL internals, and in particular the internals of the B-Tree access
30 | method and PostgreSQL buffer manager.
31 | 
32 | ### Usage
33 | 
34 | The SQL queries within `pg_query_internals.sql` are intended to be run on an
35 | ad-hoc basis.  The queries are deliberatly not packaged as functions within an
36 | extension.
37 | 
38 | ### Graphviz
39 | 
40 | The SQL query within `graphviz-query.sql` can be used to generate a graph of a
41 | PostgreSQL B-Tree using graphviz.  The bash script `generate-btree-graph.sh`
42 | gives an example of how this can be coordinated and managed.
43 | 
44 | This is based on a much earlier approach by Heikki Linnakangas.
45 | 
46 | ### Other resources
47 | 
48 | For those that wish to learn more about PostgreSQL B-Tree indexes, the
49 | following resources are suggested:
50 | 
51 | * The blogpost "Discovering the Computer Science Behind Postgres Indexes", by
52 |   Pat Shaughnessy:
53 | 
54 | http://patshaughnessy.net/2014/11/11/discovering-the-computer-science-behind-postgres-indexes
55 | 
56 | Good high-level overview.
57 | 
58 | * The PostgreSQL nbtree README.
59 | 
60 | The authoritative source of information on PostgreSQL B-Tree indexes.
61 | 
62 | * The paper "A symmetric concurrent B-tree algorithm", from Lanin & Shasha.
63 | 
64 | This is the paper that the PostgreSQL page deletion (and page recycling)
65 | algorithm is based on.  Although this isn't the original Lehman & Yao B-Tree
66 | paper that first described the optimistic technique used to avoid "crabbing" of
67 | buffer locks (these locks are sometimes called "latches" in the literature),
68 | it is the more useful resource in my opinion.  Note that the algorithm is
69 | implemented in a slightly different manner in PostgreSQL, though the
70 | differences that are directly noted in the nbtree README.
71 | 
72 | Lanin & Shasha's paper is of far more practical use to implementers, who may
73 | consider skipping the Lehman & Yao paper entirely.  For example, it
74 | specifically takes issue with a strange tacit assumption made by the Lehman &
75 | Yao paper: the assumption that page reads and writes are always atomic.  This
76 | assumption justifies the Lehman & Yao contention that their algorithm requires
77 | *no* locks during index scans.  This claim is rather a lot stronger than the
78 | claim that only one lock is required at a time during a descent of the B-Tree,
79 | which is all that PostgreSQL manages, and all that Lanin & Shasha see fit to
80 | claim for their enhanced algorithm.
81 | 
82 | The Lanin & Shasha paper actually describes a practical deletion algorithm,
83 | rather than assuming that in general page deletion can happen during a period
84 | in which the system is offline, as Lehman & Yao rather fancifully suggest.
85 | Since all practical requirements are met at once, the Lanin & Shasha design is
86 | a truly comprehensive guide to implementing a real-world, high concurrency
87 | B-Tree structure.
88 | 
89 | * "The Internals of PostgreSQL" website:
90 | 
91 | http://www.interdb.jp/pg/index.html
92 | 
93 | This website is a good general starting point for learning about PostgreSQL
94 | internals more generally.
95 | 


--------------------------------------------------------------------------------
/generate-btree-graph.sh:
--------------------------------------------------------------------------------
 1 | #!/bin/bash
 2 | #
 3 | # Generate an svg image of the B-Tree index specified within
 4 | # graphviz-query.sql.
 5 | #
 6 | # Assumes that psql and graphviz dot are in $PATH
 7 | 
 8 | echo "generating dot file..."
 9 | time psql -f graphviz-query.sql --no-psqlrc --no-align -t > /tmp/query-btree.dot
10 | echo "generating svg file..."
11 | time dot -T svg /tmp/query-btree.dot -o /tmp/query-btree.svg
12 | 


--------------------------------------------------------------------------------
/generate-demo-graphs.sh:
--------------------------------------------------------------------------------
 1 | #!/bin/bash
 2 | #
 3 | rm *.pdf
 4 | NAME="lehman-yao-orthodox-btree"
 5 | echo "Generating __$NAME.pdf..."
 6 | dot -T pdf "$NAME.dot" -o "__$NAME.pdf"
 7 | NAME="lehman-yao-orthodox-btree-suffix"
 8 | echo "Generating __$NAME.pdf..."
 9 | dot -T pdf "$NAME.dot" -o "__$NAME.pdf"
10 | NAME="lehman-yao-orthodox-btree-suffix-short"
11 | echo "Generating __$NAME.pdf..."
12 | dot -T pdf "$NAME.dot" -o "__$NAME.pdf"
13 | NAME="postgres-real-btree"
14 | echo "Generating __$NAME.pdf..."
15 | dot -T pdf "$NAME.dot" -o "__$NAME.pdf"
16 | 
17 | # Initial leaf page, about to be split
18 | NAME="leaf-page-split"
19 | echo "Generating __$NAME.pdf..."
20 | dot -T pdf "$NAME.dot" -o "__$NAME.pdf"
21 | 
22 | # Unoptimized:
23 | NAME="unoptimized-leaf-page-split-1"
24 | echo "Generating __$NAME.pdf..."
25 | dot -T pdf "$NAME.dot" -o "__$NAME.pdf"
26 | NAME="unoptimized-leaf-page-split-2"
27 | echo "Generating __$NAME.pdf..."
28 | dot -T pdf "$NAME.dot" -o "__$NAME.pdf"
29 | NAME="unoptimized-leaf-page-split-3"
30 | echo "Generating __$NAME.pdf..."
31 | dot -T pdf "$NAME.dot" -o "__$NAME.pdf"
32 | 
33 | # Optimized:
34 | NAME="optimized-leaf-page-split-1"
35 | echo "Generating __$NAME.pdf..."
36 | dot -T pdf "$NAME.dot" -o "__$NAME.pdf"
37 | NAME="optimized-leaf-page-split-2"
38 | echo "Generating __$NAME.pdf..."
39 | dot -T pdf "$NAME.dot" -o "__$NAME.pdf"
40 | NAME="optimized-leaf-page-split-3"
41 | echo "Generating __$NAME.pdf..."
42 | dot -T pdf "$NAME.dot" -o "__$NAME.pdf"
43 | 


