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Managing external data Part 1 Design of Databases Gitte Christensen Dyalog Ltd Purpose • To give you a crash course in data analysis and databases • After part 1 Design of Databases you will be able to analyse and organise data based on a requirement spec or use case. • After part 2 Database programming you will be able to use relational data in your APL applications • After part 3 Database Implementation you will be able to choose between different storage methods based on structure and use of data and performance considerations Agenda • The Relational Model – Entity/Relation model – Convert E/R to table structure – Relational Algebra • Semistructured data • Multidimensional data Data Models • A Database models some portion of the real world. • Data Model is link between user’s view of the world and bits stored in computer. • We will concentrate on the Relational Model Data Models • A data model is a collection of concepts for describing data. • A database schema is a description of a particular collection of data, using a given data model. • The relational model of data is the most widely used model today. – Main concept: relation, basically a table with rows and columns. – Every relation has a schema, which describes the columns, or fields. Levels of Abstraction • Views describe how users see the data. • Conceptual schema defines logical structure • Physical schema describes the files and indexes used. • (sometimes called the ANSI/SPARC model) Users View 1 View 2 View 3 Conceptual Schema Physical Schema DB Data Independence • A Simple Idea: Applications should be insulated from how data is structured and stored. • Logical data independence: Protection from changes in logical structure of data. • Physical data independence: Protection from changes in physical structure of data. View 1 View 2 View 3 Conceptual Schema Physical Schema DB Entity-Relationship Model 8 Purpose of E/R Model • The E/R model allows us to sketch database designs. – Kinds of data and how they connect. – Not how data changes. • Designs are pictures called entityrelationship diagrams. • Later: convert E/R designs to relational DB designs. 9 Entity Sets • Entity = “thing” or object. • Entity set = collection of similar entities. – Similar to a class in object-oriented languages. • Attribute = property of (the entities of) an entity set. – Attributes are simple values, e.g. integers or character strings. 10 E/R Diagrams • In an entity-relationship diagram: – Entity set = rectangle. – Attribute = oval, with a line to the rectangle representing its entity set. 11 Example name manf Beers • Entity set Beers has two attributes, name and manf (manufacturer). • Each Beers entity has values for these two attributes, e.g. (Bud, Anheuser-Busch) 12 Relationships • A relationship connects two or more entity sets. • It is represented by a diamond, with lines to each of the entity sets involved. 13 Example name addr Bars name Beers Sells license Frequents Note: license = beer, full, none name Likes Drinkers manf Bars sell some beers. Drinkers like some beers. Drinkers frequent some bars. addr 14 Relationship Set • The current “value” of an entity set is the set of entities that belong to it. – Example: the set of all bars in our database. • The “value” of a relationship is a set of lists of currently related entities, one from each of the related entity sets. 15 Example • For the relationship Sells, we might have a relationship set like: Bar Joe’s Bar Joe’s Bar Sue’s Bar Sue’s Bar Sue’s Bar Beer Bud Miller Bud Pete’s Ale Bud Lite 16 Case Movie Database • We want to create a movie database which will allow our users to find information about movies • Each movie has a title, a production year, lenght in minutes, whether it is color or b/w and an owner, a studio • We have adresses for the studios and the actors EntityName Relationship AttributeName AttriAbute Draw a model of the Movies database using these symbols Multiway Relationships • Sometimes, we need a relationship that connects more than two entity sets. • Suppose that drinkers will only drink certain beers at certain bars. – Our three binary relationships Likes, Sells, and Frequents do not allow us to make this distinction. – But a 3-way relationship would. 