Indexes are structures stored in the database that users manage using SQL statements. In general, index keys have two pieces, a grouping piece and a unique piece.
Bitmap indexes can process this query efficiently by counting the number of 1 values in the resulting bitmap, as illustrated in Table To identify the customers who satisfy the criteria, Oracle Database can use the resulting bitmap to access the table. Rows that satisfy some, but not all, conditions are filtered out before the table itself is accessed.
This technique improves response time, often dramatically. For each value in a table column, the index stores the rowid of the corresponding row in the indexed table. In contrast, a standard bitmap index is created on a single table. A bitmap join index is an efficient means of reducing the volume of data that must be joined by performing restrictions in advance.
For an example of when a bitmap join index would be useful, assume that users often query the number of employees with a particular job type. A typical query might look as follows:. The preceding query would typically use an index on jobs. To retrieve the data from the index itself rather than from a scan of the tables, you could create a bitmap join index as follows:.
As illustrated in Figure , the index key is jobs. A query of the number of accountants can use the index to avoid accessing the employees and jobs tables because the index itself contains the requested information. In a data warehouse, the join condition is an equijoin it uses the equality operator between the primary key columns of the dimension tables and the foreign key columns in the fact table. Bitmap join indexes are sometimes much more efficient in storage than materialized join views, an alternative for materializing joins in advance.
Oracle Database uses a B-tree index structure to store bitmaps for each indexed key. For example, if jobs. The individual bitmaps are stored in the leaf blocks. Assume that the jobs.
A bitmap index entry for this index has the following components:. In this case, the session requires exclusive access to the index key entry for the old value Shipping Clerk and the new value Stock Clerk. The data for a bitmap index is stored in one segment. Oracle Database stores each bitmap in one or more pieces. Each piece occupies part of a single data block. You can create indexes on functions and expressions that involve one or more columns in the table being indexed. A function-based index computes the value of a function or expression involving one or more columns and stores it in the index.
A function-based index can be either a B-tree or a bitmap index. For example, a function could add the values in two columns. Oracle Database Administrator's Guide to learn how to create function-based indexes. Oracle Database Performance Tuning Guide for more information about using function-based indexes. Function-based indexes are efficient for evaluating statements that contain functions in their WHERE clauses.
The database only uses the function-based index when the function is included in a query. The database can use the preceding index when processing queries such as Example partial sample output included. Example Query Containing an Arithmetic Expression. You create the following function-based index on the hr.
A function-based index is also useful for indexing only specific rows in a table. To index only the A rows, you could write a function that returns a null value for any rows other than the A rows. You could create the index as follows:.
Oracle Database Globalization Support Guide for information about linguistic indexes. The optimizer can use an index range scan on a function-based index for queries with expressions in WHERE clause. The range scan access path is especially beneficial when the predicate WHERE clause has low selectivity. A virtual column is useful for speeding access to data derived from expressions. The optimizer performs expression matching by parsing the expression in a SQL statement and then comparing the expression trees of the statement and the function-based index.
This comparison is case-insensitive and ignores blank spaces. Oracle Database Performance Tuning Guide for more information about gathering statistics. Oracle Database Administrator's Guide to learn how to add virtual columns to a table. An application domain index is a customized index specific to an application.
Oracle Database provides extensible indexing to do the following:. Accommodate indexes on customized, complex data types such as documents, spatial data, images, and video clips see "Unstructured Data".
You can encapsulate application-specific index management routines as an indextype schema object and define a domain index on table columns or attributes of an object type. Extensible indexing can efficiently process application-specific operators. The application software, called the cartridge , controls the structure and content of a domain index. The database interacts with the application to build, maintain, and search the domain index.
The index structure itself can be stored in the database as an index-organized table or externally as a file. Oracle Database stores index data in an index segment. Space available for index data in a data block is the data block size minus block overhead, entry overhead, rowid, and one length byte for each value indexed.
For ease of administration you can store an index in a separate tablespace from its table. For example, you may choose not to back up tablespaces containing only indexes, which can be rebuilt, and so decrease the time and storage required for backups.
An index-organized table is a table stored in a variation of a B-tree index structure. In a heap-organized table , rows are inserted where they fit. In an index-organized table, rows are stored in an index defined on the primary key for the table. Each index entry in the B-tree also stores the non-key column values. Thus, the index is the data, and the data is the index. Applications manipulate index-organized tables just like heap-organized tables, using SQL statements.
For an analogy of an index-organized table, suppose a human resources manager has a book case of cardboard boxes. Each box is labeled with a number—1, 2, 3, 4, and so on—but the boxes do not sit on the shelves in sequential order. Instead, each box contains a pointer to the shelf location of the next box in the sequence. Folders containing employee records are stored in each box.