--------------------------------------------------------------------------------
/graphviz-query.sql:
--------------------------------------------------------------------------------
  1 |   WITH RECURSIVE index_details AS (
  2 |   SELECT
  3 |     'pgbench_accounts_pkey'::text idx
  4 | ),
  5 | size_in_pages_index AS (
  6 |   SELECT
  7 |     (pg_relation_size(idx::regclass) / (2^13))::int4 size_pages
  8 |   FROM
  9 |     index_details
 10 | ),
 11 | page_stats AS (
 12 |   SELECT
 13 |     index_details.*,
 14 |     stats.*
 15 |   FROM
 16 |     index_details,
 17 |     size_in_pages_index,
 18 |     lateral (SELECT i FROM generate_series(1, size_pages - 1) i) series,
 19 |     lateral (SELECT * FROM bt_page_stats(idx, i)) stats
 20 | ),
 21 | meta_stats AS (
 22 |   SELECT
 23 |     *
 24 |   FROM
 25 |     index_details s,
 26 |     lateral (SELECT * FROM bt_metap(s.idx)) meta
 27 | ),
 28 | pages_raw AS (
 29 |   SELECT
 30 |     *
 31 |   FROM
 32 |     page_stats
 33 |   ORDER BY
 34 |     btpo DESC
 35 | ),
 36 | /* XXX: Note ordering dependency within this CTE */
 37 | pages_walk(item, prior, llive_items, blk, level) AS (
 38 |   SELECT
 39 |     1,
 40 |     0,
 41 |     case when btpo_next = 0 then live_items else live_items - 1 end,
 42 |     blkno,
 43 |     btpo
 44 |   FROM
 45 |     pages_raw
 46 |   WHERE
 47 |     btpo_prev = 0
 48 |     AND btpo = (SELECT level FROM meta_stats)
 49 |   UNION
 50 |   SELECT
 51 |     CASE WHEN level = btpo THEN w.item + 1 ELSE 1 END,
 52 |     CASE WHEN level != btpo then 0 else prior + llive_items END,
 53 |     case when btpo_next = 0 then live_items else live_items - 1 end,
 54 |     blkno,
 55 |     btpo
 56 |   FROM
 57 |     pages_raw i,
 58 |     pages_walk w
 59 |   WHERE
 60 |     i.btpo_prev = w.blk OR (btpo_prev = 0 AND btpo = w.level - 1)
 61 | ),
 62 | level_det as (
 63 | SELECT
 64 | format($fff$
 65 | node%1$s_%2$s[ tooltip = "Block %6$s values (high key is positioned at offset 1): &#10;%14$s" label=<<table width="210">
 66 |                   <tr>
 67 |                     -- First item on page
 68 |                     <td bgcolor='%13$s' width="30" port="f0"><font point-size="12">%3$s</font></td>
 69 |                     -- Second item on page
 70 |                     <td bgcolor='%13$s' width="30" port="f1"><font point-size="12">%4$s</font></td>
 71 |                     -- Highkey
 72 |                     <td bgcolor='#E67E22' width="30" port="f2"><font point-size="12">%5$s</font></td>
 73 |                     -- Gray box with details
 74 |                     <td bgcolor='#ECF0F1' width="120"><b><font point-size="8">Level %1$s logical page %2$s</font></b><br/><br/>Block number: %6$s<br/>live/dead items: %7$s/%8$s<br/>avg tuple width: %9$s<br/>distinct keys (no highkey): %10$s<br/>distinct block pointers: %11$s<br/>free size: %12$s</td>
 75 |                   </tr>
 76 |               </table>
 77 |              >
 78 |         ];
 79 | $fff$,
 80 | btpo, item,
 81 | /* First item */
 82 | CASE WHEN btpo != 0 THEN '-&infin;' when btpo_next = 0 then int4_from_page_data(all_items[1])::text else int4_from_page_data(all_items[2])::text end,
 83 | /* Second item */
 84 | CASE WHEN btpo_next = 0 then int4_from_page_data(all_items[2])::text else int4_from_page_data(all_items[3])::text end,
 85 | /* High key */
 86 | coalesce(CASE WHEN btpo_next != 0 THEN int4_from_page_data(all_items[1])::text END, '+&infin;'),
 87 | /* Page details */
 88 | blkno::text, live_items, dead_items, avg_item_size, distinct_real_item_keys, distinct_block_pointers, free_size,
 89 | /* Appropriate HTML color for first and second items */
 90 | case when btpo != 0 then '#F1C40F'::text else '#2ECC71'::text end,
 91 | /*
 92 |  * Tooltip values, for each page.  Doesn't seem worth using
 93 |  * int4_from_page_data() here, as that's very slow.
 94 |  */
 95 | array_to_string(all_items, '; ')
 96 | ) ||
 97 | -- Use logical block numbers to build downlinks to children
 98 | --
 99 | -- XXX: This is probably broken by page deletion, where there is no downlink in
100 | -- parent but child still has sibling pointers.  It's probably possible to fix
101 | -- this by skipping deleted pages.
102 | case when btpo != 0 then
103 |   (select string_agg(format('"node%s_%s" -> "node%s_%s":f0 ', btpo, item, btpo - 1, gg), E'\n')
104 |    from
105 |    generate_series(prior +1, prior + distinct_block_pointers) gg)
106 | else
107 |   ''
108 | end ||
109 | -- sibling pointer:
110 | case when btpo_next != 0 then
111 |   (select format(E'\n\n"node%1$s_%2$s" -> "node%1$s_%3$s"[constraint=false,color=gray,style=dashed,arrowsize=0.5]', btpo, item, item + 1))
112 | else
113 |   ''
114 | end
115 | as all_level_details,
116 | 
117 | btpo, item
118 | FROM
119 |   pages_walk w,
120 |   pages_raw i,
121 |   lateral (
122 |     SELECT
123 |     COUNT(DISTINCT (CASE WHEN btpo_next = 0 OR itemoffset > 1 THEN (DATA COLLATE "C") END)) AS distinct_real_item_keys,
124 |     COUNT(DISTINCT (CASE WHEN btpo_next = 0 OR itemoffset > 1 THEN (ctid::text::point)[0]::BIGINT END)) AS distinct_block_pointers,
125 |     /* Note: displaying all values as int4 takes rather a long time */
126 |     array_agg(nullif(data, '')) AS all_items
127 |     FROM bt_page_items(idx, blkno)
128 |   ) items
129 |   WHERE w.blk = i.blkno
130 |   /* Uncomment to avoid showing leaf level (faster): */
131 |   /* and level > 0*/
132 | ORDER BY btpo DESC, item
133 | )
134 | select
135 | $digraph$
136 | digraph nbtree {
137 | graph [fontname = "monospace"];
138 | node [shape = none,height=.1,fontname = "monospace",fontsize=6];
139 | edge [penwidth=0.5]
140 | $digraph$
141 | union all
142 | select * from (select all_level_details from level_det order by btpo DESC, item) a
143 | union all
144 | select '}';
145 | 


--------------------------------------------------------------------------------
/leaf-page-split.dot:
--------------------------------------------------------------------------------
 1 | // Example B-Tree graph
 2 | //
 3 | // Breadth-first order
 4 | //
 5 | // Start from root, go left to right
 6 | //
 7 | // Workflow:
 8 | //
 9 | // $ dot -T svg btree.dot -o btree.svg;
10 | 
11 | digraph nbtree {
12 | graph [fontname = "monospace"];
13 | node [shape = none,height=.1,fontname = "monospace",fontsize=18];
14 | // Level 0 (leaf level)
15 | leafnode_1[ label=<<table width="200">
16 |                     <tr>
17 |                         <td bgcolor='darkseagreen1' port="t2" width="50"><font color="magenta">1</font>,1</td>
18 |                         <td bgcolor='darkseagreen1' port="t3" width="50"><font color="magenta">1</font>,2</td>
19 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,3</td>
20 |                         <!-- <td align="center" border="0" bgcolor='white' port="t6">&#9986;</td> -->
21 |                         <td bgcolor='darkseagreen1' port="t7" width="50"><font color="blue">2</font>,1</td>
22 |                     </tr>
23 |                 </table>
24 |                >
25 |         ];
26 | //Force alignment from root to internal to leaf levels:
27 | //edge[style=invis];
28 | //"rootnode":d1 -> "leafnode_2":t2
29 | }
30 | 


--------------------------------------------------------------------------------
/lehman-yao-orthodox-btree-suffix-short.dot:
--------------------------------------------------------------------------------
  1 | // Example B-Tree graph
  2 | //
  3 | // Breadth-first order
  4 | //
  5 | // Start from root, go left to right
  6 | //
  7 | // Workflow:
  8 | //
  9 | // $ dot -T svg btree.dot -o btree.svg;
 10 | 
 11 | digraph nbtree {
 12 | graph [fontname = "monospace"];
 13 | node [shape = none,height=.1,fontname = "monospace",fontsize=8];
 14 | // Level 1 (root level)
 15 | // Downlinks + highkey:
 16 | rootnode[ label=<<table>
 17 |                     <tr>
 18 |                         <td bgcolor='burlywood' port="s0">-&infin;</td>
 19 |                         <td bgcolor='white' port="d0">&#8615;</td>
 20 |                         <td bgcolor='burlywood' port="s1">D</td>
 21 |                         <td bgcolor='white' port="d1">&#8615;</td>
 22 |                         <td bgcolor='burlywood' port="s2">G</td>
 23 |                         <td bgcolor='white' port="d2">&#8615;</td>
 24 |                         <td bgcolor='burlywood' port="s3">N</td>
 25 |                         <td bgcolor='white' port="d3">&#8615;</td>
 26 |                         <td bgcolor='burlywood' port="s4">P</td>
 27 |                         <td bgcolor='white' port="d4">&#8615;</td>
 28 |                         <td bgcolor='burlywood' port="s5">T</td>
 29 |                         <td bgcolor='white' port="d5">&#8615;</td>
 30 |                         <td bgcolor='burlywood' port="s6">Y</td>
 31 |                         <td bgcolor='white' port="d6">&#8615;</td>
 32 |                         <td bgcolor='burlywood' port="hk">+&infin;</td>
 33 |                     </tr>
 34 |                 </table>
 35 |                >
 36 |         ];
 37 | // Downlink arrows to children:
 38 | "rootnode":d0 -> "leafnode_1"
 39 | "rootnode":d1 -> "leafnode_2"
 40 | "rootnode":d2 -> "leafnode_3"
 41 | "rootnode":d3 -> "leafnode_4"
 42 | // Still need this, to make arrows not overlap too much:
 43 | "rootnode":d4 -> "leafnode_5":t0
 44 | "rootnode":d5 -> "leafnode_6":t0
 45 | "rootnode":d6 -> "leafnode_7":t0
 46 | 
 47 | // sibling pointer:
 48 | // (None)
 49 | 
 50 | 
 51 | // Level 0 (leaf level)
 52 | leafnode_1[ label=<<table>
 53 |                     <tr>
 54 |                         <td bgcolor='darkseagreen1' port="t0">Alfa</td>
 55 |                         <td bgcolor='darkseagreen1' port="t1">Bravo</td>
 56 |                         <td bgcolor='burlywood' port="hk">D</td>
 57 |                     </tr>
 58 |                 </table>
 59 |                >
 60 |         ];
 61 | // sibling pointer:
 62 | "leafnode_1" -> "leafnode_2"[constraint=false,color=black,style=dashed,arrowsize=0.5]
 63 | leafnode_2[ label=<<table>
 64 |                     <tr>
 65 |                         <td bgcolor='darkseagreen1' port="t0">Delta</td>
 66 |                         <td bgcolor='darkseagreen1' port="t1">Echo</td>
 67 |                         <td bgcolor='darkseagreen1' port="t2">Foxtrot</td>
 68 |                         <td bgcolor='burlywood' port="hk">G</td>
 69 |                     </tr>
 70 |                 </table>
 71 |                >
 72 |         ];
 73 | // sibling pointer:
 74 | "leafnode_2" -> "leafnode_3"[constraint=false,color=black,style=dashed,arrowsize=0.5]
 75 | leafnode_3[ label=<<table>
 76 |                     <tr>
 77 |                         <td bgcolor='darkseagreen1' port="t0">Juliet</td>
 78 |                         <td bgcolor='darkseagreen1' port="t1">Kilo</td>
 79 |                         <td bgcolor='darkseagreen1' port="t2">Lima</td>
 80 |                         <td bgcolor='darkseagreen1' port="t3">Mike</td>
 81 |                         <td bgcolor='burlywood' port="hk">N</td>
 82 |                     </tr>
 83 |                 </table>
 84 |                >
 85 |         ];
 86 | // sibling pointer:
 87 | "leafnode_3" -> "leafnode_4"[constraint=false,color=black,style=dashed,arrowsize=0.5]
 88 | leafnode_4[ label=<<table>
 89 |                     <tr>
 90 |                         <td bgcolor='darkseagreen1' port="t0">November</td>
 91 |                         <td bgcolor='darkseagreen1' port="t1">Oscar</td>
 92 |                         <td bgcolor='burlywood' port="hk">P</td>
 93 |                     </tr>
 94 |                 </table>
 95 |                >
 96 |         ];
 97 | // sibling pointer (not a cousin anymore):
 98 | "leafnode_4" -> "leafnode_5"[constraint=false,color=black,style=dashed,arrowsize=0.5]
 99 | leafnode_5[ label=<<table>
100 |                     <tr>
101 |                         <td bgcolor='darkseagreen1' port="t0">Quebec</td>
102 |                         <td bgcolor='darkseagreen1' port="t1">Romeo</td>
103 |                         <td bgcolor='darkseagreen1' port="t2">Sierra</td>
104 |                         <td bgcolor='burlywood' port="hk">T</td>
105 |                     </tr>
106 |                 </table>
107 |                >
108 |         ];
109 | // sibling pointer:
110 | "leafnode_5" -> "leafnode_6"[constraint=false,color=black,style=dashed,arrowsize=0.5]
111 | leafnode_6[ label=<<table>
112 |                     <tr>
113 |                         <td bgcolor='darkseagreen1' port="t0">Uniform</td>
114 |                         <td bgcolor='darkseagreen1' port="t1">Victor</td>
115 |                         <td bgcolor='darkseagreen1' port="t2">XRay</td>
116 |                         <td bgcolor='burlywood' port="hk">Y</td>
117 |                     </tr>
118 |                 </table>
119 |                >
120 |         ];
121 | // sibling pointer:
122 | "leafnode_6" -> "leafnode_7"[constraint=false,color=black,style=dashed,arrowsize=0.5]
123 | leafnode_7[ label=<<table>
124 |                     <tr>
125 |                         <td bgcolor='darkseagreen1' port="t0">Yankee</td>
126 |                         <td bgcolor='darkseagreen1' port="t1">Zulu</td>
127 |                         <td bgcolor='burlywood' port="hk">+&infin;</td>
128 |                     </tr>
129 |                 </table>
130 |                >
131 |         ];
132 | // sibling pointer:
133 | // (None)
134 | 
135 | //Force alignment from root to internal to leaf levels:
136 | edge[style=invis];
137 | "rootnode":s4 -> "leafnode_4":hk
138 | }
139 | 