19 Example name license addr name Bars manf Beers Preferences Drinkers name addr 20 A Typical Relationship Set Bar Joe’s Bar Sue’s Bar Sue’s Bar Joe’s Bar Joe’s Bar Joe’s Bar Sue’s Bar Drinker Ann Ann Ann Bob Bob Cal Cal Beer Miller Bud Pete’s Ale Bud Miller Miller Bud Lite 21 Case Movie Database • In each movie there are actors who are contracted by the studios • Add this relationship to your model Many-Many Relationships • Focus: binary relationships, such as Sells between Bars and Beers. • In a many-many relationship, an entity of either set can be connected to many entities of the other set. – E.g., a bar sells many beers; a beer is sold by many bars. 23 In Pictures: many-many 24 Many-One Relationships • Some binary relationships are many -one from one entity set to another. • Each entity of the first set is connected to at most one entity of the second set. • But an entity of the second set can be connected to zero, one, or many entities of the first set. 25 In Pictures: many-one 26 Example • Favorite, from Drinkers to Beers is manyone. • A drinker has at most one favorite beer. • But a beer can be the favorite of any number of drinkers, including zero. 27 One-One Relationships • In a one-one relationship, each entity of either entity set is related to at most one entity of the other set. • Example: Relationship Best-seller between entity sets Manfs (manufacturer) and Beers. – A beer cannot be made by more than one manufacturer, and no manufacturer can have more than one best-seller (assume no ties). 28 In Pictures: one-one 29 Representing “Multiplicity” • Show a many-one relationship by an arrow entering the “one” side. • Show a one-one relationship by arrows entering both entity sets. • Rounded arrow = “exactly one,” i.e., each entity of the first set is related to exactly one entity of the target set. 30 Example Drinkers Likes Beers Favorite 31 Example • Consider Best-seller between Manfs and Beers. • Some beers are not the best-seller of any manufacturer, so a rounded arrow to Manfs would be inappropriate. • But a beer manufacturer has to have a best-seller. 32 In the E/R Diagram Manfs Bestseller Beers 33 Case Movie Database • Add arrows to your diagram so it reflects the kind of relations between the entities Attributes on Relationships • Sometimes it is useful to attach an attribute to a relationship. • Think of this attribute as a property of tuples in the relationship set. 35 Example Bars Sells Beers price Price is a function of both the bar and the beer, not of one alone. 36 Equivalent Diagrams Without Attributes on Relationships • Create an entity set representing values of the attribute. • Make that entity set participate in the relationship. 37 Example Bars Sells Prices Beers Note convention: arrow from multiway relationship = “all other entity sets together determine a unique one of these.” price 38 Roles • Sometimes an entity set appears more than once in a relationship. • Label the edges between the relationship and the entity set with names called roles. 39 Example Relationship Set Husband Bob Joe … Married husband wife Drinkers 40 Wife Ann Sue … Example Relationship Set Buddies 1 2 Buddy1 Bob Joe Ann Joe … Drinkers 41 Buddy2 Ann Sue Bob Moe … Case Movie Database • The actors can be contracted either by the studio producing the movie or by another studio who rents the actor to the producing studio • We would like to record what the actor is paid for appearing in a movie • Update your model to reflect the new facts Subclasses • Subclass = special case = fewer entities = more properties. • Example: Ales are a kind of beer. – Not every beer is an ale, but some are. – Let us suppose that in addition to all the properties (attributes and relationships) of beers, ales also have the attribute color. 43 Subclasses in E/R Diagrams • Assume subclasses form a tree. – I.e., no multiple inheritance. • Isa triangles indicate the subclass relationship. – Point to the superclass. 44 Example name Beers manf isa color Ales 45 Case Movie Database • For some movies like cartoons we have a different kind of actor, voices. • Design a subclass to reflect this fact ISA E/R Vs. Object-Oriented Subclasses • In OO, objects are in one class only. – Subclasses inherit from superclasses. • In contrast, E/R entities have representatives in all subclasses to which they belong. – Rule: if entity e is represented in a subclass, then e is represented in the superclass. 47 Example name Beers manf Pete’s Ale isa color Ales 48 Keys • A key is a set of attributes for one entity set such that no two entities in this set agree on all the attributes of the key. – It is allowed for two entities to agree on some, but not all, of the key attributes. • We must designate a key for every entity set. 49 Keys in E/R Diagrams • Underline the key attribute(s). • In an Isa hierarchy, only the root entity set has a key, and it must serve as the key for all entities in the hierarchy. 50 Example: name is Key for Beers name Beers manf isa color Ales 51 Example: a Multi-attribute Key dept number hours room Courses • Note that hours and room could also serve as a key, but we must select only one key. 52 Case Movie Database • Add keys to your diagram Weak Entity Sets • Occasionally, entities of an entity set need “help” to identify them uniquely. • Entity set E is said to be weak if in order to identify entities of E uniquely, we need to follow one or more many-one relationships from E and include the key of the related entities from the connected entity sets. 54 Example • name is almost a key for football players, but there might be two with the same name. • number is certainly not a key, since players on two teams could have the same number. • But number, together with the team name related to the player by Plays-on should be unique. 