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Nested Set Model
The nested set model is a technique for representing nested set collections (also known as trees or hierarchies) in relational databases. It is based on Nested Intervals, that "are immune to hierarchy reorganization problem, and allow answering ancestor path hierarchical queries algorithmically — without accessing the stored hierarchy relation". Motivation The standard relational algebra and relational calculus, and the SQL operations based on them, are unable to express directly all desirable operations on hierarchies. The nested set model is a solution to that problem. An alternative solution is the expression of the hierarchy as a parent-child relation. Joe Celko called this the adjacency list model. If the hierarchy can have arbitrary depth, the adjacency list model does not allow the expression of operations such as comparing the contents of hierarchies of two elements, or determining whether an element is somewhere in the subhierarchy of another element. When the h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nested Set Collection
A nested set collection or nested set family is a collection of sets that consists of chains of subsets forming a hierarchical structure, like Matryoshka doll, Russian dolls. It is used as reference concept in hierarchy, scientific hierarchy definitions, and many technical approaches, like the tree (data structure), tree in Data structure, computational data structures or nested set model of relational databases. Sometimes the concept is confused with a collection of sets with a hereditary property (like finiteness in a hereditarily finite set). Formal definition Some authors regard a nested set collection as a family of sets. Others prefer to classify it relation as an inclusion order. Let ''B'' be a empty set, non-empty set and C a collection of subsets of ''B''. Then C is a nested set collection if: * B \in \mathbf (and, for some authors, \empty \notin \mathbf) * \forall H,K \in \mathbf ~:~ H \cap K \neq \empty \implies H \subset K ~\lor~ K \subset H The first condition sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
T-SQL
Transact-SQL (T-SQL) is Microsoft's and Sybase's proprietary extension to the SQL (Structured Query Language) used to interact with relational databases. T-SQL expands on the SQL standard to include procedural programming, local variables, various support functions for string processing, date processing, mathematics, etc. and changes to the DELETE and UPDATE statements. Transact-SQL is central to using Microsoft SQL Server. All applications that communicate with an instance of SQL Server do so by sending Transact-SQL statements to the server, regardless of the user interface of the application. Stored procedures in SQL Server are executable server-side routines. The advantage of stored procedures is the ability to pass parameters. Variables Transact-SQL provides the following statements to declare and set local variables: DECLARE, SET and SELECT. DECLARE @var1 NVARCHAR(30); SET @var1 = 'Some Name'; SELECT @var1 = Name FROM Sales.Store WHERE CustomerID = 100; Flow contro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calkin–Wilf Tree
In number theory, the Calkin–Wilf tree is a tree in which the vertices correspond one-to-one to the positive rational numbers. The tree is rooted at the number 1, and any rational number expressed in simplest terms as the fraction has as its two children the numbers and . Every positive rational number appears exactly once in the tree. It is named after Neil Calkin and Herbert Wilf, but appears in other works including Kepler's ''Harmonices Mundi''. The sequence of rational numbers in a breadth-first traversal of the Calkin–Wilf tree is known as the Calkin–Wilf sequence. Its sequence of numerators (or, offset by one, denominators) is Stern's diatomic series, and can be computed by the fusc function. History The Calkin–Wilf tree is named after Neil Calkin and Herbert Wilf, who considered it in a 2000 paper. In a 1997 paper, Jean Berstel and Aldo de Luca called the same tree the ''Raney tree'', since they drew some ideas from a 1973 paper by George N. Raney. Ster ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adjacency List
In graph theory and computer science, an adjacency list is a collection of unordered lists used to represent a finite graph. Each unordered list within an adjacency list describes the set of neighbors of a particular vertex in the graph. This is one of several commonly used representations of graphs for use in computer programs. Implementation details An adjacency list representation for a graph associates each vertex in the graph with the collection of its neighbouring vertices or edges. There are many variations of this basic idea, differing in the details of how they implement the association between vertices and collections, in how they implement the collections, in whether they include both vertices and edges or only vertices as first class objects, and in what kinds of objects are used to represent the vertices and edges. * An implementation suggested by Guido van Rossum uses a hash table to associate each vertex in a graph with an array of adjacent vertices. In this ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nested Intervals
In mathematics, a sequence of nested intervals can be intuitively understood as an ordered collection of Interval (mathematics), intervals I_n on the Interval (mathematics), real number line with natural number, natural numbers n=1,2,3,\dots as an index. In order for a sequence of intervals to be considered nested intervals, two conditions have to be met: # Every interval in the sequence is contained in the previous one (I_ is always a subset of I_n). # The length of the intervals get arbitrarily small (meaning the length falls below every possible threshold \varepsilon after a certain index N). In other words, the left bound of the interval I_n can only increase (a_\geq a_n), and the right bound can only decrease (b_\leq b_n). Historically - long before anyone defined nested intervals in a textbook - people implicitly constructed such nestings for concrete calculation purposes. For example, the ancient Babylonia, Babylonians discovered a Methods of computing square roots, metho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Microsoft SQL Server
Microsoft SQL Server is a proprietary relational database management system developed by Microsoft using Structured Query Language (SQL, often pronounced "sequel"). As a database server, it is a software product with the primary function of storing and retrieving data as requested by other software applications—which may run either on the same computer or on another computer across a network (including the Internet). Microsoft markets at least a dozen different editions of Microsoft SQL Server, aimed at different audiences and for workloads ranging from small single-machine applications to large Internet-facing applications with many concurrent users. History The history of Microsoft SQL Server begins with the first Microsoft SQL Server product—SQL Server 1.0, a 16-bit server for the OS/2 operating system in 1989—and extends to the current day. Its name is entirely descriptive, it being '' server'' software that responds to queries in the '' SQL'' language. Mil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oracle Database
Oracle Database (commonly referred to as Oracle DBMS, Oracle Autonomous Database, or simply as Oracle) is a proprietary multi-model database management system produced and marketed by Oracle Corporation. It is a database commonly used for running online transaction processing (OLTP), data warehousing (DW) and mixed (OLTP & DW) database workloads. Oracle Database is available by several service providers on-premises, on-cloud, or as a hybrid cloud installation. It may be run on third party servers as well as on Oracle hardware ( Exadata on-premises, on Oracle Cloud or at Cloud at Customer). Oracle Database uses SQL for database updating and retrieval. History Larry Ellison and his two friends and former co-workers, Bob Miner and Ed Oates, started a consultancy called Software Development Laboratories (SDL) in 1977, later Oracle Corporation. SDL developed the original version of the Oracle software. The name ''Oracle'' comes from the code-name of a CIA-funded proj ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PostgreSQL
PostgreSQL ( ) also known as Postgres, is a free and open-source software, free and open-source relational database management system (RDBMS) emphasizing extensibility and SQL compliance. PostgreSQL features transaction processing, transactions with atomicity (database systems), atomicity, consistency (database systems), consistency, isolation (database systems), isolation, durability (database systems), durability (ACID) properties, automatically updatable view (SQL), views, materialized views, database trigger, triggers, foreign keys, and stored procedures. It is supported on all major operating systems, including Microsoft Windows, Windows, Linux, macOS, FreeBSD, and OpenBSD, and handles a range of workloads from single machines to data warehouses, data lakes, or web services with many concurrent users. The PostgreSQL Global Development Group focuses only on developing a database engine and closely related components. This core is, technically, what comprises PostgreSQL itse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
