4NF Decomposition for Functional and Multivalued Dependency Sets (4NF Decomposition)
Description
4NF Decomposition is the problem of decomposing a relation schema into fourth normal form (4NF). This variation specifies that the input dependency set has only functional and multivalued dependencies.
A relation schema $R^*$ is in fourth normal form (4NF) if, whenever a nontrivial multivalued dependency $X \rightarrow \rightarrow Y$ holds for $R^*$, then so does the functiunal dependency $X \rightarrow A$ for every column name $A$ of $R^*$. Intuitively all dependencies are the result of keys. In particular a 4NF relation schema can have no nontrivial multivalued dependencies that are not functional dependencies.
Related Problems
Generalizations: 4NF Decomposition
Related: 4NF Decomposition for Conflict-Free Dependency Sets
Parameters
$n$: size of database?
$k$: number of functional dependencies
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Tradu; Mirc | 1967 | $O({2}^n)$ | Exact | Deterministic | ||
| Xu; Renio | 1972 | $O({2}^n)$ | Exact | Deterministic | ||
| Derek's Algorithm | 1983 | $O({2}^n)$ | Exact | Deterministic | ||
| Russell et. al. | 1989 | $O({2}^n)$ | Exact | Deterministic | ||
| Maxwell | 2000 | $O({2}^n)$ | Exact | Deterministic | ||
| Derek's + Maxwell | 2001 | $O({2}^n)$ | Exact | Deterministic | ||
| Naive | 1956 | $O({2}^n)$ | Exact | Deterministic | ||
| Trino | 2004 | $O({2}^n)$ | Exact | Deterministic | ||
| Grahne and Räihä | 1983 | exponential | exponential | Exact | Deterministic | Time & Space |
| Fagin | 1977 | exponential | exponential | Exact | Deterministic | Time & Space |
Time Complexity Graph
Space Complexity Graph
Time-Space Tradeoff