55 In E/R Diagrams name number Players name Playson Teams • Double diamond for supporting many-one relationship. • Double rectangle for the weak entity set. 56 Weak Entity-Set Rules • A weak entity set has one or more many-one relationships to other (supporting) entity sets. – Not every many-one relationship from a weak entity set need be supporting. • The key for a weak entity set is its own underlined attributes and the keys for the supporting entity sets. – E.g., (player) number and (team) name is a key for Players in the previous example. 57 Case Movie Database • We would like to record which camera crews shot a particular movie • Camera crews are numbered within each studio • Add these facts to your diagram Design Techniques 1. Avoid redundancy. 2. Limit the use of weak entity sets. 3. Don’t use an entity set when an attribute will do. 59 Avoiding Redundancy • Redundancy occurs when we say the same thing in two or more different ways. • Redundancy wastes space and (more importantly) encourages inconsistency. – The two instances of the same fact may become inconsistent if we change one and forget to change the other. 60 Example: Good name Beers name ManfBy addr Manfs This design gives the address of each manufacturer exactly once. 61 Example: Bad name Beers name ManfBy addr Manfs manf This design states the manufacturer of a beer twice: as an attribute and as a related entity. 62 Example: Bad name manf manfAddr Beers This design repeats the manufacturer’s address once for each beer and loses the address if there are temporarily no beers for a manufacturer. 63 Entity Sets Versus Attributes • An entity set should satisfy at least one of the following conditions: – It is more than the name of something; it has at least one nonkey attribute. or – It is the “many” in a many-one or manymany relationship. 64 Example: Good name Beers name ManfBy addr Manfs •Manfs deserves to be an entity set because of the nonkey attribute addr. •Beers deserves to be an entity set because it is the “many” of the many-one relationship ManfBy. 65 Example: Good name manf Beers There is no need to make the manufacturer an entity set, because we record nothing about manufacturers besides their name. 66 Example: Bad name Beers name ManfBy Manfs Since the manufacturer is nothing but a name, and is not at the “many” end of any relationship, it should not be an entity set. 67 Don’t Overuse Weak Entity Sets • Beginning database designers often doubt that anything could be a key by itself. – They make all entity sets weak, supported by all other entity sets to which they are linked. • In reality, we usually create unique ID’s for entity sets. – Examples include social-security numbers, automobile VIN’s etc. 68 When Do We Need Weak Entity Sets? • The usual reason is that there is no global authority capable of creating unique ID’s. • Example: it is unlikely that there could be an agreement to assign unique player numbers across all football teams in the world. 69 Break How to translate ER Model to Relational Model Concepts Relational Model is made up of tables • • • • • A row of table A column of table A table Cardinality Degree = a relational instance/tuple = an attribute = a schema/relation = number of rows = number of columns Example Attribute SID Name Major GPA 1234 John CS 2.8 5678 Mary EE 3.6 Cardinality = tuple/relational instance 2 4 Degree A Schema / Relation From ER Model to Relational Model So… how do we convert an ER diagram into a table?? Simple!! Basic Ideas: • Build a table for each entity set • Build a table for each relationship set if necessary (more on this later) • Make a column in the table for each attribute in the entity set • Indivisibility Rule and Ordering Rule • Primary Key Example – Strong Entity Set SID Name SSN Advisor Student Major Name Professor Dept GPA SID Name Major GPA SSN Name Dept 1234 John CS 2.8 9999 Smith Math 5678 Mary EE 3.6 8888 Lee CS Representation of Weak Entity Set • Weak Entity Set Cannot exists alone • To build a table/schema for weak entity set – Construct a table with one column for each attribute in the weak entity set – Remember to include discriminator – Augment one extra column on the right side of the table, put in there the primary key of the Strong Entity Set (the entity set that the weak entity set is depending on) – Primary Key of the weak entity set = Discriminator + foreign key Example – Weak Entity Set Age SID Name Student Major Primary key of Children is Parent_SID + Name Name owns Children GPA Age Name Parent_SID 10 Bart 1234 8 Lisa 5678 Representation of Relationship Set --This is a little more complicated-• Unary/Binary Relationship set – Depends on the