Regarding Clustered Indexes in DBMS - database

Here is one of the definitions I found for clustered Index:
When is a file is organized so that the ordering of data records is
the same as or close to the ordering of data entries in some index, we
say that the index is clustered.
I'm having trouble understanding the above sentence regarding the clustered Indexes. The things I know about clustered index are:
Clustered indexes reorders the way the records are physically stored in the table, so only one clustered index is possible
Clustered index is created on non key attribute

Well for clustered index we have many view to look into
A clustered index is a type of index where the table records are physically re-ordered to match the index.
Clustered indexes are efficient on columns that are searched for a range of values. After the row with first value is found using a clustered index, rows with subsequent index values are guaranteed to be physically adjacent, thus providing faster access for a user query or an application
You also have to understand the Non-Clustered Index
In other words, a clustered index stores the actual data, where a non-clustered index is a pointer to the data. In most DBMSs, you can only have one clustered index per table, though there are systems that support multiple clusters (DB2 being an example).
Like a regular index that is stored unsorted in a database table, a clustered index can be a composite index, such as a concatenation of first name and last name in a table of personal information.
There are several example and explanations. And this is What do Clustered and Non clustered index actually mean? one of them.

Related

Index performance, clustered vs non clustered

If a table only needs 1 index, it seems like clustered is generally the way to go. It is faster because it does not have to reference back to the data via a key, and it also doesn't take disk space the way a non clustered index does.
My question is with multiple indexes, is it better to remove clustered index all together? The logic behind this is that if you have non clustered indexes WITH a clustered index, they don't directly refer back to the actual data rows anymore, but to the clustered index instead. So it seems like there would be a significant performance hit by using the clustered index as a proxy. It seems like the best thing to do would be to not use clustered indexes at all if you think you will need more than 1 index on the table.
If the table has a proper clustered index there is no benefit to removing it.
If you have several indexes then pick the best candidate for clustered.
Typically it is your PK.
When you create a PK by default it clustered.
PK is your best candidate for clustered unless you have specific reason not to use it.
I don't follow your assertion.
"If you have non clustered indexes WITH a clustered index, they don't
refer back to the actual data rows anymore, but to the clustered index
instead. So it seems like there would be a significant performance
hit."
If the clustered index is in the data then referring to the clustered index is referring to the data. The data is physically organized by the clustered index. Where is the significant performance hit?
Clustered Index Design Guidelines
With few exceptions, every table should have a clustered index defined
If one of those few exception was another index then it would be called out.
Another non-clustered index is not a reason to not have a clustered index.
Nonclustered Index Structures
The row locators in nonclustered index rows are either a pointer to a row or are a clustered index key for a row, as described in the following:
If the table is a heap, which means it does not have a clustered
index, the row locator is a pointer to the row. The pointer is built
from the file identifier (ID), page number, and number of the row on
the page. The whole pointer is known as a Row ID (RID).
If the table has a clustered index, or the index is on an indexed
view, the row locator is the clustered index key for the row. If the
clustered index is not a unique index, SQL Server makes any duplicate
keys unique by adding an internally generated value called a
uniqueifier. This four-byte value is not visible to users. It is only
added when required to make the clustered key unique for use in
nonclustered indexes. SQL Server retrieves the data row by searching
the clustered index using the clustered index key stored in the leaf
row of the nonclustered index.
They had the option use a RID even if there was a PK. Why do you think clustered index is slower?

Nonclustered index uses key into clustered index instead of address?

In the documentation for SQL server 2008 R2 is stated:
Wide keys are a composite of several columns or several large-size columns. The key values from the clustered index are used by all nonclustered indexes as lookup keys. Any nonclustered indexes defined on the same table will be significantly larger because the nonclustered index entries contain the clustering key and also the key columns defined for that nonclustered index.
Does this mean, that when there is a search using non-clustered index, than the clustered indes is search also? I originally thought that the non-clustered index contains ditrectly the address of the page (block) with the row it references. From the text above it seems that it contains just the key from the non-clustered index instead of the address.
Could somebody explain please?
Yes, that's exactly what happens:
SQL Server searches for your search value in the non-clustered index
if a match is found, in that index entry, there's also the clustering key (the column or columns that make up the clustered index)
with that clustered key, a key lookup (often also called bookmark lookup) is now performed - the clustered index is searched for that value given
when the item is found, the entire data record at the leaf level of the clustered index navigation structure is present and can be returned
SQL Server does this, because using a physical address would be really really bad:
if a page split occurs, all the entries that are moved to a new page would be updated
for all those entries, all nonclustered indices would also have to be updated
and this is really really bad for performance.
This is one of the reasons why it is beneficial to use limited column lists in SELECT (instead of always SELECT *) and possibly even include a few extra columns in the nonclustered index (to make it a covering index). That way, you can avoid unnecessary and expensive bookmark lookups.
And because the clustering key is included in each and every nonclustered index, it's highly important that this be a small and narrow key - optimally an INT IDENTITY or something like that - and not a huge structure; the clustering key is the most replicated data structure in SQL Server and should be a small as possible.
The fact that these bookmark lookups are relatively expensive is also one of the reasons why the query optimizer might opt for an index scan as soon as you select a larger number of rows - at at time, just scanning the clustered index might be cheaper than doing a lot of key lookups.

Should every User Table have a Clustered Index?

