Lossless join decomposition

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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]

If is split into and , for this decomposition to be lossless (i.e., ) then at least one of the two following criteria should be met.

Check 1: Verify join explicitly[edit]

Projecting on and , and joining them back, results in the relation you started with.[3][unreliable source?]

Check 2: Via functional dependencies[edit]

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):[4]


  • Let be the relation schema, with attributes A, B, C and D.
  • 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 .



  1. ^ Pohler, K (2015). "Lossless-Join Decomposition: applications in quantitative computing metrics". International Journal of Applied Computer Science. 21 (4): 190–212.
  2. ^ Elmasri, Ramez (2016). Fundamentals of database systems (Seventh ed.). Hoboken, NJ: Pearson. p. 461. ISBN 978-0133970777.
  3. ^ "Lossless Join Property". Stackoverflow.com. Retrieved 2016-02-07.
  4. ^ "Lossless Join Decomposition" (PDF). University at Buffalo. Jan Chomicki. Retrieved 2012-02-08.
  5. ^ "Lossless-Join Decomposition". Cs.sfu.ca. Retrieved 2016-02-07.
  6. ^ "Archived copy". Archived from the original on 2014-02-21. Retrieved 2014-02-12.{{cite web}}: CS1 maint: archived copy as title (link)