数据库中的现代B-树技术

B+Tree

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"这篇文章是关于《Modern B-Tree Techniques》的，主要探讨了B+树在现代数据库系统中的应用和优化技术。文章涵盖了基础技术、数据结构与算法、事务处理技术等多个方面，深入讨论了B+树的关键特性，并对比了其与哈希索引的差异。同时，还涉及到了节点大小、插值搜索、变长记录处理、CPU缓存利用、重复键值处理、位图索引、数据压缩以及空间管理等具体技术点。" 在数据库系统中，B+树是一种广泛使用的数据结构，尤其适用于存储大量有序数据并支持高效的查找、插入和删除操作。本文首先介绍了B+树的背景和视角，包括它在不同硬件环境下的表现和适用场景。接着，文章详细阐述了基本技术，如B+树的数据结构设计，如节点的组织方式，以及与树高度相关的性能指标。此外，还讨论了与B+树相关的算法，如如何有效地遍历和操作树。文章中提到了B+树在数据库中的具体应用，与哈希索引的比较分析，强调了两者在不同查询场景下的优缺点。B+树的优势在于其支持范围查询，而哈希索引则在等值查询中表现出色。在数据结构部分，文章探讨了如何处理变长记录、规范化键值以及前缀B树的设计，这些都是为了提高存储效率和查询性能。文章进一步讨论了如何利用CPU缓存来提升B+树的性能，因为现代处理器的缓存机制对数据访问速度有显著影响。对于重复键值的处理，作者提出了策略，并且介绍了位图索引的应用，这种索引类型在特定场景下可以提供更紧凑的存储和更快的查询速度。数据压缩章节探讨了如何减少存储空间，同时保持高效的数据检索。在事务处理技术部分，文章详细讨论了锁和Latch机制，包括鬼记录（Ghost Records）的概念，以及如何通过键范围锁定来实现并发控制。还介绍了一种名为Blink-tree的新结构，它试图结合B+树和哈希索引的优点。最后，文章分析了在获取锁时的Latch管理以及Latch耦合问题，这些都是保证事务正确性和系统并发性的重要方面。《Modern B-Tree Techniques》全面探讨了B+树的各种现代优化技术和事务处理策略，为数据库系统设计者和开发者提供了宝贵的理论与实践指导。

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2.2 Sizes, Tree Height, etc. 215

management, there is a record count; for space management with

variable-size records, there are slot count, byte count, and lowest record

oﬀset; for data compression, there may be a shared key preﬁx including

its size plus information as required for other compression techniques;

for write-ahead logging and recovery, there usually is a Page LSN (log

sequence number) [95]; for concurrency control, in particular in shared-

memory systems, there may be information about current locks; and for

eﬃcient key range locking, consistency checking, and page movement

as in defragmentation, there may be fence keys, i.e., copies of separator

keys in ancestor pages. Each ﬁeld, its purpose, and its use are discussed

in a subsequent section.

•

Leaf nodes contain key values and some associated informa-

tion. In most B-trees, branch nodes including the root node

contain separator keys and child pointers but no associated

information.

•

Child pointers are essential. Sibling pointers are often imple-

mented but not truly required. Parent pointers are hardly

ever employed.

•

B-tree nodes usually contain a ﬁxed-format page header, a

variable-size array of ﬁxed-size slots, and a variable-size data

area. The header contains a slot counter, information per-

taining to compression and recovery, and more. The slots

serve space management for variable-size records.

2.2 Sizes, Tree Height, etc.

In traditional database designs, the typical size of a B-tree node is

4–8 KB. Larger B-tree nodes might seem more eﬃcient for today’s disk

drives based on multiple analyses [57, 86] but nonetheless are rarely

used in practice. The size of a separator key can be as large as a record

but it can also be much smaller, as discussed later in the section on

preﬁx B-trees. Thus, the typical fan-out, i.e., the number of children

or of child pointers, is sometimes only in the tens, typically in the

hundreds, and sometimes in the thousands.

