CSE 444 Homework 2

Objectives:

To be able to translate from E/R diagrams to a relational database, and to understand functional dependencies and normal forms.

Reading Assignments:

Chapters: 2, 3.2, 3.3, 3.4

Number of points:

100

Due date:

October 27th, 10:30am (in class)

Assignment Tools:

SQL Server

1. [10 points] Design an E/R diagram for geography that contains the following kinds of objects together with the listed attributes:
   • countries: name, area, population, gdp ("gross domestic product")
   • cities: name, population, longitude, latitude
   • rivers: name, length
   • seas: name, max depths
   Model the following relationships between the geographical objects:
   • each city belongs to exactly one country
   • each river crosses one or several countries
   • each river ends in another river or in a sea
2. [20 points] Consider the following E/R diagram:
    
   
   1. Create a relational schema that captures this E/R diagram. Write SQL "Create Table" statements that creates the corresponding tables. Add the necessary key, foreign key, and uniqueness constraints.
   2. Which relation in your relational schema represents the relationship "insures", in the E/R diagram and why is that your representation?
   3. Compare the representation of the relationships "drives" and "operates" in your schema, and explain why they are different.
3. [20 points] Consider the following two relational schemas and sets of functional dependencies:
   1. R(A,B,C,D,E) with functional dependencies D -> B, CE -> A.
   2. S(A,B,C,D,E) with functional dependencies A -> E, BC -> A, DE -> B.
   For each of the two schemas, do the following:
   1. Decompose the relations, as necessary, into collections of relations that are in BCNF. Show all of your work and explain which dependency violations you are correcting by your decompositions.
   2. Decompose the relations into a collection that follows 3NF instead.
   For each of the two questions above you have to turn in a description of your decomposition steps. Show: which is the relation that you are decomposing, what functional dependency do you apply, and which are the two resulting relations.
4. [15 points] We say a set of attributes X is closed (with respect to a given set of functional dependencies) if X⁺=X. Given the closed attribute sets, this gives us some information on the underlying functional dependencies.

   Consider a relation with schema R(A,B,C,D) and an unknown set of functional dependencies. For each closed attribute set below, give a set of functional dependencies that is consistent with it.

   1. All sets of attributes are closed.
   2. The only closed sets are {} and {A,B,C,D}.
   3. The only closed sets are {}, {A,B}, and {A,B,C,D}.
5. [35 points] Mr. Frumble (who is a great character for small kids that always gets into trouble) designed a simple database to record projected monthly sales in his small store. He never took a database class, so he came up with the following schema:
   Sales(name, discount, month, price)

   He inserted his data into the database, then he realized that there is something wrong with it: it was difficult to update. He hires you as a consultant to fix his data management problems. He hands you his data in this file and tells you: "fix it for me !". Help him by normalizing his database. Unfortunately you cannot sit down with Mr. Frumble and discuss his application to find out the functional dependencies, as you should normally do, because Mr. Frumble is simply too busy. So you have to reverse engineer the functional dependencies from his data instance. You should do the following steps:

   1. Create a table on SQL Server and load the data in the table. You don't need to turn in anything for this point.
   2. Find all functional dependencies in the database. This is a reverse engineering task, so expect to proceed in a trial and error fashion. Search first for the simple dependencies, say name -> discount then try the more complex ones, like name, discount -> month, as needed. To check each functional dependency you have to write a SQL query. Your challenge is to write this SQL query for every candidate functional dependency that you check, such that (a) the query's answer is always short (say: no more than ten lines or so), and (b) you can determine whether the FD holds or not by looking at the query's answer. Try to be clever in order not to check too many dependencies, but don't miss potential relevant dependencies.

      For this point you should turn in all functional dependencies that you found, and for each of them the SQL query that discovered it, together with the answer of the query. any

   3. Decompose the table in BCNF, and create SQL tables for the decomposed schema. Create keys and foreign keys where appropriate.

      For this point turn in the SQL commands for creating the tables.

   4. Populate your BCNF tables from Mr. Frumble's data. For this you need to write SQL queries that load the tables you created at point iii from the table you created at point i.

      Here, turn in the SQL queries that load the tables, and the tables' contents after loading them (obtained by running SELECT * FROM Table).