--------------------------------------------------------------------------------
/lehman-yao-orthodox-btree-suffix.dot:
--------------------------------------------------------------------------------
  1 | // Example B-Tree graph
  2 | //
  3 | // Breadth-first order
  4 | //
  5 | // Start from root, go left to right
  6 | //
  7 | // Workflow:
  8 | //
  9 | // $ dot -T svg btree.dot -o btree.svg;
 10 | 
 11 | digraph nbtree {
 12 | graph [fontname = "monospace"];
 13 | node [shape = none,height=.1,fontname = "monospace",fontsize=8];
 14 | // Level 2 (Root internal level)
 15 | rootnode[ label=<<table>
 16 |                     <tr>
 17 |                         <td bgcolor='burlywood' port="s0">-&infin;</td>
 18 |                         <td bgcolor='white' port="d0">&#8615;</td>
 19 |                         <td bgcolor='burlywood' port="s1">P</td>
 20 |                         <td bgcolor='white' port="d1">&#8615;</td>
 21 |                         <td bgcolor='burlywood' port="hk">+&infin;</td>
 22 |                     </tr>
 23 |                 </table>
 24 |                >
 25 |         ];
 26 | // Downlink arrows to children:
 27 | "rootnode":d0 -> "leftinternal"
 28 | "rootnode":d1 -> "rightinternal"
 29 | // sibling pointer:
 30 | // (None)
 31 | 
 32 | 
 33 | // Level 1 (Internal level)
 34 | // Downlinks + highkey:
 35 | leftinternal[ label=<<table>
 36 |                     <tr>
 37 |                         <td bgcolor='burlywood' port="s0">-&infin;</td>
 38 |                         <td bgcolor='white' port="d0">&#8615;</td>
 39 |                         <td bgcolor='burlywood' port="s1">D</td>
 40 |                         <td bgcolor='white' port="d1">&#8615;</td>
 41 |                         <td bgcolor='burlywood' port="s2">G</td>
 42 |                         <td bgcolor='white' port="d2">&#8615;</td>
 43 |                         <td bgcolor='burlywood' port="s3">N</td>
 44 |                         <td bgcolor='white' port="d3">&#8615;</td>
 45 |                         <td bgcolor='burlywood' port="hk">P</td>
 46 |                     </tr>
 47 |                 </table>
 48 |                >
 49 |         ];
 50 | // Downlink arrows to children:
 51 | "leftinternal":d0 -> "leftleafnode_1"
 52 | "leftinternal":d1 -> "leftleafnode_2"
 53 | "leftinternal":d2 -> "leftleafnode_3"
 54 | "leftinternal":d3 -> "leftleafnode_4"
 55 | // sibling pointer:
 56 | "leftinternal" -> "rightinternal"[constraint=false,color=black,style=dashed,arrowsize=0.5]
 57 | // Downlinks + highkey:
 58 | rightinternal[ label=<<table>
 59 |                     <tr>
 60 |                         <td bgcolor='burlywood' port="s0">&quot;-&infin;&quot;</td>
 61 |                         <td bgcolor='white' port="d0">&#8615;</td>
 62 |                         <td bgcolor='burlywood' port="s1">T</td>
 63 |                         <td bgcolor='white' port="d1">&#8615;</td>
 64 |                         <td bgcolor='burlywood' port="s2">Y</td>
 65 |                         <td bgcolor='white' port="d2">&#8615;</td>
 66 |                         <td bgcolor='burlywood' port="hk">+&infin;</td>
 67 |                     </tr>
 68 |                 </table>
 69 |                >
 70 |         ];
 71 | // Downlink arrows to children:
 72 | "rightinternal":d0 -> "rightleafnode_1":t0
 73 | "rightinternal":d1 -> "rightleafnode_2":t0
 74 | "rightinternal":d2 -> "rightleafnode_3":t0
 75 | // sibling pointer:
 76 | // (None)
 77 | 
 78 | 
 79 | // Level 0 (leaf level)
 80 | leftleafnode_1[ label=<<table>
 81 |                     <tr>
 82 |                         <td bgcolor='darkseagreen1' port="t0">Alfa</td>
 83 |                         <td bgcolor='darkseagreen1' port="t1">Bravo</td>
 84 |                         <td bgcolor='burlywood' port="hk">D</td>
 85 |                     </tr>
 86 |                 </table>
 87 |                >
 88 |         ];
 89 | // sibling pointer:
 90 | "leftleafnode_1" -> "leftleafnode_2"[constraint=false,color=black,style=dashed,arrowsize=0.5]
 91 | leftleafnode_2[ label=<<table>
 92 |                     <tr>
 93 |                         <td bgcolor='darkseagreen1' port="t0">Delta</td>
 94 |                         <td bgcolor='darkseagreen1' port="t1">Echo</td>
 95 |                         <td bgcolor='darkseagreen1' port="t2">Foxtrot</td>
 96 |                         <td bgcolor='burlywood' port="hk">G</td>
 97 |                     </tr>
 98 |                 </table>
 99 |                >
100 |         ];
101 | // sibling pointer:
102 | "leftleafnode_2" -> "leftleafnode_3"[constraint=false,color=black,style=dashed,arrowsize=0.5]
103 | leftleafnode_3[ label=<<table>
104 |                     <tr>
105 |                         <td bgcolor='darkseagreen1' port="t0">Juliet</td>
106 |                         <td bgcolor='darkseagreen1' port="t1">Kilo</td>
107 |                         <td bgcolor='darkseagreen1' port="t2">Lima</td>
108 |                         <td bgcolor='darkseagreen1' port="t3">Mike</td>
109 |                         <td bgcolor='burlywood' port="hk">N</td>
110 |                     </tr>
111 |                 </table>
112 |                >
113 |         ];
114 | // sibling pointer:
115 | "leftleafnode_3" -> "leftleafnode_4"[constraint=false,color=black,style=dashed,arrowsize=0.5]
116 | leftleafnode_4[ label=<<table>
117 |                     <tr>
118 |                         <td bgcolor='darkseagreen1' port="t0">November</td>
119 |                         <td bgcolor='darkseagreen1' port="t1">Oscar</td>
120 |                         <td bgcolor='burlywood' port="hk">P</td>
121 |                     </tr>
122 |                 </table>
123 |                >
124 |         ];
125 | // sibling/cousin pointer:
126 | "leftleafnode_4" -> "rightleafnode_1"[constraint=false,color=gray,style=dashed,arrowsize=0.5]
127 | rightleafnode_1[ label=<<table>
128 |                     <tr>
129 |                         <td bgcolor='darkseagreen1' port="t0">Quebec</td>
130 |                         <td bgcolor='darkseagreen1' port="t1">Romeo</td>
131 |                         <td bgcolor='darkseagreen1' port="t2">Sierra</td>
132 |                         <td bgcolor='burlywood' port="hk">T</td>
133 |                     </tr>
134 |                 </table>
135 |                >
136 |         ];
137 | // sibling pointer:
138 | "rightleafnode_1" -> "rightleafnode_2"[constraint=false,color=black,style=dashed,arrowsize=0.5]
139 | rightleafnode_2[ label=<<table>
140 |                     <tr>
141 |                         <td bgcolor='darkseagreen1' port="t0">Uniform</td>
142 |                         <td bgcolor='darkseagreen1' port="t1">Victor</td>
143 |                         <td bgcolor='darkseagreen1' port="t2">XRay</td>
144 |                         <td bgcolor='burlywood' port="hk">Y</td>
145 |                     </tr>
146 |                 </table>
147 |                >
148 |         ];
149 | // sibling pointer:
150 | "rightleafnode_2" -> "rightleafnode_3"[constraint=false,color=black,style=dashed,arrowsize=0.5]
151 | rightleafnode_3[ label=<<table>
152 |                     <tr>
153 |                         <td bgcolor='darkseagreen1' port="t0">Yankee</td>
154 |                         <td bgcolor='darkseagreen1' port="t1">Zulu</td>
155 |                         <td bgcolor='burlywood' port="hk">+&infin;</td>
156 |                     </tr>
157 |                 </table>
158 |                >
159 |         ];
160 | // sibling pointer:
161 | // (None)
162 | 
163 | // Force alignment from root to internal to leaf levels:
164 | edge[style=invis];
165 | "rootnode":s1 -> "leftleafnode_4":hk
166 | "leftinternal":hk -> "leftleafnode_4":hk
167 | }
168 | 


