I have explained about various normal forms in my earlier article. From my previous explanation, we can understand that whenever an n-set gets decomposed, the resulting substances have at least one field of the original n-set common to them. The common field that exists between the substances of the n-set will act as a connector between them.
There is no need to always decompose an n-set which is subjected to normalization. When an n-set and m-set which are non-decomposable, it is still possible that a connector field common to both sets exists. This connector field capture the connection between these sets.
The connection between any two vectors captured by a connector can be 1:1, 1:N or M:N. The connection between an employee and child is 1:N because an employee can have many children.
We can develop two notations, the set-theoretic and the graphical, to capture this connection. In the former. In the set-theoretic we consider only n-sets and leave the observer to identify the common field which connects the two substances together. This type of data scheme is considered as set-theoretic notation. When we make the connection between the substances apparent to the observer then the data scheme is considered as graphical notation. In this notation , when an n-set P gets split into P1 and P2 by the process of normalization, we can represent P by P1 and P2 together with a line between them.
More formally, we define a link to be non-information bearing if the information captured by it can be obtained as a closed form property from the substances connected by it. A link which does not have this property is called information bearing.
When a link is non-information bearing, it is possible to construct an algorithm by means of which substances of a data scheme can be connected together. Such an algorithm exploits the closed form property. This algorithm is of the general form as follows:
- Extract information from the connector field of a substances
- Locate a substances having this same information in its connector field
When a link is information bearing, it is not possible to construct algorithms of the form considered above. Therefore, if a data structure is built using an information bearing link, all connections have to be explicitly programmed by users. A data base management system cannot automatically construct such connections.
Since algorithm can be constructed for producing connections represented by non-information bearing links, it is not necessary to represent such links physically in a database. Each time information about connections is necessary, this algorithm can be invoked and the linkages constructed.
However this is likely to be expensive on computer time. As an alternative, one can represent a non-information bearing link physically in the machine, for example, by means of pointers. By this we could reduce machine time requirements at the expensive of some space overheads. Thus, a trade-off between time and space is involved in choosing whether a non-information bearing link should be physically represented or not.
This situation with information bearing links is considerably different. Such a link has always to be physically represented in order to extract information about connection between substances.
It must be noted that in the set-theoretic notion of a database scheme, connection information can be incorporated only by the use of a connector field.