In SQL Server 2008, how does one design a 1:1 and 1:m relationship?
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One-to-One Relationship
In this case, I can never have more than one row in the ChildTable for a given ParentTable primary key value. Note that even in a One-to-One relationship, one of the tables is the "parent" table. What differentiates a One-to-One relationship from a One-to-Many relationship purely in terms of implementation is whether the ChildTable's foreign key value has a Unique or Primary Key constraint.
One-to-Many Relationship
In this scenario, I can have multiple rows in the ChildTable for a given ParentTable primary key value.
Any relationship requires that the "parent" table (the one side) have a Primary (or unique) Key (PK), that uniquely identifies each row, and the "child" table (the other side) have a Foreign Key column or columns, that must be populated with values that are the same as some existing value[s] of the Primary Key in the parent table. If you want a one to many (1-M) relationship then the Foreign Key should be an ordinary attribute (column or columns) in the child table that can repeat (there can be many rows with the same value)
If you want a one to one (1-1) relationship then the Foreign key should itself be a Primary Key or unique index in the child table that guarantees that there may be at most one row in the child table with that value.
A 1-1 relationship effectively partitions the attributes (columns) in a table into two tables. This is called vertical segmentation. This is often done for sub-classing the table entities, or, for another reason, if the usage patterns on the columns in the table indicate that a few of the columns need to be accessed significantly more often than the rest of the columns. (Say one or two columns will be accessed 1000s of times per second and the other 40 columns will be accessed only once a month). Partitioning the table in this way in effect will optimize the storage pattern for those two different queries.
Sub-Classing. The above actually creates a 1 to zero or one relationship, which is used for what is called a sub-class or subtype relationship. This occurs when you have two different entities that share a great number of attributes, but one of the entities has additional attributes that the other does not need. A good example might be Employees, and SalariedEmployees. The Employee table would have all the attributes that all employees share, and the SalariedEmployee table would exist in a (1-0/1) relationship with Employees, with the additional attributes (Salary, AnnualVacation, etc.) that only Salaried employees need.
If you really want a 1-1 relationship, then you have to add another mechanism to guarantee that the child table will always have one record for each record/row in the parent table. Generally the only way to do this is by enforcing this in the code used to insert data (either in a trigger, stored procedure or code outside the database). This is because if you added referential integrity constraints on two tables that require that rows always be in both, it would not be possible to add a row to either one without violating one of the constraints, and you can't add a row to both tables at the same time.
A 1:1 relationship exists where table A and table B only exist once in regards to each other. Example: A student has 1 master student record. The student would be table A and the record in table B. Table B would contain a foreign key to the student record in table A (and possibly vice-versa)
A 1:m relationship exists where table A can be referenced or linked to by many entries in table B. Example: A student can take several books out from the library. The student again would be table A and the book could be the entry in table B. The entry in table B would contain a foreign key to who checked the book out, and many books could reference the same student.