The highest rated answer here mentions how in MySQL records are stored in the order of primary index. Does that mean the primary index created is a sparse index? And if so, what happens if one modifies the primary key, by changing the column on which it is constructed or modifying one of the entries.
Apologies for asking 2 questions in the same post, but I thought it was better asking them together. I came upon this doubt while dealing with tables which were extremely slow when queried, so I thought maybe inserting rows in some manner which is based on an actual column in the table would help.
I'll answer about MySQL's default storage engine, InnoDB. This is the storage engine you should use for all tables in MySQL, unless you have a very specific reason not to.
Answer to Question 1: The primary key is not a sparse index. I know that term to refer to an index that only has values for a subset of rows in the table. I.e. an index with a WHERE clause. But the primary key must account for all rows in the table. It is the column or columns you use if you need to reference any single row uniquely.
Even though the clustered index is stored in order by primary key values, it isn't necessarily stored in that order on disk. Each page in an InnoDB tablespace has a link to the "next" page, which may not be physically located immediately after. It may be much later in the file, or even earlier. The pages may be interspersed with pages for other indexes (even other table if you are using a shared tablespace). Is this what you meant by sparse index?
Answer to Question 2: If you change the column(s) of the table's primary key, the storage of the table must be restructured. InnoDB uses the primary key as the clustered index, which means the rest of the columns are stored along with leaf nodes of the B-tree data structure. Changing the primary key column(s) may change the order of storage, and also the size of each B-tree node (both internal nodes and leaf nodes).
This means while you are restructuring the primary key, your server temporarily needs a lot of extra storage space — up to double the size of the table. Once the restructuring is finished, the old version of the table is automatically dropped.
How RDBs like MySQL and PostgreSQL manage memory for new indexes?
My guess that RDB creates B-tree (or other indexes) with References/Links to real objects in memory.
Another guess that it duplicates all the data for each new index.
So basically this question is about "What B-tree consists of? References, or real objects?"
Google search is too overheat about DB topics and RDMS products. So, I also would be very grateful for good articles about this.
The details vary, but a B-tree index is a tree structure that is stored on disk. It contains duplicates of the indexed terms (the index keys) and a (direct or indirect) pointer to the indexed row in the table.
A B-tree index represents a sorted list of the index keys that allows fast searches. The tree structure speeds up searching through the list and allows inserting and deleting entries without too much data churn.
It is unclear what you mean by a "real object". The index keys are certainly real, and they are stored in the index. But if you mean the whole table row, that is only referenced from the index.
For MySQL's Engine=InnoDB, it works this way:
The data is stored in PRIMARY KEY order in a B+Tree. This makes lookups and ranges based on the PK very efficient.
Each secondary keys is also a B+Tree, but ordered by the order given by the secondary key column(s). Each "row" also has the columns of the PK, thereby providing the reference (link) to the data's BTree.
If the columns of the secondary key plus the PK are the only columns you need, then the query is performed using only the secondary key's BTree.
There is no "ROWNUM" as found in some other database brands.
If you don't hit certain limits, you could include all the table's columns in a secondary index.
Even if I don't have a primary key or unique key, InnoDB still creates a cluster index on a synthetic column as described below.
https://dev.mysql.com/doc/refman/5.5/en/innodb-index-types.html
So, why does InnoDB have to require clustered index? Is there a defenite reason clustered index must exist here?
In Oracle Database or MSSQL I don't see they require this.
Also, I don't think cluster index have so tremendous advantage comparing to ordinary table either.
It is true that looking for data using clustering key does not need an additional disk read and faster than when I don't have one but without cluster index, secondary index can look up faster by using physical rowID.
Therefore, I don't see any reason for insisting using it.
Other vendors have a "ROWNUM" or something like that. InnoDB is much simpler. Instead of having that animal, it simply requires something that you will usually want anyway. In both cases, it is a value that uniquely identifies a row. This is needed for guts of transactions -- knowing which row(s) to lock, etc, to provide transactional integrity. (I won't go into the rationale here.)
