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Rensselaer Polytechnic Institute### Database Systems{week 02}

CSCI-4380 – Database Systems

David Goldschmidt, Ph.D.

Selection (review)

- Find and select all tuples from relation Rthat satisfy some set of conditions
- Forms the basis of querying a database
- The selectionC (R) is based on Boolean condition C over attributes of relation R
- Example conditions include:
- A = e, A > e, A >= e, A < e, A <= e, A <> e
- A1 = A2, A1 <> A2
- Any combination of conditions using AND, OR, NOT

A, A1, and A2 are attributes

e is a constant or expression

Selection (review)

- Selection selects a subset of tuples in relation R (with the schema unchanged)
- C(R) = { t | t is a tuple in R and t satisfies the condition C on relation R }
- Selection conditions can only refer toattributes in the given relation R
- For conditions spanning multiple relations, we first must combine those relations (i.e. join)

Cartesian product

- The Cartesian product combinestwo relations to form a new relation
- The new relation has all of the attributesof the original two relations
- It’s often a good idea to rename attributesin the original relations such thatthere’s no ambiguity

Cartesian product

- Given two relations R and S withschemas R(A1,A2,...,An) and S(B1,B2,...,Bm)
- The Cartesian product RxS producesrelation T with schema T(A1,A2,...,An,B1,B2,...,Bm)
- We can disambiguate attributesby using R.Ax and S.By
- i.e. attributes Ax and By have the same name

Cartesian product

- The Cartesian product of relations R and S:
- RxS = { (r,s) | r is a tuple in R and s is a tuple in S }
- Note that (r,s) has all values in r and s
- The Cartesian product is like multiplicationin that it produces a tuple for every pair oftuples from R and S
- e.g. if R has 10 tuples and S has 5 tuples, then RxS will have 50 tuples

So why do we want to do this?

Join

- Cartesian product RxS is often followed by a selection condition that specifies how tuples in R should be matched to tuples in S
- name=student(Undergraduate x Advising)
- Translation: Join the Undergraduate and Advising relations by selecting tuples in which the name attribute equals the student attribute

Natural joins

- When joining two relations, we often want to join on common (same-named) attributes
- This is a natural join on relations R and Sand is denoted R⋈S
- The selection condition selects tuples that have the same values for same-named attributes
- Note that the schema does not repeat thesame-named attributes

Theta joins

- Joins based on specific conditions arecalled theta joins and are denoted R ⋈C S
- To perform a theta join, first take theproduct of relations R and S
- Next, select tuples that satisfy condition C
- The resulting schema is the union of theschemas of R and S with R.Ax and S.By prefixes,if necessary

In a theta join, nodeduplicationof attributes is performed!

Rename

- The rename operator changes thename of the attributes of relation Rwith schema R(A1,A2,...,An)
- S(B1,B2,...,Bn)(R) = relation S(B1,B2,...,Bn) in which R.A1 is renamed S.B1, R.A2 is renamed S.B2, and so on
- To only change some attribute names,simply specify Bi = Ai

Exercises

- Find all faculty who advise a student
- Find all faculty who do not adviseany students
- Find faculty who advise at least two students
- Find faculty who advise a student that is not in their department (e.g. dual majors)

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