4NF Decomposition: Difference between revisions
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== Parameters == | == Parameters == | ||
$n$: size of database? | |||
$k$: number of functional dependencies | |||
== Table of Algorithms == | == Table of Algorithms == | ||
Latest revision as of 08:22, 10 April 2023
Description
4NF Decomposition is the problem of decomposing a relation schema into fourth normal form (4NF).
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
Subproblem: 4NF Decomposition for Functional and Multivalued Dependency Sets, 4NF Decomposition for Conflict-Free Dependency Sets
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 |
| Lien | 1982 | $O(k^{2} n^{2})$ | $O(k^{2})$ | Exact | Deterministic | Time |
| Sciore | 1981 | poly-time | Exact | Deterministic | Time | |
| Fagin | 1977 | exponential | exponential | Exact | Deterministic | Time & Space |