In requiring (or providing) a PK, and in doing certain other simplifications, InnoDB sacrifices several little-used (or easily worked around) features: Multiple pks, multiple clustered indexes, no pk, etc.
Since the "synthetic column" takes 6 bytes, it is almost always better to simply provide id INT UNSIGNED NOT NULL AUTO_INCREMENT PRIMARY KEY, even if you don't use it. But if you don't use it, but do have a non-NULL UNIQUE key, then you may as well make it the PK. (As MySQL does by default.)
A lookup by a secondary key first gets the PK value from the secondary key's BTree. Then the main BTree (with the data ordered by the PK) is drilled down to find the row. Hence, secondary keys can be slower that use of the PK. (Usually this is not enough slower to matter.) So, this points out one design decision that required a PK.) (Other vendors use ROWNUM, or something, to locate the record, instead of the PK.)
Back to "Why?". There are many decisions in MySQL where the designers said "simplicity is better for this free product, let's not bother building some complex, but little-used feature. At first there were no subqueries (temp tables were a workaround). No Views (they are only syntactic sugar). No Materialized Views (OK, this may be a failing; but they can be simulated). No bit-mapped or hash or isam (etc) indexing (BTree is very good for "all-around" usage).
Also, by always "clustering" the PK with the data, lookups via the PK are inherently faster than the competition (no going through a ROWNUM). (Secondary key lookups may not be faster.)
Another difference -- MySQL was very late in implementing "index merge", wherein it uses two indexes, then ANDs or ORs the results. This can be efficient with ROWNUMs, but not with clustered PKs.
(I'm not a MySQL/MariaDB/Percona developer, but I have used them since 1999, and have been to virtually all major MySQL Conferences, where inside info is often divulged. So, I think I have enough insight into their thinking to present this answer.)
I have a limited exposure to DB and have only used DB as an application programmer. I want to know about Clustered and Non clustered indexes.
I googled and what I found was :
A clustered index is a special type of index that reorders the way
records in the table are physically
stored. Therefore table can have only
one clustered index. The leaf nodes
of a clustered index contain the data
pages. A nonclustered index is a
special type of index in which the
logical order of the index does not
match the physical stored order of
the rows on disk. The leaf node of a
nonclustered index does not consist of
the data pages. Instead, the leaf
nodes contain index rows.
What I found in SO was What are the differences between a clustered and a non-clustered index?.
Can someone explain this in plain English?
With a clustered index the rows are stored physically on the disk in the same order as the index. Therefore, there can be only one clustered index.
With a non clustered index there is a second list that has pointers to the physical rows. You can have many non clustered indices, although each new index will increase the time it takes to write new records.
It is generally faster to read from a clustered index if you want to get back all the columns. You do not have to go first to the index and then to the table.
Writing to a table with a clustered index can be slower, if there is a need to rearrange the data.
A clustered index means you are telling the database to store close values actually close to one another on the disk. This has the benefit of rapid scan / retrieval of records falling into some range of clustered index values.
For example, you have two tables, Customer and Order:
Customer
----------
ID
Name
Address
Order
----------
ID
CustomerID
Price
If you wish to quickly retrieve all orders of one particular customer, you may wish to create a clustered index on the "CustomerID" column of the Order table. This way the records with the same CustomerID will be physically stored close to each other on disk (clustered) which speeds up their retrieval.
P.S. The index on CustomerID will obviously be not unique, so you either need to add a second field to "uniquify" the index or let the database handle that for you but that's another story.
Regarding multiple indexes. You can have only one clustered index per table because this defines how the data is physically arranged. If you wish an analogy, imagine a big room with many tables in it. You can either put these tables to form several rows or pull them all together to form a big conference table, but not both ways at the same time. A table can have other indexes, they will then point to the entries in the clustered index which in its turn will finally say where to find the actual data.