--------------------------------------------------------------------------------
/lehman-yao-orthodox-btree.dot:
--------------------------------------------------------------------------------
  1 | // Example B-Tree graph
  2 | //
  3 | // Breadth-first order
  4 | //
  5 | // Start from root, go left to right
  6 | //
  7 | // Workflow:
  8 | //
  9 | // $ dot -T svg btree.dot -o btree.svg;
 10 | 
 11 | digraph nbtree {
 12 | graph [fontname = "monospace"];
 13 | node [shape = none,height=.1,fontname = "monospace",fontsize=8];
 14 | // Level 2 (Root internal level)
 15 | rootnode[ label=<<table>
 16 |                     <tr>
 17 |                         <td bgcolor='burlywood' port="s0">-&infin;</td>
 18 |                         <td bgcolor='white' port="d0">&#8615;</td>
 19 |                         <td bgcolor='burlywood' port="s1">Papa</td>
 20 |                         <td bgcolor='white' port="d1">&#8615;</td>
 21 |                         <td bgcolor='burlywood' port="hk">+&infin;</td>
 22 |                     </tr>
 23 |                 </table>
 24 |                >
 25 |         ];
 26 | // Downlink arrows to children:
 27 | "rootnode":d0 -> "leftinternal"
 28 | "rootnode":d1 -> "rightinternal"
 29 | // sibling pointer:
 30 | // (None)
 31 | 
 32 | 
 33 | // Level 1 (Internal level)
 34 | // Downlinks + highkey:
 35 | leftinternal[ label=<<table>
 36 |                     <tr>
 37 |                         <td bgcolor='burlywood' port="s0">-&infin;</td>
 38 |                         <td bgcolor='white' port="d0">&#8615;</td>
 39 |                         <td bgcolor='burlywood' port="s1">Charlie</td>
 40 |                         <td bgcolor='white' port="d1">&#8615;</td>
 41 |                         <td bgcolor='burlywood' port="s2">Golf</td>
 42 |                         <td bgcolor='white' port="d2">&#8615;</td>
 43 |                         <td bgcolor='burlywood' port="s3">Mike</td>
 44 |                         <td bgcolor='white' port="d3">&#8615;</td>
 45 |                         <td bgcolor='burlywood' port="hk">Papa</td>
 46 |                     </tr>
 47 |                 </table>
 48 |                >
 49 |         ];
 50 | // Downlink arrows to children:
 51 | "leftinternal":d0 -> "leftleafnode_1"
 52 | "leftinternal":d1 -> "leftleafnode_2"
 53 | "leftinternal":d2 -> "leftleafnode_3"
 54 | "leftinternal":d3 -> "leftleafnode_4"
 55 | // sibling pointer:
 56 | "leftinternal" -> "rightinternal"[constraint=false,color=black,style=dashed,arrowsize=0.5]
 57 | // Downlinks + highkey:
 58 | rightinternal[ label=<<table>
 59 |                     <tr>
 60 |                         <td bgcolor='burlywood' port="s0">&quot;-&infin;&quot;</td>
 61 |                         <td bgcolor='white' port="d0">&#8615;</td>
 62 |                         <td bgcolor='burlywood' port="s1">Tango</td>
 63 |                         <td bgcolor='white' port="d1">&#8615;</td>
 64 |                         <td bgcolor='burlywood' port="s2">X-Ray</td>
 65 |                         <td bgcolor='white' port="d2">&#8615;</td>
 66 |                         <td bgcolor='burlywood' port="hk">+&infin;</td>
 67 |                     </tr>
 68 |                 </table>
 69 |                >
 70 |         ];
 71 | // Downlink arrows to children:
 72 | "rightinternal":d0 -> "rightleafnode_1":t0
 73 | "rightinternal":d1 -> "rightleafnode_2":t0
 74 | "rightinternal":d2 -> "rightleafnode_3":t0
 75 | // sibling pointer:
 76 | // (None)
 77 | 
 78 | 
 79 | // Level 0 (leaf level)
 80 | leftleafnode_1[ label=<<table>
 81 |                     <tr>
 82 |                         <td bgcolor='darkseagreen1' port="t0">Alfa</td>
 83 |                         <td bgcolor='darkseagreen1' port="t1">Bravo</td>
 84 |                         <td bgcolor='burlywood' port="hk">Charlie</td>
 85 |                     </tr>
 86 |                 </table>
 87 |                >
 88 |         ];
 89 | // sibling pointer:
 90 | "leftleafnode_1" -> "leftleafnode_2"[constraint=false,color=black,style=dashed,arrowsize=0.5]
 91 | leftleafnode_2[ label=<<table>
 92 |                     <tr>
 93 |                         <td bgcolor='darkseagreen1' port="t0">Delta</td>
 94 |                         <td bgcolor='darkseagreen1' port="t1">Echo</td>
 95 |                         <td bgcolor='darkseagreen1' port="t2">Foxtrot</td>
 96 |                         <td bgcolor='burlywood' port="hk">Golf</td>
 97 |                     </tr>
 98 |                 </table>
 99 |                >
100 |         ];
101 | // sibling pointer:
102 | "leftleafnode_2" -> "leftleafnode_3"[constraint=false,color=black,style=dashed,arrowsize=0.5]
103 | leftleafnode_3[ label=<<table>
104 |                     <tr>
105 |                         <td bgcolor='darkseagreen1' port="t0">Juliet</td>
106 |                         <td bgcolor='darkseagreen1' port="t1">Kilo</td>
107 |                         <td bgcolor='darkseagreen1' port="t2">Lima</td>
108 |                         <td bgcolor='darkseagreen1' port="t3">Mike</td>
109 |                         <td bgcolor='burlywood' port="hk">Mike</td>
110 |                     </tr>
111 |                 </table>
112 |                >
113 |         ];
114 | // sibling pointer:
115 | "leftleafnode_3" -> "leftleafnode_4"[constraint=false,color=black,style=dashed,arrowsize=0.5]
116 | leftleafnode_4[ label=<<table>
117 |                     <tr>
118 |                         <td bgcolor='darkseagreen1' port="t0">November</td>
119 |                         <td bgcolor='darkseagreen1' port="t1">Oscar</td>
120 |                         <td bgcolor='burlywood' port="hk">Papa</td>
121 |                     </tr>
122 |                 </table>
123 |                >
124 |         ];
125 | // sibling/cousin pointer:
126 | "leftleafnode_4" -> "rightleafnode_1"[constraint=false,color=gray,style=dashed,arrowsize=0.5]
127 | rightleafnode_1[ label=<<table>
128 |                     <tr>
129 |                         <td bgcolor='darkseagreen1' port="t0">Quebec</td>
130 |                         <td bgcolor='darkseagreen1' port="t1">Romeo</td>
131 |                         <td bgcolor='darkseagreen1' port="t2">Sierra</td>
132 |                         <td bgcolor='burlywood' port="hk">Tango</td>
133 |                     </tr>
134 |                 </table>
135 |                >
136 |         ];
137 | // sibling pointer:
138 | "rightleafnode_1" -> "rightleafnode_2"[constraint=false,color=black,style=dashed,arrowsize=0.5]
139 | rightleafnode_2[ label=<<table>
140 |                     <tr>
141 |                         <td bgcolor='darkseagreen1' port="t0">Uniform</td>
142 |                         <td bgcolor='darkseagreen1' port="t1">Victor</td>
143 |                         <td bgcolor='darkseagreen1' port="t2">XRay</td>
144 |                         <td bgcolor='burlywood' port="hk">XRay</td>
145 |                     </tr>
146 |                 </table>
147 |                >
148 |         ];
149 | // sibling pointer:
150 | "rightleafnode_2" -> "rightleafnode_3"[constraint=false,color=black,style=dashed,arrowsize=0.5]
151 | rightleafnode_3[ label=<<table>
152 |                     <tr>
153 |                         <td bgcolor='darkseagreen1' port="t0">Yankee</td>
154 |                         <td bgcolor='darkseagreen1' port="t1">Zulu</td>
155 |                         <td bgcolor='burlywood' port="hk">+&infin;</td>
156 |                     </tr>
157 |                 </table>
158 |                >
159 |         ];
160 | // sibling pointer:
161 | // (None)
162 | 
163 | // Force alignment from root to internal to leaf levels:
164 | edge[style=invis];
165 | "rootnode":s1 -> "leftleafnode_4":hk
166 | "leftinternal":hk -> "leftleafnode_4":hk
167 | }
168 | 


