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In database design, a lossless join decomposition is a decomposition of a relation into relations such that a natural join of the two smaller relations yields back the original relation. This is central in removing redundancy safely from databases while preserving the original data. [1] Lossless join can also be called nonadditive. [2]
Let and be a decomposition of a relation .
The decomposition is lossless if and only if the natural join of and results in the original relation (i.e., ). [3][ unreliable source?]
Equivalently, the decomposition is lossless if and only if one of the sub-relations (i.e. or ) is a subset of the closure of their intersection. [4] In other words, the decomposition of is lossless if either or is true.
Multiple sub-relations have a lossless join if there is some way in which we can repeatedly perform lossless joins until all the relations have been joined into a single relation. Once we have a new sub-relation made from a lossless join, we are not allowed to use any of its isolated sub-relations to join with any of the other relations. For example, if we can do a lossless join on a pair of relations to form a new relation , we use this new relation (rather than or ) to form a lossless join with another relation (which may already be joined (e.g., )).
This article may need to be rewritten to comply with Wikipedia's
quality standards. (July 2014) |
In database design, a lossless join decomposition is a decomposition of a relation into relations such that a natural join of the two smaller relations yields back the original relation. This is central in removing redundancy safely from databases while preserving the original data. [1] Lossless join can also be called nonadditive. [2]
Let and be a decomposition of a relation .
The decomposition is lossless if and only if the natural join of and results in the original relation (i.e., ). [3][ unreliable source?]
Equivalently, the decomposition is lossless if and only if one of the sub-relations (i.e. or ) is a subset of the closure of their intersection. [4] In other words, the decomposition of is lossless if either or is true.
Multiple sub-relations have a lossless join if there is some way in which we can repeatedly perform lossless joins until all the relations have been joined into a single relation. Once we have a new sub-relation made from a lossless join, we are not allowed to use any of its isolated sub-relations to join with any of the other relations. For example, if we can do a lossless join on a pair of relations to form a new relation , we use this new relation (rather than or ) to form a lossless join with another relation (which may already be joined (e.g., )).