In SQL Server, row-oriented storage both clustered and nonclustered indexes are organized as B trees.
(Image Source)
The key difference between clustered indexes and non clustered indexes is that the leaf level of the clustered index is the table. This has two implications.
The rows on the clustered index leaf pages always contain something for each of the (non-sparse) columns in the table (either the value or a pointer to the actual value).
The clustered index is the primary copy of a table.
Non clustered indexes can also do point 1 by using the INCLUDE clause (Since SQL Server 2005) to explicitly include all non-key columns but they are secondary representations and there is always another copy of the data around (the table itself).
CREATE TABLE T
(
A INT,
B INT,
C INT,
D INT
)
CREATE UNIQUE CLUSTERED INDEX ci ON T(A, B)
CREATE UNIQUE NONCLUSTERED INDEX nci ON T(A, B) INCLUDE (C, D)
The two indexes above will be nearly identical. With the upper-level index pages containing values for the key columns A, B and the leaf level pages containing A, B, C, D
There can be only one clustered index per table, because the data rows
themselves can be sorted in only one order.
The above quote from SQL Server books online causes much confusion
In my opinion, it would be much better phrased as.
There can be only one clustered index per table because the leaf level rows of the clustered index are the table rows.
The book's online quote is not incorrect but you should be clear that the "sorting" of both non clustered and clustered indices is logical, not physical. If you read the pages at leaf level by following the linked list and read the rows on the page in slot array order then you will read the index rows in sorted order but physically the pages may not be sorted. The commonly held belief that with a clustered index the rows are always stored physically on the disk in the same order as the index key is false.
This would be an absurd implementation. For example, if a row is inserted into the middle of a 4GB table SQL Server does not have to copy 2GB of data up in the file to make room for the newly inserted row.
Instead, a page split occurs. Each page at the leaf level of both clustered and non clustered indexes has the address (File: Page) of the next and previous page in logical key order. These pages need not be either contiguous or in key order.
e.g. the linked page chain might be 1:2000 <-> 1:157 <-> 1:7053
When a page split happens a new page is allocated from anywhere in the filegroup (from either a mixed extent, for small tables or a non-empty uniform extent belonging to that object or a newly allocated uniform extent). This might not even be in the same file if the filegroup contains more than one.
The degree to which the logical order and contiguity differ from the idealized physical version is the degree of logical fragmentation.
In a newly created database with a single file, I ran the following.
CREATE TABLE T
(
X TINYINT NOT NULL,
Y CHAR(3000) NULL
);
CREATE CLUSTERED INDEX ix
ON T(X);
GO
--Insert 100 rows with values 1 - 100 in random order
DECLARE #C1 AS CURSOR,
#X AS INT
SET #C1 = CURSOR FAST_FORWARD
FOR SELECT number
FROM master..spt_values
WHERE type = 'P'
AND number BETWEEN 1 AND 100
ORDER BY CRYPT_GEN_RANDOM(4)
OPEN #C1;
FETCH NEXT FROM #C1 INTO #X;
WHILE ##FETCH_STATUS = 0
BEGIN
INSERT INTO T (X)
VALUES (#X);
FETCH NEXT FROM #C1 INTO #X;
END
Then checked the page layout with
SELECT page_id,
X,
geometry::Point(page_id, X, 0).STBuffer(1)
FROM T
CROSS APPLY sys.fn_PhysLocCracker( %% physloc %% )
ORDER BY page_id
The results were all over the place. The first row in key order (with value 1 - highlighted with an arrow below) was on nearly the last physical page.
Fragmentation can be reduced or removed by rebuilding or reorganizing an index to increase the correlation between logical order and physical order.
After running
ALTER INDEX ix ON T REBUILD;
I got the following
If the table has no clustered index it is called a heap.
Non clustered indexes can be built on either a heap or a clustered index. They always contain a row locator back to the base table. In the case of a heap, this is a physical row identifier (rid) and consists of three components (File:Page: Slot). In the case of a Clustered index, the row locator is logical (the clustered index key).
