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| --- | ||
| title: "CS134-lecture-20210614" | ||
| # date: 2021-06-14T13:45:19-07:00 | ||
| draft: false | ||
| bookToc: true | ||
| tags: ["relational algebra"] | ||
| --- | ||
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| {{< hint warning >}} | ||
| Announcements | ||
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| - Assignment 2 is posted | ||
| {{< /hint >}} | ||
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| ## Relational algebra cont. | ||
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| ### `SELECT` cont. | ||
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| When cascaded: the conditions can be in different order but they will produce the same output. | ||
| The conditions can be connected by logical and. | ||
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| If we compose 2 select operations | ||
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| {{<k display>}} | ||
| \begin{aligned} | ||
| \sigma_{\text{salary } > 7300} ( \sigma_{\text{dno = } 5 } (\text{ employee })) | ||
| \end{aligned} | ||
| {{</k>}} | ||
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| We can combine the 2 conditions with a logical and | ||
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| {{<k display>}} | ||
| \begin{aligned} | ||
| \sigma_{\text{salary > 7300} \text{ and } \text{ dno } = 5 } (\text{ employee }) | ||
| \end{aligned} | ||
| {{</k>}} | ||
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| Selection is a filter, so the input schema is the same as the output schema, however the number of tuples is equal to or less than the input. | ||
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| ### Exercise | ||
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| {{< hint danger >}} | ||
| This is part of the weekly exercise homework. | ||
| {{< /hint >}} | ||
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|  | ||
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| 1. Retrieve each female employee | ||
| {{<k display>}} | ||
| \begin{aligned} | ||
| \text{result} \leftarrow \sigma_{\text{ sex = 'F' }} ( \text{ employee }) | ||
| \end{aligned} | ||
| {{</k>}} | ||
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| 2. Retrieve each female employee whose salary is greater than 30000 | ||
| {{<k display>}} | ||
| \begin{aligned} | ||
| \text{result} \leftarrow \sigma_{\text{ sex = 'F' and salary > 30000}} ( \text{ employee }) | ||
| \end{aligned} | ||
| {{</k>}} | ||
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| ### Projection operation | ||
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|  | ||
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| In the projection operation, the input schema can be different than the output schema. | ||
| It allows you to select certain columns and discard the other ones. | ||
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| Projection is notated using {{<k>}} \pi {{</k>}}, for example | ||
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| {{<k display>}} | ||
| \begin{aligned} | ||
| \pi_{\text{<list>}}(R) | ||
| \end{aligned} | ||
| {{</k>}} | ||
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| Where | ||
| - {{<k>}} \text{list} {{</k>}} is a list of attributes, and | ||
| - {{<k>}} R {{</k>}} is the entity | ||
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| For example, | ||
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| {{<k display>}} | ||
| \begin{aligned} | ||
| \text{result} \leftarrow \pi_\text{<fname, lname, ssn>} (\text{ employee }) | ||
| \end{aligned} | ||
| {{</k>}} | ||
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| Note that the output schema only has 3 columns. | ||
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|  | ||
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| Consider | ||
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| {{<k display>}} | ||
| \begin{aligned} | ||
| \text{result} \leftarrow \pi_\text{<salary>} (\text{ employee }) | ||
| \end{aligned} | ||
| {{</k>}} | ||
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| Our result will only have 1 columns. | ||
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|  | ||
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| We have 8 tuples, but 3 of them are 25000 (duplicates). | ||
| By definition, relational model is set based (and so relational algebra is too), so we do not allow duplicate tuples. | ||
| Any duplicate tuples will be removed in the returned table. | ||
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|  | ||
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| The attributes in the list must be a subset of the attributes of the entity. | ||
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| The last projection is what really matters, | ||
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| {{<k display>}} | ||
| \begin{aligned} | ||
| \text{result} &\leftarrow \pi_\text{<fname>}(\pi_\text{<ssn, fname>} (\text{ employee })) \\ | ||
| &= \pi_\text{<fname>} (\text{ employee }) | ||
| \end{aligned} | ||
| {{</k>}} | ||
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| ### Sequence of operations | ||
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| If we want to compose selection and projection: | ||
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|  | ||
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| {{<k display>}} | ||
| \begin{aligned} | ||
| \text{result} &\leftarrow \pi_\text{<fname, lname, salary>} (\sigma_\text{dno = 5} (\text{ employee })) \\ | ||
| \text{temp} &\leftarrow \sigma_\text{dno = 5} (\text{ employee }) \\ | ||
| \text{result} &\leftarrow \pi_\text{<fname, lname, salary>} (\text{ temp }) | ||
| \end{aligned} | ||
| {{</k>}} | ||
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| ### Rename operation | ||
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|  | ||
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| We can use this operator to rename the output of an expression. | ||
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|  | ||
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| If {{<k>}} R {{</k>}} is a relation, we can rename the relation to {{<k>}} S {{</k>}}, and/or rename the attributes name one by one. | ||
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| {{<k display>}} | ||
| \begin{aligned} | ||
| &\text{R} \leftarrow \pi_\text{<fname, lname, salary>} (\text{ employee }) \\ | ||
| & \rho_\text{S (fn, ln, sal)} (\text{R}) &\text{new relation named S}\\ | ||
| & \rho_\text{(fn, ln, sal)} (\text{R}) &\text{new relation still named R}\\ | ||
| & \rho_\text{S}(\text{R}) &\text{new relation named S}\\ | ||
| &&\text{ but no new attribute names} | ||
| \end{aligned} | ||
| {{</k>}} | ||
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| ### Union operator | ||
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| No duplicates allowed, it is a set. | ||
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| For example, | ||
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| Example | ||
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| {{<k display>}} | ||
| \begin{aligned} | ||
| \text{dept5 emps} &\leftarrow \sigma_\text{dno = 5} (\text{ employee }) \\ | ||
| \text{result1} &\leftarrow \pi_\text{ssn} (\text{dept5 emps}) \\ | ||
| \text{result2}\underbrace{(\text{ssn})}_\text{rename} &\leftarrow \pi_\text{superssn} (\text{dept5 emps}) \\ | ||
| \text{result} &\leftarrow \text{result1} \cup \text{result2} | ||
| \end{aligned} | ||
| {{</k>}} | ||
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