Database Systems {week 02}

1. Rensselaer Polytechnic Institute CSCI-4380 – Database Systems David Goldschmidt, Ph.D. Database Systems{week 02}

2. Selection (review) • Find and select all tuples from relation Rthat satisfy some set of conditions • Forms the basis of querying a database • The selectionC (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

3. 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)

4. 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

5. 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

6. 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?

7. 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

8. 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

9. 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!

10. 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

11. 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)