cardinality and participation of the relationship – Two possible approaches • N-ary (multiple) Relationship set – Primary Key Issue • Identifying Relationship – No relational model representation necessary Representing Relationship Set Unary/Binary Relationship • For one-to-one relationship w/out total participation – Build a table with two columns, one column for each participating entity set’s primary key. Add successive columns, one for each descriptive attributes of the relationship set (if any). • For one-to-one relationship with one entity set having total participation – Augment one extra column on the right side of the table of the entity set with total participation, put in there the primary key of the entity set without complete participation as per to the relationship. Example – One-to-One Relationship Set Degree SID Name Student Major ID Code study Major GPA Primary key can be either SID or Maj_ID_Co SID Maj_ID Co S_Degree 9999 07 1234 8888 05 5678 Example – One-to-One Relationship Set Condition SID Name 1:1 Relationship Student Major S/N # Have Laptop GPA Brand SID Name Major GPA LP_S/N Hav_Cond 9999 Bart Economy -4.0 123-456 Own 8888 Lisa Physics 4.0 567-890 Loan * Primary key can be either SID or LP_S/N Representing Relationship Set Unary/Binary Relationship • For one-to-many relationship w/out total participation – Same thing as one-to-one • For one-to-many/many-to-one relationship with one entity set having total participation on “many” side – Augment one extra column on the right side of the table of the entity set on the “many” side, put in there the primary key of the entity set on the “one” side as per to the relationship. Example – Many-to-One Relationship Set Semester SID Name N:1 Relationship Advisor Student Major SSN Professor GPA Dept Name SID Name Major GPA Pro_SSN Ad_Sem 9999 Bart Economy -4.0 123-456 Fall 2006 8888 Lisa Physics 4.0 567-890 Fall 2005 * Primary key of this table is SID Representing Relationship Set Unary/Binary Relationship • For many-to-many relationship – Same thing as one-to-one relationship without total participation. – Primary key of this new schema is the union of the foreign keys of both entity sets. – No augmentation approach possible… Representing Relationship Set N-ary Relationship • Intuitively Simple – Build a new table with as many columns as there are attributes for the union of the primary keys of all participating entity sets. – Augment additional columns for descriptive attributes of the relationship set (if necessary) – The primary key of this table is the union of all primary keys of entity sets that are on “many” side – That is it, we are done. Example – N-ary Relationship Set P-Key1 D-Attribute A-Key E-Set 1 P-Key2 A relationship Another Set E-Set 2 P-Key3 E-Set 3 P-Key1 P-Key2 P-Key3 A-Key D-Attribute 9999 8888 7777 6666 Yes 1234 5678 9012 3456 No * Primary key of this table is P-Key1 + P-Key2 + P-Key3 Representing Relationship Set Identifying Relationship • This is what you have to know – You DON’T have to build a table/schema for the identifying relationship set once you have built a table/schema for the corresponding weak entity set – Reason: • A special case of one-to-many with total participation • Reduce Redundancy Representing Composite Attribute • Relational Model Indivisibility Rule Applies • One column for each component attribute • NO column for the composite attribute itself SSN SSN Name Street City 9999 Dr. Smith 50 1st St. Fake City 8888 Dr. Lee 1 B St. San Jose Name Professor Address Street City Representing Multivalue Attribute • For each multivalue attribute in an entity set/relationship set – Build a new relation schema with two columns – One column for the primary keys of the entity set/relationship set that has the multivalue attribute – Another column for the multivalue attributes. Each cell of this column holds only one value. So each value is represented as an unique tuple – Primary key for this schema is the union of all attributes Example – Multivalue attribute SID Name Children Student Major The primary key for this table is Student_SID + Children, the union of all attributes GPA SID Name Major GPA 1234 John CS 2.8 5678 Homer EE 3.6 Stud_SID Children 1234 Johnson 1234 Mary 5678 Bart 5678 Lisa 5678 Maggie Representing Class Hierarchy • Two general approaches depending on disjointness and completeness – For non-disjoint and/or non-complete class hierarchy: • create a table for each super class entity set according to normal entity set translation method. • Create a table for each subclass entity set with a column for each of the attributes of that entity set plus one for each attributes of the primary key of the super class entity set • This primary key from super class entity set is also used as the primary key for this new table SSN Example Name Person SID Status Gender ISA Student Major GPA SSN Name Gender 1234 Homer Male 5678 Marge Female SSN