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Can also be called Nonadditive. If you decompose a relation into relations you will have a Lossless-Join if a natural join of the two smaller relations yields back the original relation, i .e.;
If is split into and , for this decomposition to be lossless then at least one of the two following criteria should be met.
Check 1: Verify join explicitly
Projecting on and , and joining back, results in the relation you started with.
Check 2: Via functional dependencies
Let be a relation schema.
Let F be a set of functional dependencies on .
Let and form a decomposition of .
The decomposition is a lossless-join decomposition of if at least one of the following functional dependencies are in F+ (where F+ stands for the closure for every attribute or attribute sets in F):
- Let be the relation schema, with A, B, C and D attributes.
- Let be the set of functional dependencies.
- Decomposition into and is lossless under F because . A is a superkey in , meaning we have a functional dependency . In other words, now we have proven that .
- Pohler, K (2015). "Lossless-Join Decomposition: applications in quantitative computing metrics". International Journal of Applied Computer Science. 21 (4): 190–212.
- "Lossless Join Property". Stackoverflow.com. Retrieved 2016-02-07.
- "Lossless Join Decomposition" (PDF). University at Buffalo. Jan Chomicki. Retrieved 2012-02-08.
- "Lossless-Join Decomposition". Cs.sfu.ca. Retrieved 2016-02-07.
- "Archived copy". Archived from the original on 2014-02-21. Retrieved 2014-02-12.CS1 maint: archived copy as title (link)