Decisional BCNF (BCNF Decomposition)

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Decisional BCNF is the problem of deciding whether or not a relation schema can be turned into Boyce-Codd normal form (BCNF).

A relation schema $R$ is in Boyce Codd Normal Form (abbr. BCNF) if for all non-trivial FDs $X \rightarrow Y$ in $F^+$, $X$ is a superkey. In extending this notion to database schemas, we must be conscious of the UR-assumption. We say that $R_i = <ATTR_i,F_i>$ is in BCNF if the schema $<ATTR_i, F^+(ATTR_i)>$ is in BCNF, and $D$ is in BCNF if each $R_i$ is.

Related Problems

Related: BCNF Decomposition


$n$: size of database?

$k$: number of functional dependencies

Table of Algorithms

Name Year Time Space Approximation Factor Model Reference
Liu 1992 $O(kn^{2})$ $O(n)$ Exact Deterministic Time

Time Complexity Graph

BCNF Decomposition - Decisional BCNF - Time.png