If a B-tree contains N records and L records per leaf, the B-tree

requires N/L leaf nodes. If the average number of children per parent

216 Basic Techniques

is F , the number of branch levels is log

(N/L). For example, the B-tree

in Figure 2.3 has 9 leaf nodes, a fan-out F = 3, and thus log

9=2

branch levels. Depending on the convention, the height of this B-tree

is 2 (levels above the leaves) or 3 (levels including the leaves). In order

to reﬂect the fact that the root node usually has a diﬀerent fan-out,

this expression is rounded up. In fact, after some random insertions

and deletions, space utilization in the nodes will vary among nodes.

The average space utilization in B-trees is usually given as about 70%

[75], but various policies used in practice and discussed later may result

in higher space utilization. Our goal here is not to be precise but to

show crucial eﬀects, basic calculations, and the orders of magnitude of

various choices and parameters.

If a single branch node can point to hundreds of children, then

the distance between root and leaves is usually very small and 99% or

more of all B-tree nodes are leaves. In other words, great-grandparents

and even more distant ancestors are rare in practice. Thus, for the

performance of random searches based on root-to-leaf B-tree traversals,

treatment of only 1% of a B-tree index and thus perhaps only 1% of

a database determine much of the performance. For example, keeping

the root of a frequently used B-tree index in memory beneﬁts many

searches with little cost in memory or cache space.

•

The B-tree depth (nodes along a root-to-leaf path) is loga-

rithmic in the number of records. It is usually small.

•

Often more than 99% of all nodes in a B-tree are leaf nodes.

•

B-tree pages are ﬁlled between 50% and 100%, permitting

insertions and deletions as well as splitting and merging nodes.

Average utilization after random updates is about 70%.

2.3 Algorithms

The most basic, and also the most crucial, algorithm for B-trees is

search. Given a speciﬁc value for the search key of a B-tree or for a

preﬁx thereof, the goal is to ﬁnd, correctly and as eﬃciently as possible,

all entries in the B-tree matching the search key. For range queries, the

search ﬁnds the lowest key satisfying the predicate.

218 Basic Techniques

level. This is because the purpose of most B-tree searches is retrieving

the information attached to each key and information contents exists

only in leaves in most B-tree implementations. Moreover, as can be

seen for key value 15 in Figure 2.4, a key that might have existed at

some time in a valid leaf entry may continue to serve as separator key

in a nonleaf node even after the leaf entry has been removed.

An exact-match query is complete after the search, but a range

query must scan leaf nodes from the low end of the range to the high

end. The scan can employ neighbor pointers if they exist in the B-tree.

Otherwise, parent and grandparent nodes and their child pointers must

be employed. In order to exploit multiple asynchronous requests, e.g.,

for a B-tree index stored in a disk array or in network-attached stor-

age, parent and grandparent nodes are needed. Range scans relying on

neighbor pointers are limited to one asynchronous prefetch at-a-time

and therefore unsuitable for arrays of storage devices or for virtualized

storage.

Insertions start with a search for the correct leaf to place the new

record. If that leaf has the required free space, the insertion is complete.

Otherwise, a case called “overﬂow,” the leaf needs to be split into two

leaves and a new separator key must be inserted into the parent. If the

parent is already full, the parent is split and a separator key is inserted

into the appropriate grandparent node. If the root node needs to be

split, the B-tree grows by one more level, i.e., a new root node with two

children and only one separator key. In other words, whereas the depth

of many tree data structures grows at the leaves, the depth of B-trees

grows at the root. This is what guarantees perfect balance in a B-tree.

At the leaf level, B-trees grow only in width, enabled by the variable

number of child nodes in each parent node. In some implementations

of B-trees, the old root page becomes the new root page and the old

root contents are distributed into the two newly allocated nodes. This

is a valuable technique if modifying the page identiﬁer of the root node

in the database catalogs is expensive or if the page identiﬁer is cached

in compiled query execution plans.

Figure 2.5 shows the B-tree of Figure 2.4 after insertion of the key 22

and a resulting leaf split. Note that the separator key propagated to

the parent node can be chosen freely; any key value that separates the

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