Join dependency

In the area of computer science known as dependency theory, a join dependency is a constraint on the set of legal relations over a database scheme. A table is subject to a join dependency if can always be recreated by joining multiple tables each having a subset of the attributes of . If one of the tables in the join has all the attributes of the table , the join dependency is called trivial.

The join dependency plays an important role in the Fifth normal form, also known as project-join normal form, because it can be proven that if a scheme is decomposed in tables to , the decomposition will be a lossless-join decomposition if the legal relations on are restricted to a join dependency on called .

Another way to describe a join dependency is to say that the relationships in the join dependency are independent of each other.

Unlike in the case of functional dependencies, there is no sound and complete axiomatization for join dependencies,[1] though axiomatization exist for more expressive dependency languages such as full typed dependencies.[2]:Chapter 8 However, implication of join dependencies is decidable.[2]:Theorem 8.4.12

Formal definition

Let be a relation schema and let be a decomposition of .

The relation satisfies the join dependency


A join dependency is trivial if one of the is itself.[3]

2-ary join dependencies are called multivalued dependency as a historical artifact of the fact that they were studied before the general case. More specifically if U is a set of attributes and R a relation over it, then R satisfies if and only if R satisfies


Given a pizza-chain that models purchases in table Customer = {order-number, customer-name, pizza-name, courier}. The following relations can be derived:

  • customer-name depends on order-number
  • pizza-name depends on order-number
  • courier depends on order-number

Since the relationships are independent there is a join dependency as follows: *((order-number, customer-name), (order-number, pizza-name), (order-number,courier)).

If each customer has his own courier however, there can be a join-dependency like this: *((order-number, customer-name), (order-number, pizza-name), (order-number, courier), (customer-name, courier)), but *((order-number, customer-name, courier), (order-number, pizza-name)) would be valid as well. This makes it obvious that just having a join dependency is not enough to normalize a database scheme.

See also


  1. Petrov, S. V. (1989). "Finite axiomatization of languages for representation of system properties". Information Sciences. 47: 339–372. doi:10.1016/0020-0255(89)90006-6.
  2. Abiteboul; Hull; Vianu. Foundations of databases.
  3. Silberschatz, Korth. Database System Concepts (1st ed.).
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.