This document discusses B+-trees, which are commonly used to index data in databases. It provides an overview of the structure and functionality of B+-trees, including keys, pointers, fanout, leaf nodes, and internal nodes. It also describes Btree4j, an open source Java implementation of B+-trees that supports features like paging, prefix indexing, and bulk loading. The document aims to revisit the disk-based structure and implementation of B+-trees.

1. Tutorial: Revisiting Disk-based B+-trees
Research Engineer, Treasure Data
Makoto YUI @myui
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B+-trees

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データベース研究者ならB-treeぐらい書けますよね？

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…

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https://github.com/myui/btree4j
XML
B+-Trees

6. History of B+-Trees
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Douglas Comer. 1979. Ubiquitous B-Tree. ACM Comput. Surv. 11, 2 (June 1979),
bit.ly/bit-btree Bit’79

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B+-Trees
CPU
→

8. B+-Trees
• B
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9. B+-Trees
• B
•
•
•
• B Fanout
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B+-Trees
key, pointer
key, value, rightlink

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B+-Trees
RDB value
Fanout

12. Btree4j (1/2)
• B+-trees
•
• Paging using LRU cache replacement policy / Freespace mgmt.
• Key Value
• Prefix B-trees
Rudolf Bayer and Karl Unterauer. "Prefix B-trees", Proc. ACM Trans. Database Syst. 2, 1,
pp.11-26), March 1977.
• 8 bytes Variable-bytes coding
keys/values
• value key
• DB unique non-unique
• Delete/Update
• Prefix search, Range , wildcard LIKE
• DB
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13. Btree4j (2/2)
• Bulk-loading
•
• Indexed File)
• Fanout leaf value RDB ) . value
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14. Btree4j (2/2)
• Bulk-loading
•
• Indexed File)
• Fanout leaf value RDB ) . value
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Cons (Disclaimer)
• 2006 (Java5 ) Xindice B-tree
Modern Java
→ Lambda, Stream API Preconditions
• read-most XML-DB
read-write
→ OLTP
PR ;-) 2-3weeks (?)

15. Why prefix B-trees?
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1. Goetz Graefe (2011), "Modern B-Tree Techniques", Foundations and Trends in Databases: Vol. 3: No. 4, pp 203-402.
2. Douglas Comer. Ubiquitous B-Tree. ACM Comput. Surv. 11, 2 (June 1979)

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Prefix B-trees
computer electronic
”e”
→ …
BTreeNode# getSeparator() leaf split

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Btree4j Internal - Paged file
(Paged) File Header 4k bytes
Page 4k bytes
Page header 127 bytes
https://xml.apache.org/xindice/dev/guide-internals.html

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Btree4j Internal – File header

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Btree4j Internal – Page header
next_page right link
page in-memory LRU .
Dirty Page
leftmost key rightmost key prefix
aaaa, aaabb, aaaccc, aaaddd ”aaa” prefix
a, bb, ccc, ddd fanout

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Btree4j Internal – Pages and records
1 page = 4k bytes
btree4j Datapage
Datapage
Fragmentation Freespace
Freespace

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Btree4j Internal – Overflow page

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Indexed file range scan

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https://github.com/apache/derby/tree/trunk/java/engine/org/apache/derby/impl/store/access/btree
http://svn.apache.org/repos/asf/xml/xindice/trunk/java/src/org/apache/xindice/core/filer/
https://github.com/postgres/postgres/tree/master/src/backend/access/nbtree
http://pages.cs.wisc.edu/~jignesh/cs564/schedule.html
DB 3NF