Recently I found a couple of tables in a Database with no Clustered Indexes defined.
But there are non-clustered indexes defined, so they are on HEAP.
On analysis I found that select statements were using filter on the columns defined in non-clustered indexes.
Not having a clustered index on these tables affect performance?
It's hard to state this more succinctly than SQL Server MVP Brad McGehee:
As a rule of thumb, every table should have a clustered index. Generally, but not always, the clustered index should be on a column that monotonically increases–such as an identity column, or some other column where the value is increasing–and is unique. In many cases, the primary key is the ideal column for a clustered index.
BOL echoes this sentiment:
With few exceptions, every table should have a clustered index.
The reasons for doing this are many and are primarily based upon the fact that a clustered index physically orders your data in storage.
If your clustered index is on a single column monotonically increases, inserts occur in order on your storage device and page splits will not happen.
Clustered indexes are efficient for finding a specific row when the indexed value is unique, such as the common pattern of selecting a row based upon the primary key.
A clustered index often allows for efficient queries on columns that are often searched for ranges of values (between, >, etc.).
Clustering can speed up queries where data is commonly sorted by a specific column or columns.
A clustered index can be rebuilt or reorganized on demand to control table fragmentation.
These benefits can even be applied to views.
You may not want to have a clustered index on:
Columns that have frequent data changes, as SQL Server must then physically re-order the data in storage.
Columns that are already covered by other indexes.
Wide keys, as the clustered index is also used in non-clustered index lookups.
GUID columns, which are larger than identities and also effectively random values (not likely to be sorted upon), though newsequentialid() could be used to help mitigate physical reordering during inserts.
A rare reason to use a heap (table without a clustered index) is if the data is always accessed through nonclustered indexes and the RID (SQL Server internal row identifier) is known to be smaller than a clustered index key.
Because of these and other considerations, such as your particular application workloads, you should carefully select your clustered indexes to get maximum benefit for your queries.
Also note that when you create a primary key on a table in SQL Server, it will by default create a unique clustered index (if it doesn't already have one). This means that if you find a table that doesn't have a clustered index, but does have a primary key (as all tables should), a developer had previously made the decision to create it that way. You may want to have a compelling reason to change that (of which there are many, as we've seen). Adding, changing or dropping the clustered index requires rewriting the entire table and any non-clustered indexes, so this can take some time on a large table.
I would not say "Every table should have a clustered index", I would say "Look carefully at every table and how they are accessed and try to define a clustered index on it if it makes sense". It's a plus, like a Joker, you have only one Joker per table, but you don't have to use it. Other database systems don't have this, at least in this form, BTW.
Putting clustered indices everywhere without understanding what you're doing can also kill your performance (in general, the INSERT performance because a clustered index means physical re-ordering on the disk, or at least it's a good way to understand it), for example with GUID primary keys as we see more and more.
So, read Tim Lehner's exceptions and reason.
Performance is a big hairy problem. Make sure you are optimizing for the right thing.
Free advice is always worth it's price, and there is no substitute for actual experimentation.
The purpose of an index is to find matching rows and help retrieve the data when found.
A non-clustered index on your search criteria will help to find rows, but there needs to be additional operation to get at the row's data.
If there is no clustered index, SQL uses an internal rowId to point to the location of the data.
However, If there is a clustered index on the table, that rowId is replaced by the data values in the clustered index.
So the step of reading the rows data would not be needed, and would be covered by the values in the index.
Even if a clustered index isn't very good at being selective, if those keys are frequently most or all of the results requested - it may be helpful to have them as the leaf of the non-clustered index.
Yes you should have clustered index on a table.So that all nonclustered indexes perform in better way.
Consider using a clustered index when Columns that contain a large number of distinct values so to avoid the need for SQL Server to add a "uniqueifier" to duplicate key values
Disadvantage : It takes longer to update records if only when the fields in the clustering index are changed.
Avoid clustering index constructions where there is a risk that many concurrent inserts will happen on almost the same clustering index value
Searches against a nonclustered index will appear slower is the clustered index isn't build correctly, or it does not include all the columns needed to return the data back to the calling application. In the event that the non-clustered index doesn't contain all the needed data then the SQL Server will go to the clustered index to get the missing data (via a lookup) which will make the query run slower as the lookup is done row by row.
Yes, every table should have a clustered index. The clustered index sets the physical order of data in a table. You can compare this to the ordering of music at a store, by bands name and or Yellow pages ordered by a last name. Since this deals with the physical order you can have only one it can be comprised by many columns but you can only have one.
It’s best to place the clustered index on columns often searched for a range of values. Example would be a date range. Clustered indexes are also efficient for finding a specific row when the indexed value is unique. Microsoft SQL will place clustered indexes on a PRIMARY KEY constraint automatically if no clustered indexes are defined.
Clustered indexes are not a good choice for:
Columns that undergo frequent changes
This results in the entire row moving (because SQL Server must keep
the data values of a row in physical order). This is an important
consideration in high-volume transaction processing systems where
data tends to be volatile.
Wide keys
The key values from the clustered index are used by all
nonclustered indexes as lookup keys and therefore are stored in each
nonclustered index leaf entry.

SQL Server Indexes - Non-Clustered Index on HEAP

We have got 221gb table in our SQL Database, mainly duplicate data.
Team has created NON-CLUSTERED index on HEAP. Does really this help in terms of performannce?
Should we put IDENTITY column in table and then create CLUSTERED index AND after that we can create NON clustered indexes.
It Depends
On the usage pattern and structure of the data.
Is the non-clustered index covering?
Is the data in the table ever changing?
A heap table with a non-clustered index (or indexes) which are covering can outperform a clustered index where the clustered index is the only "index" (a clustered index is obviously always covering, but may not be optimal for seeks)
Remember a clustered index is not an index (in the sense of a lookup based on a key into a location where the data is stored), it's the whole table organized by a choice of index. In a real (non-clustered) index, only the keys and included columns are included in the index and this means that (generally) more rows can be stored per database page and less data is read unnecessarily.
Most tables should have a clustered index, but the choice of non-clustered indexes is where most of your performance comes from.

What do Clustered and Non-Clustered index actually mean?

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.

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