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376a. Database Design

376a. Database Design. Dept. of Computer Science Vassar College http://www.cs.vassar.edu/~cs376 Class 6: Converting ER and EER diagrams to Relational Mapping. Housekeeping. Homework for Oct 2nd. 4.19, 7.20, 7.26, 9.11, 9.15, 9.20 (except h) Potential midterm for October 14?. More queries.

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376a. Database Design

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  1. 376a. Database Design Dept. of Computer Science Vassar College http://www.cs.vassar.edu/~cs376 Class 6: Converting ER and EER diagrams to Relational Mapping Prof. Billibon Yoshimi

  2. Housekeeping • Homework for Oct 2nd. • 4.19, 7.20, 7.26, 9.11, 9.15, 9.20 (except h) • Potential midterm for October 14? Prof. Billibon Yoshimi

  3. More queries • How many employees have more than 1 child. • How many employees have no children? Prof. Billibon Yoshimi

  4. Now to chapter 9, mapping ER and EER to relational model • How to convert from an ER or EER model (a graph) to a relational model (using tables)? • 7 steps (+2 extra for EER) • Have a graph describing the entities and relationships (also the subclasses and categories in the case of EER) => tables Prof. Billibon Yoshimi

  5. 1. Convert strong types • Create relation R that includes all simple attributes of E. • Flatten composite attributes into simple attributes. • Do NOT add mutivalued attributes yet. • Select key of E to be key of R. Key may include several attributes. • E.g. EMPLOYEE Prof. Billibon Yoshimi

  6. 2. Convert weak entities • Create relation R include foreign key of E (the owner of weak entity W) • Create new primary key for R using E foreign key and key of weak entity. • E.g. DEPENDENTS Prof. Billibon Yoshimi

  7. 3. Convert 1:1 relations • For entities S and T that participate in R. • If S participates totally in R, use S’s primary key and T as foreign key in R. • If both participate totally, combine entity types and relationship into single relation. (merge two entity types.) • E.g. EMPLOYEE MANAGES DEPT Prof. Billibon Yoshimi

  8. 4. Convert 1:N relations • S - n - R - 1 - T • Make relation S • Use T as foreign key in S since each instance in S is related to at most one T. • E.g. EMPLOYEE - n - WORKS_FOR - 1 - DEPT Prof. Billibon Yoshimi

  9. 5. Convert M:N relations • Create new relation S to represent R. Use primary keys of both relations as super key in S. • Attach any attributes to relation to this relation. • E.g. EMPLOYEE-n-WORKS_ON-m-PROJECT (with HOURS attribute) Prof. Billibon Yoshimi

  10. 6. Convert multi-valued attributes • A - Multi-valued attribute • S - entity A is associated with. • Create a new relation R has K the primary key of S and A as attributes. • Primary key of S is A and K. • E.g. DEPARTMENT_LOCATIONS Prof. Billibon Yoshimi

  11. 7. Convert n-ary relations • Create new relation S. • Primary key of S contains as foreign key keys of individual entities. • If cardinality constraint of any of relation is 1, don’t add its key to the super key (fully specified by other keys…) • E.g. SUPPLIES for (SUPPLIER, PART, PROJNAME) Prof. Billibon Yoshimi

  12. 8. For subclasses • Create a relationship for superclass ( C(k, a1, a2…an ) )and each child Si(bi1,..bim) • 4 choices: 1. create L(k, a1, a2…an ) and Li (k  {bi1..b1m} ) PK(Li) = k 2. create Li({bi1..bim}  {k, a1..an})and PK(Li) = k 3. create L({b11..b1m} {b21..b2m}…{bh1..bhm} {k, a1..an} {t})and PK(Li) = k 4. same as above + {t1, t2…tm} Prof. Billibon Yoshimi