The folders are sorted by employee ID. The folder for employee is on top of , is on top of , and so on until box 1 is full.
The next folder in the sequence is at the bottom of box 2. In this analogy, ordering folders by employee ID makes it possible to search efficiently for folders without having to maintain a separate index. Suppose a user requests the records for employees , , and Instead of searching an index in one step and retrieving the folders in a separate step, the manager can search the folders in sequential order and retrieve each folder as found.
Index-organized tables provide faster access to table rows by primary key or a valid prefix of the key. For example, the salary of employee is stored in the index row itself.
Another benefit is the avoidance of the space overhead of a separate primary key index. Index-organized tables are useful when related pieces of data must be stored together or data must be physically stored in a specific order. Oracle Database Administrator's Guide to learn how to manage index-organized tables. Oracle Database Performance Tuning Guide to learn how to use index-organized tables to improve performance. The database system performs all operations on index-organized tables by manipulating the B-tree index structure.
Table summarizes the differences between index-organized tables and heap-organized tables. The rowid uniquely identifies a row.
Primary key constraint may optionally be defined. Sequential full table scan returns all rows in some order. A full index scan or fast full index scan returns all rows in some order.
Can be stored in a table cluster with other tables. Can contain virtual columns only relational heap tables are supported. Figure illustrates the structure of an index-organized departments table.
The leaf blocks contain the rows of the table, ordered sequentially by primary key. For example, the first value in the first leaf block shows a department ID of 20 , department name of Marketing , manager ID of , and location ID of An index-organized table stores all data in the same structure and does not need to store the rowid. As shown in Figure , leaf block 1 in an index-organized table might contain entries as follows, ordered by primary key:. A scan of the index-organized table rows in primary key order reads the blocks in the following sequence:.
To contrast data access in a heap-organized table to an index-organized table, suppose block 1 of a heap-organized departments table segment contains rows as follows:. A B-tree index leaf block for this heap-organized table contains the following entries, where the first value is the primary key and the second is the rowid:.
A scan of the table rows in primary key order reads the table segment blocks in the following sequence:. When creating an index-organized table, you can specify a separate segment as a row overflow area. In index-organized tables, B-tree index entries can be large because they contain an entire row, so a separate segment to contain the entries is useful.
In contrast, B-tree entries are usually small because they consist of the key and rowid. If a row overflow area is specified, then the database can divide a row in an index-organized table into the following parts:. This part contains column values for all the primary key columns, a physical rowid that points to the overflow part of the row, and optionally a few of the non-key columns.
This part is stored in the index segment. This part contains column values for the remaining non-key columns. This part is stored in the overflow storage area segment.
A secondary index is an index on an index-organized table. In a sense, it is an index on an index. The secondary index is an independent schema object and is stored separately from the index-organized table.
As explained in "Rowid Data Types" , Oracle Database uses row identifiers called logical rowids for index-organized tables. A logical rowid is a baseencoded representation of the table primary key. The logical rowid length depends on the primary key length. Rows in index leaf blocks can move within or between blocks because of insertions. Rows in index-organized tables do not migrate as heap-organized rows do see "Chained and Migrated Rows".
Because rows in index-organized tables do not have permanent physical addresses, the database uses logical rowids based on primary key. For example, assume that the departments table is index-organized. The table stores rows as follows, with the last value as the location ID:. Secondary indexes provide fast and efficient access to index-organized tables using columns that are neither the primary key nor a prefix of the primary key. For example, a query of the names of departments whose ID is greater than could use the secondary index to speed data access.
Oracle Database Administrator's Guide to learn how to create secondary indexes on an index-organized table. Secondary indexes use the logical rowids to locate table rows.
A logical rowid includes a physical guess , which is the physical rowid of the index entry when it was first made. Oracle Database can use physical guesses to probe directly into the leaf block of the index-organized table, bypassing the primary key search.
When the physical location of a row changes, the logical rowid remains valid even if it contains a physical guess that is stale. For index-organized tables, access by a secondary index varies, depending on the use and accuracy of physical guesses:. Without physical guesses, access involves two index scans: A secondary index on an index-organized table can be a bitmap index.
As explained in "Bitmap Indexes" , a bitmap index stores a bitmap for each index key. When bitmap indexes exist on an index-organized table, all the bitmap indexes use a heap-organized mapping table. The mapping table stores the logical rowids of the index-organized table.
Each mapping table row stores one logical rowid for the corresponding index-organized table row. The database accesses a bitmap index using a search key. If the database finds the key, then the bitmap entry is converted to a physical rowid. With heap-organized tables, the database uses the physical rowid to access the base table.