--------------------------------------------------------------------------------
/optimized-leaf-page-split-1.dot:
--------------------------------------------------------------------------------
 1 | // Example B-Tree graph
 2 | //
 3 | // Breadth-first order
 4 | //
 5 | // Start from root, go left to right
 6 | //
 7 | // Workflow:
 8 | //
 9 | // $ dot -T svg btree.dot -o btree.svg;
10 | 
11 | digraph nbtree {
12 | graph [fontname = "monospace"];
13 | node [shape = none,height=.1,fontname = "monospace",fontsize=18];
14 | // Level 0 (leaf level)
15 | leafnode_2[ label=<<table width="200">
16 |                     <tr>
17 |                         <td bgcolor='darkseagreen1' port="t2" width="50"><font color="magenta">1</font>,1</td>
18 |                         <td bgcolor='darkseagreen1' port="t3" width="50"><font color="magenta">1</font>,2</td>
19 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,3</td>
20 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,4</td>
21 |                     </tr>
22 |                 </table>
23 |                >
24 |         ];
25 | edge[style=invis];
26 | "leafnode_2" -> "leafnode_3"
27 | leafnode_3[ label=<<table width="200">
28 |                     <tr>
29 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,5</td>
30 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,6</td>
31 |                         <td bgcolor='white' port="t3" width="50"></td>
32 |                         <td bgcolor='white' port="t3" width="50"></td>
33 |                     </tr>
34 |                 </table>
35 |                >
36 |         ];
37 | edge[style=invis];
38 | "leafnode_3" -> "leafnode_4"
39 | leafnode_4[ label=<<table width="200">
40 |                     <tr>
41 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="blue">2</font>,1</td>
42 |                         <td bgcolor='white' port="t3" width="50"></td>
43 |                         <td bgcolor='white' port="t3" width="50"></td>
44 |                         <td bgcolor='white' port="t3" width="50"></td>
45 |                     </tr>
46 |                 </table>
47 |                >
48 |         ];
49 | //Force alignment from root to internal to leaf levels:
50 | //edge[style=invis];
51 | //"rootnode":d1 -> "leafnode_2":t2
52 | }
53 | 


--------------------------------------------------------------------------------
/optimized-leaf-page-split-2.dot:
--------------------------------------------------------------------------------
 1 | // Example B-Tree graph
 2 | //
 3 | // Breadth-first order
 4 | //
 5 | // Start from root, go left to right
 6 | //
 7 | // Workflow:
 8 | //
 9 | // $ dot -T svg btree.dot -o btree.svg;
10 | 
11 | digraph nbtree {
12 | graph [fontname = "monospace"];
13 | node [shape = none,height=.1,fontname = "monospace",fontsize=18];
14 | // Level 0 (leaf level)
15 | leafnode_2[ label=<<table width="200">
16 |                     <tr>
17 |                         <td bgcolor='darkseagreen1' port="t2" width="50"><font color="magenta">1</font>,1</td>
18 |                         <td bgcolor='darkseagreen1' port="t3" width="50"><font color="magenta">1</font>,2</td>
19 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,3</td>
20 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,4</td>
21 |                     </tr>
22 |                 </table>
23 |                >
24 |         ];
25 | edge[style=invis];
26 | "leafnode_2" -> "leafnode_3"
27 | leafnode_3[ label=<<table width="200">
28 |                     <tr>
29 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,5</td>
30 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,6</td>
31 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,7</td>
32 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,8</td>
33 |                     </tr>
34 |                 </table>
35 |                >
36 |         ];
37 | edge[style=invis];
38 | "leafnode_3" -> "leafnode_4"
39 | leafnode_4[ label=<<table width="200">
40 |                     <tr>
41 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,9</td>
42 |                         <td bgcolor='white' port="t3" width="50"></td>
43 |                         <td bgcolor='white' port="t3" width="50"></td>
44 |                         <td bgcolor='white' port="t3" width="50"></td>
45 |                     </tr>
46 |                 </table>
47 |                >
48 |         ];
49 | edge[style=invis];
50 | "leafnode_4" -> "leafnode_5"
51 | leafnode_5[ label=<<table width="200">
52 |                     <tr>
53 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="blue">2</font>,1</td>
54 |                         <td bgcolor='white' port="t3" width="50"></td>
55 |                         <td bgcolor='white' port="t3" width="50"></td>
56 |                         <td bgcolor='white' port="t3" width="50"></td>
57 |                     </tr>
58 |                 </table>
59 |                >
60 |         ];
61 | //Force alignment from root to internal to leaf levels:
62 | //edge[style=invis];
63 | //"rootnode":d1 -> "leafnode_2":t2
64 | }
65 | 


--------------------------------------------------------------------------------
/optimized-leaf-page-split-3.dot:
--------------------------------------------------------------------------------
 1 | // Example B-Tree graph
 2 | //
 3 | // Breadth-first order
 4 | //
 5 | // Start from root, go left to right
 6 | //
 7 | // Workflow:
 8 | //
 9 | // $ dot -T svg btree.dot -o btree.svg;
10 | 
11 | digraph nbtree {
12 | graph [fontname = "monospace"];
13 | node [shape = none,height=.1,fontname = "monospace",fontsize=18];
14 | // Level 0 (leaf level)
15 | leafnode_2[ label=<<table width="200">
16 |                     <tr>
17 |                         <td bgcolor='darkseagreen1' port="t2" width="50"><font color="magenta">1</font>,1</td>
18 |                         <td bgcolor='darkseagreen1' port="t3" width="50"><font color="magenta">1</font>,2</td>
19 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,3</td>
20 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,4</td>
21 |                     </tr>
22 |                 </table>
23 |                >
24 |         ];
25 | edge[style=invis];
26 | "leafnode_2" -> "leafnode_3"
27 | leafnode_3[ label=<<table width="200">
28 |                     <tr>
29 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,5</td>
30 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,6</td>
31 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,7</td>
32 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,8</td>
33 |                     </tr>
34 |                 </table>
35 |                >
36 |         ];
37 | edge[style=invis];
38 | "leafnode_3" -> "leafnode_4"
39 | leafnode_4[ label=<<table width="200">
40 |                     <tr>
41 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,9</td>
42 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,10</td>
43 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,11</td>
44 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,12</td>
45 |                     </tr>
46 |                 </table>
47 |                >
48 |         ];
49 | edge[style=invis];
50 | "leafnode_4" -> "leafnode_5"
51 | leafnode_5[ label=<<table width="200">
52 |                     <tr>
53 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="blue">2</font>,1</td>
54 |                         <td bgcolor='white' port="t3" width="50"></td>
55 |                         <td bgcolor='white' port="t3" width="50"></td>
56 |                         <td bgcolor='white' port="t3" width="50"></td>
57 |                     </tr>
58 |                 </table>
59 |                >
60 |         ];
61 | //Force alignment from root to internal to leaf levels:
62 | //edge[style=invis];
63 | //"rootnode":d1 -> "leafnode_2":t2
64 | }
65 | 