For the latter case if the non clustered index already naturally includes the CI key column(s) either as NCI key columns or INCLUDE-d columns then nothing is added. Otherwise, the missing CI key column(s) silently gets added to the NCI.
SQL Server always ensures that the key columns are unique for both types of indexes. The mechanism in which this is enforced for indexes not declared as unique differs between the two index types, however.
Clustered indexes get a uniquifier added for any rows with key values that duplicate an existing row. This is just an ascending integer.
For non clustered indexes not declared as unique SQL Server silently adds the row locator into the non clustered index key. This applies to all rows, not just those that are actually duplicates.
The clustered vs non clustered nomenclature is also used for column store indexes. The paper Enhancements to SQL Server Column Stores states
Although column store data is not really "clustered" on any key, we
decided to retain the traditional SQL Server convention of referring
to the primary index as a clustered index.
I realize this is a very old question, but I thought I would offer an analogy to help illustrate the fine answers above.
CLUSTERED INDEX
If you walk into a public library, you will find that the books are all arranged in a particular order (most likely the Dewey Decimal System, or DDS). This corresponds to the "clustered index" of the books. If the DDS# for the book you want was 005.7565 F736s, you would start by locating the row of bookshelves that is labeled 001-099 or something like that. (This endcap sign at the end of the stack corresponds to an "intermediate node" in the index.) Eventually you would drill down to the specific shelf labelled 005.7450 - 005.7600, then you would scan until you found the book with the specified DDS#, and at that point you have found your book.
NON-CLUSTERED INDEX
But if you didn't come into the library with the DDS# of your book memorized, then you would need a second index to assist you. In the olden days you would find at the front of the library a wonderful bureau of drawers known as the "Card Catalog". In it were thousands of 3x5 cards -- one for each book, sorted in alphabetical order (by title, perhaps). This corresponds to the "non-clustered index". These card catalogs were organized in a hierarchical structure, so that each drawer would be labeled with the range of cards it contained (Ka - Kl, for example; i.e., the "intermediate node"). Once again, you would drill in until you found your book, but in this case, once you have found it (i.e, the "leaf node"), you don't have the book itself, but just a card with an index number (the DDS#) with which you could find the actual book in the clustered index.
Of course, nothing would stop the librarian from photocopying all the cards and sorting them in a different order in a separate card catalog. (Typically there were at least two such catalogs: one sorted by author name, and one by title.) In principle, you could have as many of these "non-clustered" indexes as you want.
Find below some characteristics of clustered and non-clustered indexes:
Clustered Indexes
Clustered indexes are indexes that uniquely identify the rows in an SQL table.
Every table can have exactly one clustered index.
You can create a clustered index that covers more than one column. For example: create Index index_name(col1, col2, col.....).
By default, a column with a primary key already has a clustered index.
Non-clustered Indexes
Non-clustered indexes are like simple indexes. They are just used for fast retrieval of data. Not sure to have unique data.
Clustered Index
A clustered index determines the physical order of DATA in a table. For this reason, a table has only one clustered index(Primary key/composite key).
"Dictionary" No need of any other Index, its already Index according to words
Nonclustered Index
A non-clustered index is analogous to an index in a Book. The data is stored in one place. The index is stored in another place and the index has pointers to the storage location. this help in the fast search of data. For this reason, a table has more than 1 Nonclustered index.
"Biology Book" at starting there is a separate index to point Chapter location and At the "END" there is another Index pointing the common WORDS location
A very simple, non-technical rule-of-thumb would be that clustered indexes are usually used for your primary key (or, at least, a unique column) and that non-clustered are used for other situations (maybe a foreign key). Indeed, SQL Server will by default create a clustered index on your primary key column(s). As you will have learnt, the clustered index relates to the way data is physically sorted on disk, which means it's a good all-round choice for most situations.