With index-organized tables, the database uses the physical rowid to access the mapping table, which in turn yields a logical rowid that the database uses to access the index-organized table. This chapter contains the following sections: Overview of Indexes Overview of Index-Organized Tables Overview of Indexes An index is an optional structure, associated with a table or table cluster , that can sometimes speed data access. To speed access, the manager could create an index that sequentially lists every employee ID with its folder location: Box 3, position 1 bottom ID Box 7, position 8 ID Box 1, position In general, consider creating an index on a column in any of the following situations: Chapter 5, "Data Integrity".
Index Characteristics Indexes are schema objects that are logically and physically independent of the data in the objects with which they are associated.
If you drop an index, then applications still work. However, access of previously indexed data can be slower. Keys and Columns A key is a set of columns or expressions on which you can build an index.
Primary and unique keys automatically have indexes, but you might want to create an index on a foreign key. Composite Indexes A composite index , also called a concatenated index , is an index on multiple columns in a table. You create an index with the following column order: In some cases, such as when the leading column has very low cardinality, the database may use a skip scan of this index see "Index Skip Scan".
Oracle Database Performance Tuning Guide for more information about using composite indexes. Unique and Nonunique Indexes Indexes can be unique or nonunique. Types of Indexes Oracle Database provides several indexing schemes, which provide complementary performance functionality. The indexes can be categorized as follows: B-tree indexes These indexes are the standard index type.
B-tree indexes have the following subtypes: Index-organized tables An index-organized table differs from a heap-organized because the data is itself the index. Reverse key indexes In this type of index, the bytes of the index key are reversed, for example, is stored as Descending indexes This type of index stores data on a particular column or columns in descending order.
B-tree cluster indexes This type of index is used to index a table cluster key. Bitmap and bitmap join indexes In a bitmap index, an index entry uses a bitmap to point to multiple rows. Function-based indexes This type of index includes columns that are either transformed by a function, such as the UPPER function, or included in an expression. Application domain indexes This type of index is created by a user for data in an application-specific domain. Oracle Database Performance Tuning Guide to learn about different index types.
B-Tree Indexes B-trees, short for balanced trees , are the most common type of database index. Indexes in columns with character data are based on the binary values of the characters in the database character set.
Index Scans In an index scan , the database retrieves a row by traversing the index, using the indexed column values specified by the statement. Oracle Database Performance Tuning Guide for detailed information about index scans. Full Index Scan In a full index scan , the database reads the entire index in order. Suppose that an application runs the following query: For example, the full scan could read the index entries as follows: Fast Full Index Scan A fast full index scan is a full index scan in which the database accesses the data in the index itself without accessing the table, and the database reads the index blocks in no particular order.
Fast full index scans are an alternative to a full table scan when both of the following conditions are met: The index must contain all columns needed for the query. For this result to be guaranteed, at least one column in the index must have either: If the last name and salary are a composite key in an index, then a fast full index scan can read the index entries to obtain the requested information: Baida,,rowid Zlotkey,,rowid Austin,,rowid Baer,,rowid Atkinson,,rowid Austin,,rowid.
Index Range Scan An index range scan is an ordered scan of an index that has the following characteristics: Index Unique Scan In contrast to an index range scan, an index unique scan must have either 0 or 1 rowid associated with an index key. As an illustration, suppose that a user runs the following query: Index Skip Scan An index skip scan uses logical subindexes of a composite index.
Oracle Database Performance Tuning Guide to learn more about skip scans. Index Clustering Factor The index clustering factor measures row order in relation to an indexed value such as employee last name. The clustering factor is relevant for index scans because it can show: Whether the database will use an index for large range scans The degree of table organization in relation to the index key Whether you should consider using an index-organized table, partitioning, or table cluster if rows must be ordered by the index key For example, assume that the employees table fits into two data blocks.
Reverse Key Indexes A reverse key index is a type of B-tree index that physically reverses the bytes of each index key while keeping the column order. Oracle Database Performance Tuning Guide to learn about design considerations for reverse key indexes.
Ascending and Descending Indexes In an ascending index , Oracle Database stores data in ascending order. For an example of an ascending index, consider the following SQL statement: Key Compression Oracle Database can use key compression to compress portions of the primary key column values in a B-tree index or an index-organized table.
If a key is not defined to have a unique piece, then the database provides one by appending a rowid to the grouping piece. Bitmap Indexes In a bitmap index , the database stores a bitmap for each index key. Situations that may call for a bitmap index include: Oracle Database Performance Tuning Guide to learn how to use bitmap indexes for performance Oracle Database Data Warehousing Guide to learn how to use bitmap indexes in a data warehouse.
Bitmap Indexes on a Single Table Example shows a query of the sh. Bitmap indexes can include keys that consist entirely of null values, unlike B-tree indexes. Bitmap Join Indexes A bitmap join index is a bitmap index for the join of two or more tables.