SID Status Major GPA 1234 9999 Full CS 2.8 5678 8888 Part EE 3.6 Case Movie Database • Convert your E/R diagram to relational tables Relational Algebra Relational Algebra Relational Algebra is : • the formal description of how a relational database operates • the mathematics which underpin SQL operations. Operators in relational algebra are not necessarily the same as SQL operators, even if they have the same name. Terminology • Relation - a set of tuples. • Tuple - a collection of attributes which describe some real world entity. • Attribute - a real world role played by a named domain. • Domain - a set of atomic values. • Set - a mathematical definition for a collection of objects which contains no duplicates. Operators - Write • INSERT - provides a list of attribute values for a new tuple in a relation. This operator is the same as SQL. • DELETE - provides a condition on the attributes of a relation to determine which tuple(s) to remove from the relation. This operator is the same as SQL. • MODIFY - changes the values of one or more attributes in one or more tuples of a relation, as identified by a condition operating on the attributes of the relation. This is equivalent to SQL UPDATE. Operators - Retrieval There are two groups of operations: • Mathematical set theory based relations: UNION, INTERSECTION, DIFFERENCE, and CARTESIAN PRODUCT. • Special database operations: SELECT (not the same as SQL SELECT), PROJECT, and JOIN. Relational SELECT SELECT is used to obtain a subset of the tuples of a relation that satisfy a select condition. For example, find all employees born after 1st Jan 1950: SELECT dob > ’01/JAN/1950’ (employee) Relational PROJECT The PROJECT operation is used to select a subset of the attributes of a relation by specifying the names of the required attributes. For example, to get a list of all employees surnames and employee numbers: PROJECT surname,empno (employee) SELECT and PROJECT SELECT and PROJECT can be combined together. For example, to get a list of employee numbers for employees in department 1:= 1 (employee)) PROJECT empno number (SELECT depno Mapping this back to SQL gives: SELECT empno FROM employee WHERE depno = 1; Set Operations - semantics Consider two relations R and S. • UNION of R and S the union of two relations is a relation that includes all the tuples that are either in R or in S or in both R and S. Duplicate tuples are eliminated. • INTERSECTION of R and S the intersection of R and S is a relation that includes all tuples that are both in R and S. • DIFFERENCE of R and S the difference of R and S is the relation that contains all the tuples that are in R but that are not in S. SET Operations - requirements For set operations to function correctly the relations R and S must be union compatible. Two relations are union compatible if – they have the same number of attributes – the domain of each attribute in column order is the same in both R and S. UNION Example INTERSECTION Example DIFFERENCE Example CARTESIAN PRODUCT The Cartesian Product is also an operator which works on two sets. It is sometimes called the CROSS PRODUCT or CROSS JOIN. It combines the tuples of one relation with all the tuples of the other relation. CARTESIAN PRODUCT Example JOIN Operator JOIN is used to combine related tuples from two relations: • In its simplest form the JOIN operator is just the cross product of the two relations. • As the join becomes more complex, tuples are removed within the cross product to make the result of the join more meaningful. • JOIN allows you to evaluate a join condition between the attributes of the relations on which the join is undertaken. The notation used is R JOIN join condition S JOIN Example Natural Join Invariably the JOIN involves an equality test, and thus is often described as an equi-join. Such joins result in two attributes in the resulting relation having exactly the same value. A ‘natural join’ will remove the duplicate attribute(s). – In most systems a natural join will require that the attributes have the same name to identify the attribute(s) to be used in the join. This may require a renaming mechanism. – If you do use natural joins make sure that the relations do not have two attributes with the same name by accident. OUTER JOINs Notice that much of the data is lost when applying a join to two relations. In some cases this lost data might hold useful information. An outer join retains the information that would have been lost from the tables, replacing missing data with nulls. There are three forms of the outer join, depending on which data is to be kept. • LEFT OUTER JOIN - keep data from the left-hand table • RIGHT OUTER JOIN - keep data from the right-hand table • FULL OUTER JOIN - keep data from both tables OUTER JOIN Example 1 OUTER JOIN Example 2 Semistructured data star Root starIn starOf mh city city street cf starOf starIn sw Multidimensional data End of Part 1