  13. 8. Observations • 1 and 2 are multiple relations. • 3 and 4 are single relations. • 1 works in disjoint and overlapping and total and partial constraint situations. • 2 works only when disjoint and total participation (why?) • 3 and 4 have NULLs for unused attributes. • 3 disjoint one t for type. • 4 overlapping, multiple t’s for inclusion. Prof. Billibon Yoshimi

  14. 9. Mapping categories • Create new relation R. • Create surrogate key, K in R. • Create a type attribute A. • Add surrogate key K as foreign key in each relation S in the union. Prof. Billibon Yoshimi

  15. Relational Calculus • Declarative expressions similar to SQL. • Do not specify how to retrieve data (unlike relational algebra) only what data is retrieved. • Non procedural, declaritive • Same expressive power as RA (if can find mapping between language and RC then language is relationally complete) • Can’t express  -operations Prof. Billibon Yoshimi

  16. Definitions • Tuple variable - a variable taking the value of any tuple in a range. • Range relation - R(t) where R is a relation where tuple t is drawn from. Prof. Billibon Yoshimi

  17. A relational calculus query • {t | COND (t)} returns tuples which satisfy condition COND. • E.g. {x | EMPLOYEE(x) and x.salary>20000} • Range relation EMPLOYEE(x) indicates that x takes on the value of any tuple in EMPLOYEE relation. • Every tuple is evaluated against both conditions to identify selected valid (TRUE) combinations. Prof. Billibon Yoshimi

  18. Example RC query Retrieve Name and Address of employees in department number 5 {e.name, e.address | EMPLOYEE(e) and e.DNO = 5} Prof. Billibon Yoshimi

  19. How to construct expressions and formulas Expressions are {t1..A1, t2.A2, tn.An | COND (t1, t2..tn..tn+m) } t1..tn are tuple variables and Ai is an attribute of ti Left side are requested attributes. Right side is a condition or formula. Prof. Billibon Yoshimi

  20. Rules for making formulas Valid atoms 1. Can be an atom R(ti) - R is relation and t is a tuple variable. Tuples are assigned a member of the relation R. 2. Can be an atom ti..Ai op tj..Aj where op  { =, > , , <, , }. Assigned tuples which make atom evaluate to true. 3. Can be an atom ti..Ai op cwhere op  { =, > , , <, , } Assigned tuples which make atom evaluate to true. Prof. Billibon Yoshimi

  21. Create valid formulas • Atoms are formulas • If F1 & F2 are formulas -> (F1 and F2), (F1 or F2), not (F1) and not (F2) are formulas. • Normal truth tables apply to these evaluations. Prof. Billibon Yoshimi

  22. Existential and Universal quantifiers • Existential and Universal quantifiers are bound tuple variables. • Add two more valid formulas • If F is a valid formula and x is a tuple variable, then (x)(F) is a valid formula. It is true if there exists at least one tuple x which make F true. • If F is a valid formula and t is a tuple variable, then (x)(F) is a valid formula. True if any tuple assigned to x makes F true. Prof. Billibon Yoshimi

  23. Examples from book • Retrieve names and address of employees from research department. Prof. Billibon Yoshimi

  24. Design in two halfs • First, what are the desired attributes • E.name and e.address Prof. Billibon Yoshimi

  25. Next design the formula • Only free tuple variables should be on left side of bar. Other variables should be bound on right side of bar. EMPLOYEE(e) and (d) (DEPARTMENT(d)) and d.DNAME=“research” and d.DNUMBER=e.DNO Prof. Billibon Yoshimi

  26. Finally {e.name, e.address | EMPLOYEE(e) and (d) (DEPARTMENT(d) and d.DNAME=“research” and d.DNUMBER=e.DNO) • Only free tuple variables should be on left side of bar. Prof. Billibon Yoshimi

  27. Another example • For every project in ‘Stafford’, list the project number, the controlling department, the department manager’s last name, birthdate and address. Prof. Billibon Yoshimi