Clustered Index
A Clustered Index is basically a tree-organized table. Instead of storing the records in an unsorted Heap table space, the clustered index is actually B+Tree index having the Leaf Nodes, which are ordered by the clusters key column value, store the actual table records, as illustrated by the following diagram.
The Clustered Index is the default table structure in SQL Server and MySQL. While MySQL adds a hidden clusters index even if a table doesn't have a Primary Key, SQL Server always builds a Clustered Index if a table has a Primary Key column. Otherwise, the SQL Server is stored as a Heap Table.
The Clustered Index can speed up queries that filter records by the clustered index key, like the usual CRUD statements. Since the records are located in the Leaf Nodes, there's no additional lookup for extra column values when locating records by their Primary Key values.
For example, when executing the following SQL query on SQL Server:
SELECT PostId, Title
FROM Post
WHERE PostId = ?
You can see that the Execution Plan uses a Clustered Index Seek operation to locate the Leaf Node containing the Post record, and there are only two logical reads required to scan the Clustered Index nodes:
|StmtText |
|-------------------------------------------------------------------------------------|
|SELECT PostId, Title FROM Post WHERE PostId = #P0 |
| |--Clustered Index Seek(OBJECT:([high_performance_sql].[dbo].[Post].[PK_Post_Id]), |
| SEEK:([high_performance_sql].[dbo].[Post].[PostID]=[#P0]) ORDERED FORWARD) |
Table 'Post'. Scan count 0, logical reads 2, physical reads 0
Non-Clustered Index
Since the Clustered Index is usually built using the Primary Key column values, if you want to speed up queries that use some other column, then you'll have to add a Secondary Non-Clustered Index.
The Secondary Index is going to store the Primary Key value in its Leaf Nodes, as illustrated by the following diagram:
So, if we create a Secondary Index on the Title column of the Post table:
CREATE INDEX IDX_Post_Title on Post (Title)
And we execute the following SQL query:
SELECT PostId, Title
FROM Post
WHERE Title = ?
We can see that an Index Seek operation is used to locate the Leaf Node in the IDX_Post_Title index that can provide the SQL query projection we are interested in:
|StmtText |
|------------------------------------------------------------------------------|
|SELECT PostId, Title FROM Post WHERE Title = #P0 |
| |--Index Seek(OBJECT:([high_performance_sql].[dbo].[Post].[IDX_Post_Title]),|
| SEEK:([high_performance_sql].[dbo].[Post].[Title]=[#P0]) ORDERED FORWARD)|
Table 'Post'. Scan count 1, logical reads 2, physical reads 0
Since the associated PostId Primary Key column value is stored in the IDX_Post_Title Leaf Node, this query doesn't need an extra lookup to locate the Post row in the Clustered Index.
Clustered Index
Clustered indexes sort and store the data rows in the table or view based on their key values. These are the columns included in the index definition. There can be only one clustered index per table, because the data rows themselves can be sorted in only one order.
The only time the data rows in a table are stored in sorted order is when the table contains a clustered index. When a table has a clustered index, the table is called a clustered table. If a table has no clustered index, its data rows are stored in an unordered structure called a heap.
Nonclustered
Nonclustered indexes have a structure separate from the data rows. A nonclustered index contains the nonclustered index key values and each key value entry has a pointer to the data row that contains the key value.
The pointer from an index row in a nonclustered index to a data row is called a row locator. The structure of the row locator depends on whether the data pages are stored in a heap or a clustered table. For a heap, a row locator is a pointer to the row. For a clustered table, the row locator is the clustered index key.
You can add nonkey columns to the leaf level of the nonclustered index to by-pass existing index key limits, and execute fully covered, indexed, queries. For more information, see Create Indexes with Included Columns. For details about index key limits see Maximum Capacity Specifications for SQL Server.
