The depth of an index: primer

April 9, 2009

InnoDB and MyISAM use B+ and B trees for indexes (InnoDB also has internal hash index).

In both these structures, the depth of the index is an important factor. When looking for an indexed row, a search is made on the index, from root to leaves.

Assuming the index is not in memory, the depth of the index represents the minimal cost (in I/O operation) for an index based lookup. Of course, most of the time we expect large portions of the indexes to be cached in memory. Even so, the depth of the index is an important factor. The deeper the index is, the worse it performs: there are simply more lookups on index nodes.

What affects the depth of an index?

There are quite a few structural issues, but it boils down to two important factors:

  1. The number of rows in the table: obviously, more rows leads to larger index, larger indexes grow in depth.
  2. The size of the indexed column(s). An index on an INT column can be expected to be shallower than an index on a CHAR(32) column (on a very small number of rows they may have the same depth, so we'll assume a large number of rows).

Of course, these two factors also affect the total size of the index, hence its disk usage, but I wish to concentrate on the index depth.

Let's emphasize the second factor. It is best to index shorter columns, if that is possible. It is the reason behind using an index on a VARCHAR's prefix (e.g. KEY(email_address(16)). It is also a reason to use INT, instead of BIGINT columns for your primary key, when BIGINT is not required.

The larger the indexed data type is (or the total size of data types for all columns in a combined index), the less values that can fit in an index node. The less values in a node, the more node splits occur; the more nodes are required to build the index. The less values in the node, the less wide the index tree is. The less wide an index tree is, and the more nodes it has - the deeper it gets.

So bigger data types lead to deeper trees. Deeper trees lead to more IO operations on lookup.

InnoDB

On InnoDB there's another issue: all tables are clustered by primary key. Any access to table data requires diving into, or traversing the primary key tree.

On InnoDB, a secondary index (any index which is not the primary key) does not lead to table data. Instead, the "data" in the leaf nodes of a secondary index - are the primary key values.

And so, when looking up a value on an InnoDB table using a secondary key, we first search the secondary key to retrieve the primary key value, then go to the primary key tree to retrieve the data.

This means two index lookups, one of which is always the primary key.

On InnoDB, it is therefore in particular important to keep the primary key small. Have small data types. Prefer an SMALLINT to INT, if possible. Prefer an INT to BIGINT, if possible. Prefer an integer value over some VARCHAR text.

With long data types used in an InnoDB primary key, not only is the primary key index bloated (deep), but also every other index gets to be bloated, as the leaf values in all other indexes are those same long data types.

MyISAM

MyISAM does not use clustered trees, hence the primary key is just a regular unique key. All indexes are created equal and an index lookup only consists of a single index search. Therefore, two indexes do no affect one another, with the exception that they are competing on the same key cache.

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posted in MySQL by shlomi

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2 Comments to "The depth of an index: primer"

  1. The Depth of a B-tree | Tokutek wrote:

    [...] Noach recently wrote a useful primer on the depth of B-trees and how that plays out for point queries — in both clustered indexes, like InnoDB, and in [...]

  2. Reducing locks by narrowing primary key | code.openark.org wrote:

    [...] the fact that a bloated PRIMARY KEY bloats the entire clustered index and secondary keys (see: The depth of an index: primer), it is also a source for locks. It’s true that any UNIQUE KEY can serve as a PRIMARY KEY. [...]

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