--------------------------------------------------------------------------------
/pg_query_internals.sql:
--------------------------------------------------------------------------------
  1 | ------------------
  2 | -- Dependencies --
  3 | ------------------
  4 | create extension pageinspect;
  5 | create extension pg_buffercache;
  6 | 
  7 | --------------------------
  8 | -- B-Tree balance stats --
  9 | --------------------------
 10 | --
 11 | -- Among B-Tree indexes, what proportion are leaf pages, internal pages and
 12 | -- root pages?  Note that a single non-meta page B-Tree, which has only a root
 13 | -- page yet to undergo a root page split counts as only having a single leaf
 14 | -- page.
 15 | with tots as (
 16 |   SELECT
 17 |     count(*) c,
 18 |     avg(live_items) avg_live_items,
 19 |     avg(dead_items) avg_dead_items,
 20 |     avg(avg_item_size) avg_item_size,
 21 |     u.type,
 22 |     r.oid
 23 |   from
 24 |     (select
 25 |       c.oid,
 26 |       -- Don't count meta-page, or trust pg_class.relpages:
 27 |       generate_series(1, (select (pg_relation_size(c.oid) / (2^13))::int4) - 1) i
 28 |     from
 29 |       pg_index i
 30 |       join pg_opclass op on i.indclass[0] = op.oid
 31 |       join pg_am am on op.opcmethod = am.oid
 32 |       join pg_class c on i.indexrelid = c.oid
 33 |     where am.amname = 'btree') r,
 34 |     lateral (select * from bt_page_stats(r.oid::regclass::text, i)) u
 35 | group by r.oid, type)
 36 | select
 37 |   ct.relname table_name,
 38 |   tots.oid::regclass::text index_name,
 39 |   upper(type) page_type,
 40 |   c npages,
 41 |   to_char(avg_live_items, '990.999') as avg_live_items,
 42 |   to_char(avg_dead_items, '990.999') as avg_dead_items,
 43 |   to_char(avg_item_size, '990.999') as avg_item_size,
 44 |   to_char(c/sum(c) over(partition by tots.oid) * 100, '990.999') || ' %' as prop_of_index
 45 | from tots
 46 |   join pg_index i on i.indexrelid = tots.oid
 47 |   join pg_class ct on ct.oid = i.indrelid
 48 | order by ct.relnamespace, table_name, index_name, npages, type;
 49 | 
 50 | ----------------------------
 51 | -- B-Tree root page stats --
 52 | ----------------------------
 53 | with index_details as (
 54 |   select
 55 |     'some_index'::text idx
 56 | ),
 57 | meta_stats as (
 58 |   select
 59 |   *
 60 |   from index_details s,
 61 |   lateral (select * from bt_metap(s.idx)) meta),
 62 | root_stats as (
 63 |   select
 64 |     idx,
 65 |     root,
 66 |     level,
 67 |     fastroot,
 68 |     fastlevel,
 69 |     stats.*
 70 |   from
 71 |     meta_stats s,
 72 |     lateral (select * from bt_page_stats(idx, root)) stats)
 73 | select
 74 |   root_stats.*
 75 | from
 76 |   root_stats;
 77 | 
 78 | ------------------------------------------------------------
 79 | -- Summarize internal (non-leaf) B-Tree levels, key space --
 80 | ------------------------------------------------------------
 81 | --
 82 | -- Shows internal pages (including root page) in logical order, along with high
 83 | -- key data that determines logically ordering. (This is an upper bound on page
 84 | -- data).
 85 | --
 86 | -- Should work with most types of data.  Things like varlena headers will look
 87 | -- a bit funny, but this should be easy enough to wade through or tweak.
 88 | with recursive index_details as (
 89 |   select
 90 |     'some_text_index'::text idx
 91 | ),
 92 | size_in_pages_index as (
 93 |   select
 94 |     (pg_relation_size(idx::regclass) / (2^13))::int4 size_pages
 95 |   from
 96 |     index_details
 97 | ),
 98 | page_stats as (
 99 |   select
100 |     index_details.*,
101 |     stats.*
102 |   from
103 |     index_details,
104 |     size_in_pages_index,
105 |     lateral (select i from generate_series(1, size_pages - 1) i) series,
106 |     lateral (select * from bt_page_stats(idx, i)) stats),
107 | internal_page_stats as (
108 |   select
109 |     *
110 |   from
111 |     page_stats
112 |   where
113 |     type != 'l'),
114 | meta_stats as (
115 |   select
116 |     *
117 |   from
118 |     index_details s,
119 |     lateral (select * from bt_metap(s.idx)) meta),
120 | internal_items as (
121 |   select
122 |     *
123 |   from
124 |     internal_page_stats
125 |   order by
126 |     btpo desc),
127 | -- XXX: Note ordering dependency within this CTE, on internal_items
128 | ordered_internal_items(item, blk, level) as (
129 |   select
130 |     1,
131 |     blkno,
132 |     btpo
133 |   from
134 |     internal_items
135 |   where
136 |     btpo_prev = 0
137 |     and btpo = (select level from meta_stats)
138 |   union
139 |   select
140 |     case when level = btpo then o.item + 1 else 1 end,
141 |     blkno,
142 |     btpo
143 |   from
144 |     internal_items i,
145 |     ordered_internal_items o
146 |   where
147 |     i.btpo_prev = o.blk or (btpo_prev = 0 and btpo = o.level - 1)
148 | )
149 | select
150 |   idx,
151 |   btpo as level,
152 |   item as l_item,
153 |   blkno,
154 |   btpo_prev,
155 |   btpo_next,
156 |   btpo_flags,
157 |   type,
158 |   live_items,
159 |   dead_items,
160 |   avg_item_size,
161 |   page_size,
162 |   free_size,
163 |   -- Only non-rightmost pages have high key.
164 |   --
165 |   -- XXX: To get this to work with a non-text index, fiddle with the expression
166 |   -- that extracts from the "data" bt_page_items column.
167 |   --
168 |   -- Data is formed starting after varlena header bytes. NUL bytes often appear
169 |   -- due to alignment considerations, but aren't valid utf-8.  We switch NUL
170 |   -- bytes with raw bytes that make what looks like a text output function
171 |   -- escaped NUL byte (non-NUL special bytes will look like this without our
172 |   -- help, but we need to take special measures for NUL)
173 |   case when btpo_next != 0 then (select convert_from(decode(regexp_replace(data, ' 0{2}', '5C783030', 'g'), 'hex'), 'utf-8')
174 |                                  from bt_page_items(idx, blkno) where itemoffset = 1) end as highkey
175 | from
176 |   ordered_internal_items o
177 |   join internal_items i on o.blk = i.blkno
178 | order by btpo desc, item;
179 | 
180 | ---------------------------------------------------------
181 | -- Get a quick view of B-Tree buffercache usage counts --
182 | ---------------------------------------------------------
183 | select
184 |   c.relname,
185 |   bt.type,
186 |   count(*),
187 |   rl.*,
188 |   avg(case when bf.isdirty then 1.0 else 0.0 end) as avg_is_dirty,
189 |   avg(bf.usagecount) as avg_usagecount
190 | from
191 |   pg_buffercache bf
192 |   join pg_class c on c.oid = pg_filenode_relation(bf.reltablespace, bf.relfilenode)
193 |   join pg_index i on i.indexrelid = c.oid
194 |   join pg_opclass op on i.indclass[0] = op.oid
195 |   join pg_am am on op.opcmethod = am.oid
196 |   join lateral bt_page_stats(c.oid::regclass::text, bf.relblocknumber::int4) as bt on true
197 |   join lateral pg_relation_size(c.oid) as rl on true
198 | where am.amname = 'btree' and bf.relblocknumber > 0
199 | group by c.relname, bt.type
200 | order by c.relname, bt.type;
201 | 
202 | -------------------------------------------------------------------------------
203 | -- Details caching analysis, for testing clocksweep efficiency in production --
204 | -------------------------------------------------------------------------------
205 | 
206 | -- In first pass, create materialized copy of pg_buffercache view:
207 | create materialized view bufcacheview as
208 | select * from pg_buffercache;
209 | 
210 | -- Then, materialize bt page stats (this needs to happen afterwards, to not
211 | -- spoil cache):
212 | create materialized view btree_pages as
213 | select
214 |   r.oid as pg_class_oid,
215 |   r.i as relblocknumber,
216 |   upper(u.type) as type,
217 |   live_items,
218 |   dead_items,
219 |   avg_item_size
220 | from
221 |   (select
222 |      c.oid,
223 |      -- Don't rely on potentially stale pg_class.relpages here:
224 |      generate_series(1, (select (pg_relation_size(c.oid) / (2^13))::int4) - 1) i
225 |    from
226 |      pg_index i
227 |      join pg_opclass op on i.indclass[0] = op.oid
228 |      join pg_am am on op.opcmethod = am.oid
229 |      join pg_class c on i.indexrelid = c.oid
230 |    where am.amname = 'btree') r,
231 |   lateral (select * from bt_page_stats(r.oid::regclass::text, i)) u
232 | order by r.oid, u.type, r.i;
233 | 
234 | -- Finally, put it together.  Show how well each class of B-Tree page is
235 | -- cached, with standard buffercache statistics for each, rolled-up:
236 | select
237 |   pg_class_oid::regclass as index_name,
238 |   pg_size_pretty(pg_relation_size(pg_class_oid)) as index_relation_size,
239 |   type,
240 |   count(*) as blocks,
241 |   sum(case when bc.relblocknumber is null then 0 else 1 end) as buffers,
242 |   sum(case when bc.relblocknumber is null then 0.0 else 1.0 end) / count(*) as prop_cached,
243 |   sum(case when bc.isdirty then 1 else 0 end) as are_dirty,
244 |   avg(coalesce(usagecount, 0)) as avg_usagecount,
245 |   avg(pinning_backends) as avg_pinning_backends_in_cache,
246 |   var_pop(bc.relblocknumber) as var_pop_blocks_in_cache
247 | from
248 |   btree_pages btp
249 |   join pg_class c on btp.pg_class_oid = c.oid
250 |   left join bufcacheview bc on c.relfilenode = bc.relfilenode
251 |                                and btp.relblocknumber = bc.relblocknumber
252 | group by rollup(pg_class_oid, type)
253 | order by pg_relation_size(pg_class_oid) desc nulls last, pg_class_oid,
254 |   -- Force "Root, internal, leaf" ordering ("nulls last" avoids breaking
255 |   -- "rollup"):
256 |   case type when 'R' then 0 when 'I' then 2 when 'L' then 3 end nulls last;
257 | 
258 | -------------------------------------------------
259 | -- Higher-level summary of entire buffer cache --
260 | -------------------------------------------------
261 | --
262 | -- (Note: this isn't exactly comparable to above, since proportions are stuff
263 | -- in cache only here, not all blocks.  Actually, some thigns above are for
264 | -- buffer cache only, others are all blocks.)
265 | select
266 |   c.oid::regclass,
267 |   pg_size_pretty(pg_relation_size(c.oid)) as index_relation_size,
268 |   c.relkind,
269 |   case relforknumber
270 |   when 0 then
271 |     'Main Fork'
272 |   when 1 then
273 |     'Freespace Map'
274 |   when 2 then
275 |     'Visibility Map'
276 |   when 3 then
277 |     'Init Fork'
278 |   end page_type,
279 |   count(*) as buffers,
280 |   sum(case when bc.isdirty then 1 else 0 end) as are_dirty,
281 |   avg(usagecount) as avg_usagecount,
282 |   avg(pinning_backends) as avg_pinning_backends,
283 |   var_pop(bc.relblocknumber) as var_pop_blocks_in_cache
284 | from
285 |   bufcacheview bc
286 |   join pg_class c on bc.relfilenode = c.relfilenode
287 | group by rollup(c.oid, c.relkind, relforknumber)
288 | order by pg_relation_size(c.oid) desc nulls last, c.oid, relforknumber;
289 | 
290 | --
291 | -- Working with int4 indexes + bt_page_items() convenience functions.
292 | --
293 | -- Sources:
294 | --
295 | -- https://stackoverflow.com/questions/17208945/whats-the-easiest-way-to-represent-a-bytea-as-a-single-integer-in-postgresql
296 | -- https://stackoverflow.com/questions/11142235/convert-bigint-to-bytea-but-swap-the-byte-order
297 | --
298 | create or replace function reverse_bytes_iter(bytes bytea, length int, midpoint int, index int)
299 | returns bytea as
300 | $$
301 |   select case when index >= midpoint then bytes else
302 |     reverse_bytes_iter(
303 |       set_byte(
304 |         set_byte(bytes, index, get_byte(bytes, length-index)),
305 |         length-index, get_byte(bytes, index)
306 |       ),
307 |       length, midpoint, index + 1
308 |     )
309 |   end;
310 | $$ language sql immutable;
311 | 
312 | create or replace function reverse_bytes(bytes bytea) returns bytea as
313 | $$
314 | select reverse_bytes_iter(bytes, octet_length(bytes)-1, octet_length(bytes)/2, 0)
315 | $$
316 | language sql immutable;
317 | 
318 | create or replace function int4_from_bytea(bytea) returns int4
319 | as $$
320 | select ('x' || right($1::text, 6))::bit(24)::int;
321 | $$
322 | language sql immutable;
323 | 
324 | create or replace function int4_from_page_data(text) returns int4
325 | as $$
326 | select int4_from_bytea(reverse_bytes(decode($1, 'hex')));
327 | $$
328 | language sql immutable;
329 | 
330 | --
331 | -- Use:
332 | --
333 | --  postgres=# select *, int4_from_page_data(data) from bt_page_items('f', 1) limit 15;
334 | --   itemoffset │    ctid    │ itemlen │ nulls │ vars │          data           │ int4_from_page_data
335 | --  ────────────┼────────────┼─────────┼───────┼──────┼─────────────────────────┼─────────────────────
336 | --            1 │ (17698,69) │      16 │ f     │ f    │ 5c 00 00 00 00 00 00 00 │                  92
337 | --            2 │ (0,1)      │      16 │ f     │ f    │ 01 00 00 00 00 00 00 00 │                   1
338 | --            3 │ (8849,126) │      16 │ f     │ f    │ 01 00 00 00 00 00 00 00 │                   1
339 | --            4 │ (17699,25) │      16 │ f     │ f    │ 01 00 00 00 00 00 00 00 │                   1
340 | --            5 │ (17699,26) │      16 │ f     │ f    │ 01 00 00 00 00 00 00 00 │                   1
341 | --            6 │ (0,2)      │      16 │ f     │ f    │ 02 00 00 00 00 00 00 00 │                   2
342 | --            7 │ (8849,125) │      16 │ f     │ f    │ 02 00 00 00 00 00 00 00 │                   2
343 | --            8 │ (17699,23) │      16 │ f     │ f    │ 02 00 00 00 00 00 00 00 │                   2
344 | --            9 │ (17699,24) │      16 │ f     │ f    │ 02 00 00 00 00 00 00 00 │                   2
345 | --           10 │ (0,3)      │      16 │ f     │ f    │ 03 00 00 00 00 00 00 00 │                   3
346 | --           11 │ (8849,124) │      16 │ f     │ f    │ 03 00 00 00 00 00 00 00 │                   3
347 | --           12 │ (17699,21) │      16 │ f     │ f    │ 03 00 00 00 00 00 00 00 │                   3
348 | --           13 │ (17699,22) │      16 │ f     │ f    │ 03 00 00 00 00 00 00 00 │                   3
349 | --           14 │ (0,4)      │      16 │ f     │ f    │ 04 00 00 00 00 00 00 00 │                   4
350 | --           15 │ (8849,123) │      16 │ f     │ f    │ 04 00 00 00 00 00 00 00 │                   4
351 | --  (15 rows)
352 | 
353 | -- Spurious unfrozen row catcher query.  From
354 | -- https://www.postgresql.org/message-id/20180319181723.ugaf7hfkluqyos5d@alap3.anarazel.de :
355 | create or replace function check_rel(rel regclass, out blockno int8, out lp int2, out xmin xid)
356 | returns setof record
357 | language sql
358 | as $$
359 |     select blockno, lp, t_xmin
360 |     from
361 |         generate_series(0, pg_relation_size($1::text) / 8192 - 1) blockno, -- every block in the relation
362 |         heap_page_items(get_raw_page($1::text, blockno::int4)) -- every item on the page
363 |     where
364 |         t_xmin is not null -- filter out empty items
365 |         and t_xmin != 1 -- filter out bootstrap
366 |         and t_xmin != 2 -- filter out frozen transaction id
367 |         and (t_infomask & ((x'0100' | x'0200')::int)) != ((x'0100' | x'0200')::int) -- filter out frozen rows with xid present
368 |         and age(t_xmin) > age((select relfrozenxid from pg_class where oid = $1)) -- xid cutoff filter
369 | $$;
370 | 
371 | -- Usage:
372 | --
373 | -- select * from check_rel('pg_authid') limit 100;
374 | 