Reference: https://learn.microsoft.com/en-us/sql/relational-databases/indexes/clustered-and-nonclustered-indexes-described
Let me offer a textbook definition on "clustering index", which is taken from 15.6.1 from Database Systems: The Complete Book:
We may also speak of clustering indexes, which are indexes on an attribute or attributes such that all of tuples with a fixed value for the search key of this index appear on roughly as few blocks as can hold them.
To understand the definition, let's take a look at Example 15.10 provided by the textbook:
A relation R(a,b) that is sorted on attribute a and stored in that
order, packed into blocks, is surely clusterd. An index on a is a
clustering index, since for a given a-value a1, all the tuples with
that value for a are consecutive. They thus appear packed into
blocks, execept possibly for the first and last blocks that contain
a-value a1, as suggested in Fig.15.14. However, an index on b is
unlikely to be clustering, since the tuples with a fixed b-value
will be spread all over the file unless the values of a and b are
very closely correlated.
Note that the definition does not enforce the data blocks have to be contiguous on the disk; it only says tuples with the search key are packed into as few data blocks as possible.
A related concept is clustered relation. A relation is "clustered" if its tuples are packed into roughly as few blocks as can possibly hold those tuples. In other words, from a disk block perspective, if it contains tuples from different relations, then those relations cannot be clustered (i.e., there is a more packed way to store such relation by swapping the tuples of that relation from other disk blocks with the tuples the doesn't belong to the relation in the current disk block). Clearly, R(a,b) in example above is clustered.
To connect two concepts together, a clustered relation can have a clustering index and nonclustering index. However, for non-clustered relation, clustering index is not possible unless the index is built on top of the primary key of the relation.
"Cluster" as a word is spammed across all abstraction levels of database storage side (three levels of abstraction: tuples, blocks, file). A concept called "clustered file", which describes whether a file (an abstraction for a group of blocks (one or more disk blocks)) contains tuples from one relation or different relations. It doesn't relate to the clustering index concept as it is on file level.
However, some teaching material likes to define clustering index based on the clustered file definition. Those two types of definitions are the same on clustered relation level, no matter whether they define clustered relation in terms of data disk block or file. From the link in this paragraph,
An index on attribute(s) A on a file is a clustering index when: All tuples with attribute value A = a are stored sequentially (= consecutively) in the data file
Storing tuples consecutively is the same as saying "tuples are packed into roughly as few blocks as can possibly hold those tuples" (with minor difference on one talking about file, the other talking about disk). It's because storing tuple consecutively is the way to achieve "packed into roughly as few blocks as can possibly hold those tuples".
Clustered Index:
Primary Key constraint creates clustered Index automatically if no clustered Index already exists on the table. Actual data of clustered index can be stored at leaf level of Index.
Non Clustered Index:
Actual data of non clustered index is not directly found at leaf node, instead it has to take an additional step to find because it has only values of row locators pointing towards actual data.
Non clustered Index can't be sorted as clustered index. There can be multiple non clustered indexes per table, actually it depends on the sql server version we are using. Basically Sql server 2005 allows 249 Non Clustered Indexes and for above versions like 2008, 2016 it allows 999 Non Clustered Indexes per table.
Clustered Index - A clustered index defines the order in which data is physically stored in a table. Table data can be sorted in only way, therefore, there can be only one clustered index per table. In SQL Server, the primary key constraint automatically creates a clustered index on that particular column.
Non-Clustered Index - A non-clustered index doesn’t sort the physical data inside the table. In fact, a non-clustered index is stored at one place and table data is stored in another place. This is similar to a textbook where the book content is located in one place and the index is located in another. This allows for more than one non-clustered index per table.It is important to mention here that inside the table the data will be sorted by a clustered index. However, inside the non-clustered index data is stored in the specified order. The index contains column values on which the index is created and the address of the record that the column value belongs to.When a query is issued against a column on which the index is created, the database will first go to the index and look for the address of the corresponding row in the table. It will then go to that row address and fetch other column values. It is due to this additional step that non-clustered indexes are slower than clustered indexes
Differences between clustered and Non-clustered index
There can be only one clustered index per table. However, you can
create multiple non-clustered indexes on a single table.
