Introduction to Data Management CSE 344. Lectures 8: Relational Algebra
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1 Introduction to Data Management CSE 344 Lectures 8: Relational Algebra CSE Winter
2 Announcements Homework 3 is posted Microsoft Azure Cloud services! Use the promotion code you received Due on 2/1 Make sure you read the textbook! Very good coverage of RA 2
3 Where We Are Data models SQL, SQL, SQL Declaring the schema for our data (CREATE TABLE) Inserting data one row at a time or in bulk (INSERT/.import) Querying the data (SELECT) Modifying the schema and updating the data (ALTER/UPDATE) Next step: More knowledge of how DBMSs work Relational algebra, query execution, and physical tuning Client-server architecture CSE Winter
4 Query Evaluation Steps SQL query Translate query string into internal representation Logical plan à physical plan Parse & Check Query Decide how best to answer query: query optimization Check syntax, access control, table names, etc. Relational Algebra Query Execution Return Results Query Evaluation CSE Winter
5 The WHAT and the HOW SQL = WHAT we want to get from the data Relational Algebra = HOW to get the data we want The passage from WHAT to HOW is called query optimization SQL à Logical Plan à Physical Plan Logical plan expressed using relational algebra CSE Winter
6 Relational Algebra CSE Winter
7 Turing Awards in Data Management Charles Bachman, 1973 IDS and CODASYL Ted Codd, 1981 Relational model Jim Gray, 1998 Transaction processing Michael Stonebraker, 2014 INGRES and Postgres CSE Winter
8 Sets v.s. Bags Sets: {a,b,c}, {a,d,e,f}, { },... Bags: {a, a, b, c}, {b, b, b, b, b},... Relational Algebra has two semantics: Set semantics = standard Relational Algebra Bag semantics = extended Relational Algebra DB systems implement bag semantics (Why?) CSE Winter
9 Relational Algebra Operators Union, intersection, difference - Selection σ Projection π Cartesian product X, join Rename ρ Duplicate elimination δ Grouping and aggregation ɣ Sorting τ RA Extended RA All operators take in 1 or more relations as inputs and return another relation CSE Winter
10 Union and Difference R1 R2 R1 R2 What do they mean over bags? CSE Winter
11 What about Intersection? Derived operator using minus R1 R2 = R1 (R1 R2) Only makes sense if result is 0 Derived using join R1 R2 = R1 R2 Only makes sense if R1 and R2 have the same schema CSE Winter
12 Selection Returns all tuples which satisfy a condition Examples σ c (R) σ Salary > (Employee) σ name = Smith (Employee) The condition c can be =, <, <=, >, >=, <> combined with AND, OR, NOT CSE Winter
13 Employee SSN Name Salary John Smith Fred σ Salary > (Employee) SSN Name Salary Smith Fred CSE Winter
14 Projection Eliminates columns π A1,,An (R) Example: project social-security number and names: π SSN, Name (Employee) à Answer(SSN, Name) Different semantics CSE 344 over - Winter 2017 sets or bags! Why? 14
15 Employee SSN Name Salary John John John π Name,Salary (Employee) Name Salary John John John Bag semantics Name Salary John John Set semantics CSE Winter 2017 Which is more efficient? 15
16 Composing RA Operators Patient no name zip disease 1 p flu 2 p heart 3 p lung 4 p heart π zip,disease (Patient) zip disease flu heart lung heart σ disease= heart (Patient) no name zip disease 2 p heart 4 p heart π zip,disease (σ disease= heart (Patient)) zip disease heart heart CSE Winter
17 Cartesian Product Each tuple in R1 with each tuple in R2 R1 X R2 Rare in practice; mainly used to express joins CSE Winter
18 Cross-Product Example Employee Name SSN John Tony Dependent EmpSSN DepName Emily Joe Employee X Dependent Name SSN EmpSSN DepName John Emily John Joe Tony Emily Tony Joe CSE Winter
19 Renaming Changes the schema, not the instance Example: ρ B1,,Bn (R) Given Employee(Name, SSN) ρ N, S (Employee) à Answer(N, S) Not really used by systems, but needed on paper CSE Winter
20 Natural Join R1 R2 Meaning: R1 R2 = Π A (σ θ (R1 R2)) Where: Selection σ θ checks equality of all common attributes (i.e., attributes with same names) Projection Π A eliminates duplicate common attributes CSE Winter
21 Natural Join Example R A B S B C X Y Z U X Z V W Y Z Z V Z V R S = Π ABC (σ R.B=S.B (R S)) A B C X Z U X Z V Y Z U Y Z V Z V W CSE Winter
22 Natural Join Example 2 AnonPatient P age zip disease heart flu Voters V name age zip p p P V age zip disease name heart p flu p2 CSE Winter
23 Natural Join Given schemas R(A, B, C, D), S(A, C, E), what is the schema of R S? Given R(A, B, C), S(D, E), what is R S? Given R(A, B), S(A, B), what is R S? CSE Winter
24 AnonPatient (age, zip, disease) Voters (name, age, zip) Theta Join A join that involves a predicate R1 θ R2 = σ θ (R1 X R2) Here θ can be any condition No projection in this case! For our voters/patients example: P P.zip = V.zip and P.age >= V.age -1 and P.age <= V.age +1 V 24
25 Equijoin A theta join where θ is an equality predicate Projection drops all redundant attributes R1 θ R2 = π A (σ θ (R1 X R2)) By far the most used variant of join in practice What is the relationship with natural join? CSE Winter
26 Equijoin Example AnonPatient P age zip disease heart flu Voters V name age zip p p P P.age=V.age V age P.zip disease name V.zip heart p flu p CSE Winter
27 Join Summary Theta-join: R θ S = σ θ (R x S) Join of R and S with a join condition θ Cross-product followed by selection θ Equijoin: R θ S = π A (σ θ (R x S)) Join condition θ consists only of equalities Projection π A drops all redundant attributes Natural join: R S = π A (σ θ (R x S)) Equality on all fields with same name in R and in S Projection π A drops all redundant attributes CSE Winter
28 So Which Join Is It? When we write R S we usually mean an equijoin, but we often omit the equality predicate when it is clear from the context CSE Winter
29 More Joins Outer join Include tuples with no matches in the output Use NULL values for missing attributes Does not eliminate duplicate columns Variants Left outer join Right outer join Full outer join CSE Winter
30 AnonPatient P age zip disease heart flu lung Outer Join Example AnnonJob J job age zip lawyer cashier P.age P.zip disease job J.age J.zip P J heart lawyer flu cashier lung null CSE Winter
31 Some Examples Supplier(sno,sname,scity,sstate) Part(pno,pname,psize,pcolor) Supply(sno,pno,qty,price) Name of supplier of parts with size greater than 10 π sname (Supplier Supply (σ psize>10 (Part)) Name of supplier of red parts or parts with size greater than 10 π sname (Supplier Supply (σ psize>10 (Part) σ pcolor= red (Part) ) ) Can be represented as trees as well (as seen from last class) CSE Winter
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