Functional Dependency Inference Problem: Difference between revisions
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== Parameters == | == Parameters == | ||
$n$: number of attributes | |||
$p$: number of tuples/rows/data points | |||
== Table of Algorithms == | == Table of Algorithms == | ||
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| [[Brute force algorithm (Functional Dependency Inference Problem Dependency Inference Problem)|Brute force algorithm]] || 1967 || $O(n^{2} {2}^n p log p)$ || $O(n2^n)$? || Exact || Deterministic || [https://www.sciencedirect.com/science/article/pii/0166218X92900315 Time] | | [[Brute force algorithm (Functional Dependency Inference Problem Dependency Inference Problem)|Brute force algorithm]] || 1967 || $O(n^{2} {2}^n p \log p)$ || $O(n2^n)$? || Exact || Deterministic || [https://www.sciencedirect.com/science/article/pii/0166218X92900315 Time] | ||
|- | |- | ||
| [[Schlimmer (Functional Dependency Inference Problem Dependency Inference Problem)|Schlimmer]] || 1993 || $O(n {2}^n p)$ || $O({2}^n)$ || Exact || Deterministic || [https://www.aaai.org/Papers/Workshops/1993/WS-93-02/WS93-02-017.pdf Time] | | [[Schlimmer (Functional Dependency Inference Problem Dependency Inference Problem)|Schlimmer]] || 1993 || $O(n {2}^n p)$ || $O({2}^n)$ || Exact || Deterministic || [https://www.aaai.org/Papers/Workshops/1993/WS-93-02/WS93-02-017.pdf Time] | ||
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[[File:Dependency Inference Problem - Functional Dependency Inference Problem - Time.png|1000px]] | [[File:Dependency Inference Problem - Functional Dependency Inference Problem - Time.png|1000px]] | ||
== References/Citation == | == References/Citation == | ||
https://www.sciencedirect.com/science/article/pii/0166218X92900315 | https://www.sciencedirect.com/science/article/pii/0166218X92900315 | ||
Latest revision as of 09:09, 28 April 2023
Description
The functional dependency inference problem is to find a cover for the set of functional dependencies that hold in a given relation.
A functional dependency (abbr. FD), $f$, is a statement $f: X \rightarrow Y$ where $X$ and $Y$ are sets of attributes. If $R(X, Y, \ldots)$ is a relation on a set of attributes that contains $X$ and $Y$, then $R$ obeys the FD $f$ if every two tuples of $R$ which have the same projection on $X$ also have the same projection on $Y$. Given $f: X \rightarrow Y$, we say that $f$ is a functional dependency from $X$ to $Y$, that $Y$ is functionally dependent on $X$ or that $X$ functionally determines $Y$. From the definition it follows that for each pair of sets $X$ and $Y$ there is at most one functional dependency from $X$ to $Y$. Therefore, we usually omit the name of the FD and write $X \rightarrow Y$.
Related Problems
Related: Multivalued Dependency Inference Problem
Parameters
$n$: number of attributes
$p$: number of tuples/rows/data points
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Brute force algorithm | 1967 | $O(n^{2} {2}^n p \log p)$ | $O(n2^n)$? | Exact | Deterministic | Time |
| Schlimmer | 1993 | $O(n {2}^n p)$ | $O({2}^n)$ | Exact | Deterministic | Time |
Time Complexity Graph
References/Citation
https://www.sciencedirect.com/science/article/pii/0166218X92900315