--------------------------------------------------------------------------------
/postgres-real-btree.dot:
--------------------------------------------------------------------------------
 1 | // Example B-Tree graph
 2 | //
 3 | // Breadth-first order
 4 | //
 5 | // Start from root, go left to right
 6 | //
 7 | // Workflow:
 8 | //
 9 | // $ dot -T svg btree.dot -o btree.svg;
10 | 
11 | digraph nbtree {
12 | graph [fontname = "monospace"];
13 | node [shape = none,height=.1,fontname = "monospace",fontsize=8];
14 | // Level 1 (root level)
15 | // Downlinks + highkey:
16 | rootnode[ label=<<table>
17 |                     <tr>
18 |                         <td bgcolor='burlywood' port="s0">-&infin;</td>
19 |                         <td bgcolor='white' port="d0">&#8615;</td>
20 |                         <td bgcolor='burlywood' port="s1">367, <font color="blue">'-&infin;'</font></td>
21 |                         <td bgcolor='white' port="d1">&#8615;</td>
22 |                         <td bgcolor='burlywood' port="s2">733, <font color="blue">'-&infin;'</font></td>
23 |                         <td bgcolor='white' port="d2">&#8615;</td>
24 |                         <td bgcolor='burlywood' port="hk">+&infin;</td>
25 |                     </tr>
26 |                 </table>
27 |                >
28 |         ];
29 | // Downlink arrows to children:
30 | "rootnode":d0 -> "leafnode_1":t0
31 | "rootnode":d1 -> "leafnode_2":t0
32 | "rootnode":d2 -> "leafnode_3":t0
33 | 
34 | // sibling pointer:
35 | // (None)
36 | 
37 | 
38 | // Level 0 (leaf level)
39 | leafnode_1[ label=<<table>
40 |                     <tr>
41 |                         <td bgcolor='darkseagreen1' port="t0">1, <font color="blue">'(0,1)'</font></td>
42 |                         <td bgcolor='darkseagreen1' port="t1">2, <font color="blue">'(0,2)'</font></td>
43 |                         <td border="0" bgcolor='white' port="t2">...</td>
44 |                         <td bgcolor='darkseagreen1' port="t1">366, <font color="blue">'(5,61)'</font></td>
45 |                         <td bgcolor='burlywood' port="hk">367, <font color="blue">'-&infin;'</font></td>
46 |                     </tr>
47 |                     <tr>
48 |                         <td colspan="5" border="0" bgcolor='white'>366 non-pivot items &amp; high key</td>
49 |                     </tr>
50 |                 </table>
51 |                >
52 |         ];
53 | // sibling pointer:
54 | "leafnode_1" -> "leafnode_2"[constraint=false,color=black,style=dashed,arrowsize=0.5]
55 | leafnode_2[ label=<<table>
56 |                     <tr>
57 |                         <td bgcolor='darkseagreen1' port="t0">367, <font color="blue">'(6,1)'</font></td>
58 |                         <td bgcolor='darkseagreen1' port="t1">368, <font color="blue">'(6,2)'</font></td>
59 |                         <td border="0" bgcolor='white' port="t2">...</td>
60 |                         <td bgcolor='darkseagreen1' port="t3">732, <font color="blue">'(11,61)'</font></td>
61 |                         <td bgcolor='burlywood' port="hk">733, <font color="blue">'-&infin;'</font></td>
62 |                     </tr>
63 |                     <tr>
64 |                         <td colspan="5" border="0" bgcolor='white'>366 non-pivot items &amp; high key</td>
65 |                     </tr>
66 |                 </table>
67 |                >
68 |         ];
69 | // sibling pointer:
70 | "leafnode_2" -> "leafnode_3"[constraint=false,color=black,style=dashed,arrowsize=0.5]
71 | leafnode_3[ label=<<table>
72 |                     <tr>
73 |                         <td bgcolor='darkseagreen1' port="t0">733, <font color="blue">'(12,1)'</font></td>
74 |                         <td bgcolor='darkseagreen1' port="t1">734, <font color="blue">'(12,2)'</font></td>
75 |                         <td border="0" bgcolor='white' port="t2">...</td>
76 |                         <td bgcolor='burlywood' port="hk">+&infin;</td>
77 |                     </tr>
78 |                     <tr>
79 |                         <td colspan="4" border="0" bgcolor='white'>2+ non-pivot items, implicit +&infin; high key</td>
80 |                     </tr>
81 |                 </table>
82 |                >
83 |         ];
84 | 
85 | //Force alignment from root to internal to leaf levels:
86 | edge[style=invis];
87 | "rootnode":d1 -> "leafnode_2":t2
88 | }
89 | 


