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Homework 3} +\author{Sean Rettig} + +\begin{document} +\maketitle + +\section{ (1.0 Point)} +Specify the following queries in relational algebra (R.A.) on the COMPANY database schema +shown in Figure 5.5 in the Textbook. Do not use any other information from the database state +on Figure 5.6 to build the queries. +\begin{enumerate} [label=(\alph*)] + \item List names of employees (Fname, Minit, Lname) who are directly supervised by a female supervisor. + \item List names of employees (Fname, Minit, Lname) who are NOT assigned to every project. + \item List names of employees (Fname, Minit, Lname) in Departments with locations in Houston or Sugarland. + \item List the names of department managers (Fname, Minit, Lname) who have no dependents. +\end{enumerate} +\textbf{Answer:}\\ +\begin{enumerate} [label=(\alph*)] + \item $\pi_{\text{Fname, Minit, Lname}}(\text{EMPLOYEE}* (\rho_{(\text{Super\_ssn})}(\pi_{\text{Ssn}}(\sigma_{\text{Sex=female}}(\text{EMPLOYEE})))))$ + \item (EMPLOYEE - (EMPLOYEE $\div \pi_{\text{Pnumber}}(\text{PROJECT})$)) + \item $\pi_{\text{Fname, Minit, Lname}}($\\ + $\text{EMPLOYEE}\bowtie_{\text{Dno=Dnumber}} (\sigma_{\text{Dlocation='Houston' OR Dlocation='Sugarland'}}(\text{DEPT\_LOCATIONS}))$\\ + $)$ + \item $\pi_{\text{Fname, Minit, Lname}}($\\ + $(\text{EMPLOYEE}\bowtie_{\text{Ssn=Mgr\_ssn}}(\text{DEPARTMENT})) * (\pi_{\text{Ssn}}(\text{EMPLOYEE}) - \rho_{(\text{Ssn})}(\pi_{\text{Essn}}(\text{DEPENDENT})))$ + \\ $)$ +\end{enumerate} + +\section{1.0 Point} +Consider SQL queries Q13 and Q4A in Chapter 6. +\begin{enumerate} [label=(\alph*)] + \item Draw the initial query tree for each of these queries, and then show how the query tree is + optimized by the algorithm outlined in Section 19.1. + \item For each query, compare the initial query and the final query tree. Discuss the difference + between each tree. +\end{enumerate} +\noindent +\textbf{Answer:}\\ +\textbf{Q13 Unoptimized:}\\ +\includegraphics[width=0.8\textwidth]{Q13 UNOPT.jpg}\\ +Step 1 specified a break up of any SELECT operations, and that was used to break up the third to final SELECT operation +into multiple cascading SELECT Operations. I used Step 2 and 4 to move the SELECT Operations down as far as they can, as well as combining them +with their respective CARTESION PRODUCT into a JOIN operation. I followed Step 3 by moving the most restricive SELECT +down to the bottom of the tree. Step 5 was used to move project operations as far down the tree as needed.\\ +\newpage +\textbf{Q13 Optimized:}\\ +\includegraphics[width=0.8\textwidth]{Q13 OPT.jpg}\\ +\textbf{Q4A Unoptimized:}\\ +\includegraphics[width=0.8\textwidth]{Q4A UNOPT.jpg}\\ +Step 1 specified a break up of any SELECT operations, and that was used to break up the two third to final SELECT operations +into multiple cascading SELECT Operations. I used Step 2 and 4 to move the SELECT Operations down as far as they can, as well as combining them +with their respective CARTESION PRODUCT into a JOIN operation. I followed Step 3 by moving the most restricive SELECT operations +down to the bottom of the tree. Step 5 was used to move project operations as far down the tree as needed.\\ +\textbf{Q4A Optimized:}\\ +\includegraphics[width=0.8\textwidth]{Q4A OPT.jpg} + +\newpage +\section{1.0 Point} +Suppose that a disk unit has the following parameters: seek time s = 20 msec; rotational delay rd += 10 msec; block transfer time btt = 1 msec; block size B = 2400 bytes; interblock gap size G = +600 bytes. An EMPLOYEE file has the following fields: Ssn , 9 bytes; Last\_name , 20 bytes; +First\_name , 20 bytes; Middle\_init , 1 byte; Birth\_date , 10 bytes; Address , 35 bytes; Phone , 12 +bytes; Supervisor\_ssn , 9 bytes; Department , 4 bytes; Job\_code , 4 bytes; deletion marker, 1 +byte. The EMPLOYEE file has r = 30,000 records, fixed-length format, and unspanned blocking. +Write appropriate formulas and calculate the following values for the above EMPLOYEE file: + +\begin{enumerate} [label=(\alph*)] + \item \textbf{Calculate the record size R (including the deletion marker), the blocking factor bfr, and the number of disk blocks b.}\\ + Record size:\\ + Ssn + Last\_name + First\_name + Middle\_init + Birth\_date + Address + Phone + Supervisor\_ssn + Department + Job\_code + deletion marker\\ + \[= 9 + 20 + 20 + 1 + 10 + 35 + 12 + 9 + 4 + 4 + 1 = 125\text{ bytes}\] + $bfr = \lfloor B/R \rfloor = \lfloor 2400 / 125 \rfloor = 19$\\ + Number of disk blocks required $= \lceil r / bfr \rceil = \lceil 30000 / 19 \rceil = 1579$ blocks + \item \textbf{Calculate the wasted space in each disk block because of the unspanned organization.}\\ + Unused space $= B - (bfr * R) = 2400 - (19 *125) = 25$ bytes + \item \textbf{Calculate the transfer rate tr and the bulk transfer rate btr for this disk unit (see Appendix B in the textbook for definitions of tr and btr).}\\ + $tr = B/btt = 2400 / 1 = 2400$ bytes/msec\\ + $btr = (B/(B+G)) * tr = (2400/(2400+600)) * 2400 = 1920$ bytes/msec + \item \textbf{Calculate the average number of block accesses needed to search for an arbitrary record in the file, using linear search.}\\ + average block accesses for linear search = $b/2 = 1579 / 2 = 789.5$ blocks + \item \textbf{Calculate in msec the average time needed to search for an arbitrary record in the file, + using linear search, if the file blocks are stored on consecutive disk blocks and double + buffering is used.}\\ + Average time to search for an arbitrary record = average blocks * average time = $b/2 * (s+rd+(k*B/btr)) = 1579/2 * (20 + 10 +(1579*(2400/1920))) = 1581960.625$ msec +\end{enumerate} + +\end{document} \ No newline at end of file