  28. Another example • For every project in ‘Stafford’, list the project number, the controlling department, the department manager’s last name, birthdate and address. • Left side • p.PNUMBER, p.DUM, e.LNAME, e.BDATE, e.ADDRESS • Right side • What are the free variables and what are the bound variables? Prof. Billibon Yoshimi

  29. Example cont. • P is free and e is free. (both on left side) what else is needed to solve the problem? • PROJECT(p) and EMPLOYEE(e) and DEPARTMENT(d) and p.DNUM = d.DNUMBER and d.MGRSSN = e.SSN • Problem: d is not bound in formula • Correct this. Prof. Billibon Yoshimi

  30. Query 3 • Find the name of all employees who work on some project controlled by department number 5. • Returned value is e.LNAME, e.FNAME • Use existential quantifiers for PROJECT and WORKS_ON Prof. Billibon Yoshimi

  31. Converting between Universal and Existential quantifiers • ( x) (P(x)) = not ( x) (not P(x)) • ( x) (P(x)) = not ( x) (not P(x)) • ( x) (P(x) or Q(x)) = not ( x) (not (P(x)) and not (Q(x))) • Most important relationship to remember is • If x then y => (not (x) or y) • And many more on page 305. Prof. Billibon Yoshimi

  32. Using the Universal quantifier • Find the names of employees who work on all projects in department number 5. • {e.FNAME, e.LNAME | EMPLOYEE(e) and ( ( x) (not (PROJECT(x) or not (x.DNUM=5) or (( w) (WORKS_ON(w) and w.ESSN=e.SSN and x.PNUMBER=w.PNO)))) } • Remember x must be true for all tuples in the universe! (need to cover whole space). Prof. Billibon Yoshimi

  33. Can transform it to using only existential quantifiers • Use ( x) (P(x) or Q(x)) = not ( x) (not (P(x)) and not (Q(x))) Prof. Billibon Yoshimi

  34. Safe expressions • Expressions should return finite number of results. • {t | not (EMPLOYEE(t)) } is not safe. • Only considered safe if the results are from the domain of the range relation (right side). • Not (EMPLOYEE(t)) has tuples from outside the EMPLOYEE(t) relation. Prof. Billibon Yoshimi

  35. One more calculus: Domain Relational Calculus • Domain relational calculus used in query by example. • Variables range of domains of attributes (instead of tuples.) • E.g. {x1, x2..xn| COND(x1, x2..xn, ..xn+m} xi range of domain of attribute Ai Prof. Billibon Yoshimi

  36. Atoms are different Atom may be… 1. R(x1, x2, … xn) where r is a relation with degree n and each xi is a domain variable. In short hand R(x1 x2 … xn) no commas 2. xi. op xj. where op  { =, > , , <, , }. x’s are domain variables. 3. xi. op c where op  { =, > , , <, , } and xi is a domain variable. *Normally use lowercase l-z for domain vars Prof. Billibon Yoshimi

  37. Example Get birthdate and address of person named “John B. Smith” { uv | ( q) ( r) ( s) ( t) ( w) ( x) ( y) ( z) (EMPLOYEE (qrstwxyz) and q = ‘John’ and r=‘B.’ and s=‘Smith’)} Every attribute of EMPLOYEE is assigned a domain var. only U and V are free. Prof. Billibon Yoshimi

  38. Another way {q | EMPLOYEE( ‘John’,’B.’,’Smith’,t, u, v, w, x, y, z) } All variables are free. Prof. Billibon Yoshimi

  39. Example Name and address of everyone in research department {qsv | ( z) ( l) ( m) (EMPLOYEE(qrstuvwxyz) and DEPT(lmno) and l=‘research’ and m=z) Prof. Billibon Yoshimi

  40. Try a few For every project in Stafford, list the controlling manager’s name and birthdate. Find employees with no dependents. List names of all managers with one dependent. Prof. Billibon Yoshimi

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