--------------------------------------------------------------------------------
/unoptimized-leaf-page-split-1.dot:
--------------------------------------------------------------------------------
 1 | // Example B-Tree graph
 2 | //
 3 | // Breadth-first order
 4 | //
 5 | // Start from root, go left to right
 6 | //
 7 | // Workflow:
 8 | //
 9 | // $ dot -T svg btree.dot -o btree.svg;
10 | 
11 | digraph nbtree {
12 | graph [fontname = "monospace"];
13 | node [shape = none,height=.1,fontname = "monospace",fontsize=18];
14 | // Level 0 (leaf level)
15 | leafnode_2[ label=<<table width="200">
16 |                     <tr>
17 |                         <td bgcolor='darkseagreen1' port="t2" width="50"><font color="magenta">1</font>,1</td>
18 |                         <td bgcolor='darkseagreen1' port="t3" width="50"><font color="magenta">1</font>,2</td>
19 |                         <td bgcolor='white' port="t3" width="50"></td>
20 |                         <td bgcolor='white' port="t3" width="50"></td>
21 |                     </tr>
22 |                 </table>
23 |                >
24 |         ];
25 | edge[style=invis];
26 | "leafnode_2" -> "leafnode_3"
27 | leafnode_3[ label=<<table width="200">
28 |                     <tr>
29 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,3</td>
30 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,4</td>
31 |                         <td bgcolor='white' port="t3" width="50"></td>
32 |                         <td bgcolor='white' port="t3" width="50"></td>
33 |                     </tr>
34 |                 </table>
35 |                >
36 |         ];
37 | edge[style=invis];
38 | "leafnode_3" -> "leafnode_4"
39 | leafnode_4[ label=<<table width="200">
40 |                     <tr>
41 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,5</td>
42 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,6</td>
43 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="blue">2</font>,1</td>
44 |                         <td bgcolor='white' port="t3" width="50"></td>
45 |                     </tr>
46 |                 </table>
47 |                >
48 |         ];
49 | //Force alignment from root to internal to leaf levels:
50 | //edge[style=invis];
51 | //"rootnode":d1 -> "leafnode_2":t2
52 | }
53 | 


--------------------------------------------------------------------------------
/unoptimized-leaf-page-split-2.dot:
--------------------------------------------------------------------------------
 1 | // Example B-Tree graph
 2 | //
 3 | // Breadth-first order
 4 | //
 5 | // Start from root, go left to right
 6 | //
 7 | // Workflow:
 8 | //
 9 | // $ dot -T svg btree.dot -o btree.svg;
10 | 
11 | digraph nbtree {
12 | graph [fontname = "monospace"];
13 | node [shape = none,height=.1,fontname = "monospace",fontsize=18];
14 | // Level 0 (leaf level)
15 | leafnode_2[ label=<<table width="200">
16 |                     <tr>
17 |                         <td bgcolor='darkseagreen1' port="t2" width="50"><font color="magenta">1</font>,1</td>
18 |                         <td bgcolor='darkseagreen1' port="t3" width="50"><font color="magenta">1</font>,2</td>
19 |                         <td bgcolor='white' port="t3" width="50"></td>
20 |                         <td bgcolor='white' port="t3" width="50"></td>
21 |                     </tr>
22 |                 </table>
23 |                >
24 |         ];
25 | edge[style=invis];
26 | "leafnode_2" -> "leafnode_3"
27 | leafnode_3[ label=<<table width="200">
28 |                     <tr>
29 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,3</td>
30 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,4</td>
31 |                         <td bgcolor='white' port="t3" width="50"></td>
32 |                         <td bgcolor='white' port="t3" width="50"></td>
33 |                     </tr>
34 |                 </table>
35 |                >
36 |         ];
37 | edge[style=invis];
38 | "leafnode_3" -> "leafnode_4"
39 | leafnode_4[ label=<<table width="200">
40 |                     <tr>
41 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,5</td>
42 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,6</td>
43 |                         <td bgcolor='white' port="t3" width="50"></td>
44 |                         <td bgcolor='white' port="t3" width="50"></td>
45 |                     </tr>
46 |                 </table>
47 |                >
48 |         ];
49 | edge[style=invis];
50 | "leafnode_4" -> "leafnode_5"
51 | leafnode_5[ label=<<table width="200">
52 |                     <tr>
53 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,7</td>
54 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,8</td>
55 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,9</td>
56 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="blue">2</font>,1</td>
57 |                     </tr>
58 |                 </table>
59 |                >
60 |         ];
61 | //Force alignment from root to internal to leaf levels:
62 | //edge[style=invis];
63 | //"rootnode":d1 -> "leafnode_2":t2
64 | }
65 | 


--------------------------------------------------------------------------------
/unoptimized-leaf-page-split-3.dot:
--------------------------------------------------------------------------------
 1 | // Example B-Tree graph
 2 | //
 3 | // Breadth-first order
 4 | //
 5 | // Start from root, go left to right
 6 | //
 7 | // Workflow:
 8 | //
 9 | // $ dot -T svg btree.dot -o btree.svg;
10 | 
11 | digraph nbtree {
12 | graph [fontname = "monospace"];
13 | node [shape = none,height=.1,fontname = "monospace",fontsize=18];
14 | // Level 0 (leaf level)
15 | leafnode_2[ label=<<table width="200">
16 |                     <tr>
17 |                         <td bgcolor='darkseagreen1' port="t2" width="50"><font color="magenta">1</font>,1</td>
18 |                         <td bgcolor='darkseagreen1' port="t3" width="50"><font color="magenta">1</font>,2</td>
19 |                         <td bgcolor='white' port="t3" width="50"></td>
20 |                         <td bgcolor='white' port="t3" width="50"></td>
21 |                     </tr>
22 |                 </table>
23 |                >
24 |         ];
25 | edge[style=invis];
26 | "leafnode_2" -> "leafnode_3"
27 | leafnode_3[ label=<<table width="200">
28 |                     <tr>
29 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,3</td>
30 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,4</td>
31 |                         <td bgcolor='white' port="t3" width="50"></td>
32 |                         <td bgcolor='white' port="t3" width="50"></td>
33 |                     </tr>
34 |                 </table>
35 |                >
36 |         ];
37 | edge[style=invis];
38 | "leafnode_3" -> "leafnode_4"
39 | leafnode_4[ label=<<table width="200">
40 |                     <tr>
41 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,5</td>
42 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,6</td>
43 |                         <td bgcolor='white' port="t3" width="50"></td>
44 |                         <td bgcolor='white' port="t3" width="50"></td>
45 |                     </tr>
46 |                 </table>
47 |                >
48 |         ];
49 | edge[style=invis];
50 | "leafnode_4" -> "leafnode_5"
51 | leafnode_5[ label=<<table width="200">
52 |                     <tr>
53 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,7</td>
54 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,8</td>
55 |                         <td bgcolor='white' port="t3" width="50"></td>
56 |                         <td bgcolor='white' port="t3" width="50"></td>
57 |                     </tr>
58 |                 </table>
59 |                >
60 |         ];
61 | edge[style=invis];
62 | "leafnode_5" -> "leafnode_6"
63 | leafnode_6[ label=<<table>
64 |                     <tr>
65 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,9</td>
66 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,10</td>
67 |                         <td bgcolor='white' port="t3" width="50"></td>
68 |                         <td bgcolor='white' port="t3" width="50"></td>
69 |                     </tr>
70 |                 </table>
71 |                >
72 |         ];
73 | edge[style=invis];
74 | "leafnode_6" -> "leafnode_7"
75 | leafnode_7[ label=<<table>
76 |                     <tr>
77 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,11</td>
78 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="magenta">1</font>,12</td>
79 |                         <td bgcolor='darkseagreen1' port="t4" width="50"><font color="blue">2</font>,1</td>
80 |                         <td bgcolor='white' port="t3" width="50"></td>
81 |                     </tr>
82 |                 </table>
83 |                >
84 |         ];
85 | //Force alignment from root to internal to leaf levels:
86 | //edge[style=invis];
87 | //"rootnode":d1 -> "leafnode_2":t2
88 | }
89 | 


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