Clustered indexes only sort tables. Therefore, they do not consume
extra storage. Non-clustered indexes are stored in a separate place
from the actual table claiming more storage space.
Clustered indexes are faster than non-clustered indexes since they
don’t involve any extra lookup step.
For more information refer to this article.
How are duplicate keys handled in InnoDB's implementation of B+ tree for it's indexes.
For example, if there is a table with 1 million rows having a column with cardinality of 10. If we create an index on this column, how will the resulting B+ tree would look like?
Will it just have 10 keys and the value of each key is the list of primary keys which belong to that key (if yes, in what structure? Linked list?) or will it have 1M keys (if yes, then B+ tree would have to be handled differently)?
In some sense, an InnoDB BTree has no duplicates. This is because the columns of the PRIMARY KEY are appended to the columns specified for a secondary key. That leads to a fully-ordered list.
When you lookup via a secondary key (or the initial part of a key), the query will drill down the BTree to find the first row in the index matching what you gave, then scan forward to get any others. To get the rest of the columns, it takes the PRIMARY KEY columns to do a second BTree lookup.
The Optimizer will rarely use an index with "low cardinality". For example, a yes/no or true/false or male/female column should not be indexed. The Optimizer would find it faster to simply scan the table rather than bounce back and forth between the index and (via the PK columns) the main BTree.
The cutoff for when to use the index versus punting is somewhere around 20%, depending on the phase of the moon.
Bad index
The case you propose is a bad one for a B+ tree. A cardinality of 10 means only 10 of the 1 million values are unique. Actually it is not only bad for a B+ tree, it is a bad index in general. Based on this index you will on average be left with a subset of approx. 100,000 values, which you either have to look through or use another value to filter further.
B+ tree properties
Concerning the structure of the resulting tree there are some things to keep in mind here:
A node cannot contain arbitrary much data.
Inserts may require splits if the leaf node is full
Occasionally the split of a leaf node necessitates split of the next higher node
In worst case scenarios the split may cascade all the way up to the root node
https://www.percona.com/files/presentations/percona-live/london-2011/PLUK2011-b-
Leafs are linked as a double-linked list.
Leaf nodes are linked together as doubly linked list
[…]
Entire tree may be scanned without visiting the higher nodes at all
https://www.percona.com/files/presentations/percona-live/london-2011/PLUK2011-b-
Expectation
If you insert a lot of data with keys which more or less belong all to the same equivalence class, I would expect a tree, which will not help a lot. The 10 keys might be present solely in the root node, and all data deeper in the tree will just be unsorted (because there is nothing left to sort it).
Due to the fact that the leafs are double-linked lists you are basically left with what I've written in the beginning: You have to traverse a big subset of the values. Concerning the given index this had to be expected and the B+ tree might doing well given the circumstances (a list is ok for just going through all data).
Actually this goes one abstraction deeper: The leafs are double-linked, but there are multiple values in each leaf (data or link to PK). Nevertheless these are in a list too, so if you just traverse everything it makes not much of a difference.
Examining InnoDB space
Please see that you can also investigate what MySQL is really building. There are tools to inspect the built index data structures, see for example
https://blog.jcole.us/2013/01/10/btree-index-structures-in-innodb/
https://github.com/jeremycole/innodb_ruby
InnoDB stores table in B+ tree index called internally PRIMARY. The key of the index is your primary key fields.
If you define a secondary index there will be additional B+ tree index(in .ibd or ibdata1) where the key is the secondary index fields and value is the primary key.
B+ tree itself doesn't require key to be unique. Uniqueness of PRIMARY and all UNIQUE indexes are enforced at server level.
Here're some slides about how InnoDB organizes indexes and uses them to access the data. http://www.slideshare.net/akuzminsky/efficient-indexes-in-mysql#downloads-panel