A typical query might look as follows: To retrieve the data from the index itself rather than from a scan of the tables, you could create a bitmap join index as follows: Oracle Database Data Warehousing Guide for more information on bitmap join indexes.
Bitmap Storage Structure Oracle Database uses a B-tree index structure to store bitmaps for each indexed key. A bitmap index entry for this index has the following components: The job title as the index key A low rowid and high rowid for a range of rowids A bitmap for specific rowids in the range Conceptually, an index leaf block in this index could contain entries as follows: The same job title appears in multiple entries because the rowid range differs.
Function-Based Indexes You can create indexes on functions and expressions that involve one or more columns in the table being indexed. Oracle Database Administrator's Guide to learn how to create function-based indexes Oracle Database Performance Tuning Guide for more information about using function-based indexes Oracle Database SQL Language Reference for restrictions and usage notes for function-based indexes.
For example, suppose you create the following function-based index: Application Domain Indexes An application domain index is a customized index specific to an application. Oracle Database provides extensible indexing to do the following: Accommodate indexes on customized, complex data types such as documents, spatial data, images, and video clips see "Unstructured Data" Make use of specialized indexing techniques You can encapsulate application-specific index management routines as an indextype schema object and define a domain index on table columns or attributes of an object type.
Oracle Database Data Cartridge Developer's Guide for information about using data cartridges within the Oracle Database extensibility architecture. Index Storage Oracle Database stores index data in an index segment. Chapter 12, "Logical Storage Structures".
Overview of Index-Organized Tables An index-organized table is a table stored in a variation of a B-tree index structure. Index-Organized Table Characteristics The database system performs all operations on index-organized tables by manipulating the B-tree index structure. Primary key uniquely identifies a row. Primary key constraint must be defined. Individual rows may be accessed directly by rowid. Access to individual rows may be achieved indirectly by primary key. Cannot be stored in a table cluster.
Cannot contain virtual columns. Index-Organized Tables with Row Overflow Area When creating an index-organized table, you can specify a separate segment as a row overflow area. If a row overflow area is specified, then the database can divide a row in an index-organized table into the following parts: The index entry This part contains column values for all the primary key columns, a physical rowid that points to the overflow part of the row, and optionally a few of the non-key columns.
The overflow part This part contains column values for the remaining non-key columns. Secondary Indexes on Index-Organized Tables A secondary index is an index on an index-organized table. The table stores rows as follows, with the last value as the location ID: Oracle Database Administrator's Guide to learn how to create secondary indexes on an index-organized table Oracle Database VLDB and Partitioning Guide to learn about creating secondary indexes on indexed-organized table partitions.
Logical Rowids and Physical Guesses Secondary indexes use the logical rowids to locate table rows. In general, the transformational nature of a Lorentz tensor [ clarification needed ] can be identified by its tensor order , which is the number of free indices it has.
No indices implies it is a scalar, one implies that it is a vector, etc. Some tensors with a physical interpretation are listed below. In standard field theory, there are very strict and severe constraints on marginal and relevant Lorentz violating operators within both QED and the Standard Model.
Irrelevant Lorentz violating operators may be suppressed by a high cutoff scale, but they typically induce marginal and relevant Lorentz violating operators via radiative corrections.
So, we also have very strict and severe constraints on irrelevant Lorentz violating operators. Since some approaches to quantum gravity lead to violations of Lorentz invariance,  these studies are part of Phenomenological Quantum Gravity.
Lorentz violations are allowed in string theory , supersymmetry and Horava-Lifshitz gravity. Lorentz violating models typically fall into four classes: Models belonging to the first two classes can be consistent with experiment if Lorentz breaking happens at Planck scale or beyond it, or even before it in suitable preonic models,  and if Lorentz symmetry violation is governed by a suitable energy-dependent parameter.
This is also true for the third class, which is furthermore protected from radiative corrections as one still has an exact quantum symmetry. Even though there is no evidence of the violation of Lorentz invariance, several experimental searches for such violations have been performed during recent years.
Lorentz invariance is also violated in QFT assuming non-zero temperature. There is also growing evidence of Lorentz violation in Weyl semimetals and Dirac semimetals. From Wikipedia, the free encyclopedia. Lorentz covariance has two distinct, but closely related meanings: A physical quantity is said to be Lorentz covariant if it transforms under a given representation of the Lorentz group.
According to the representation theory of the Lorentz group , these quantities are built out of scalars , four-vectors , four-tensors , and spinors. In particular, a Lorentz covariant scalar e. An equation is said to be Lorentz covariant if it can be written in terms of Lorentz covariant quantities confusingly, some use the term invariant here. The key property of such equations is that if they hold in one inertial frame, then they hold in any inertial frame; this follows from the result that if all the components of a tensor vanish in one frame, they vanish in every frame.
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