Boyce-Codd Normal Form
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1. This design states the manufacturer of a beer twice as an attribute and as a related entity Example Bad ED Gat Gp This design repeats the manufacturer s address once for each beer and loses the address if there are temporarily no beers for a manufacturer 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 Itis the many in a many one or many many relationship Example Good name name Gaar a e Manfs deserves to be an entity set because of the nonkey attribute addr e Beers deserves to be an entity set because it is the many of the many one relationship ManfBy Example Good fname man There is no need to make the manufacturer an entity set because we record nothing about manufacturers besides their name Example Bad name D 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 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 CPR numbers car s license plates etc When Do We Need Weak Entity Sets2. 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 From E R Diagrams to Relations Entity set relation Attributes attributes Relationships relations whose attributes are only The keys of the connected entity sets Attributes of the relationship itself Entity Set Relation name man Relation Beers name manf Relationship Relation Likes drinker beer Favorite drinker beer Buddies namel name2 Married husband wife 94 Combining Relations OK to combine into one relation 1 The relation for an entity set 2 The relations for many one relationships of which E is the many Example Drinkers name addr and Favorite drinker beer combine to make Drinkeri name addr favBeer Risk with Many Many Relationships Combining Drinkers with Likes would be a mistake It leads to redundancy as name addr beer Peter Ce 1pl Od Cl Erd W Redundancy Handling Weak Entity Sets Relation for a weak entity set must include attributes for its complete key including those belonging to other entity sets as well as its own nonkey attributes A supporting relationship is redundant and yields no relation unless jt has attributes Example Weak Entity Set Relation Hosts hostN
3. 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 and recursively up the tree Example Representatives of Entities Pete s Ale 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 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 Example name is Key for Beers Example a Multi attribute Key Cdep number hours room e Note that hours and room could also serve as a key but we must select only one key 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 Example Weak Entity Set name is almost a key for football players but there might be two with t
4. a list of components for restocking on Saturday morning computer store restocks his inventory every Saturday at his distributor 112 Selling Price Selling price for a component is the price 30 Selling price for a computer system is sum of the selling prices of the components rounded up to next 99 Rebate System total price is reduced by 2 for each additional computer system ordered maximal 20 rebate 113 Example Selling Price computer system for which the components are worth DKK 1984 the selling price of the components is 1984 1 3 2579 2 It would be sold for DKK 2599 Order of 3 systems DKK 7485 i e DKK 2495 per system Order of 11 23 or 42 systems DKK 2079 per system 114 Functionality of the System List of all components in the system and their current amount List of all computer systems in the system and how many of each could be build from the current stock Price list including all components and their selling prices grouped by kind all computers systems that could be build from the current stock including their components and selling price i Functionality of the System Price offer given the computer system and the quantity Sell a component or a computer system by updating the current stock Restocking list including names and amounts of all components needed for restocking to the preferred level 116 Limitations for the Project N
5. decompose into AC BC We Cannot Enforce FD s The problem is that if we use AC and BC as our database schema we cannot enforce the FD AB C by checking FD s in these decomposed relations Example with A street B city and C post code on the next slide An Unenforceable FD Campusvej 5230 Vestergade Odense 5000 No FD s were violated in the decomposed relations and FD street city post holds for the database as a whole 13 An Unenforceable FD post Hjallesevej Hjallesevej Hjallesevej 5230 Hjallesevej Odense 5000 Although no FD s were violated in the decomposed relations FD street city post is violated by the database as a whole 14 Another Unenforcable FD Departures time track train time track train and train track Two keys time track and time train train track is a BCNF violation so we must decompose into Departuresi time train Departures2 track train Another Unenforceable FD tracktrain 19 08 ICL54 4 ICL54 19 16 IC852 3 IC852 Join tuples with equal train code ICL54 i IC852 No FD s were violated in the decomposed relations FD time track train holds for the database as a whole 16 Another Unenforceable FD tracktrain 19 08 ICL54 4 ICL54 19 08 IC 42 4 IC 42 Join tuples with equal train code Although no FD s were violated in the decomposed relations FD time track train is v
6. in the join Then is the join of projections of some tuples of R one for each R of the decomposition Can we use the given FD s to show that one of these tuples must be t The Chase 2 Start by assuming t abc For each there is a tuple s of R that has a b c in the attributes of R 5 can have any values in other attributes We Il use the same letter as in t but with a subscript for these components Example The Chase Let R ABCD and the decomposition be AB BC and CD Let the given FD s be C D and B A Suppose the tuple t abcd is the join of tuples projected onto AB BC CD The tuples of R pro The Tableau jected onto AB BC CD Use B A Use C D We ve proved the second tuple must be t 26 Summary of the Chase If two rows agree in the left side of a FD make their right sides agree too Always replace a subscripted symbol by the corresponding unsubscripted one if possible If we ever get an unsubscripted row we know any tuple in the project join is in the original the join is lossless Otherwise the final tableau is a counterexample 21 Example Lossy Join Same relation R ABCD and same decomposition But with only the FD C D The Tableau These projections rejoin to form abcd These three tuples are an example Use C gt D R that shows the join lossy abcd is not in R but we can project and rejoin to
7. the left side name name addr favBeer Decomposed relations 1 Drinkersi name addr favBeer 2 Drinkers2 name beersLiked manf Example BCNF Decomposition We are not done we need to check Drinkersi and Drinkers2 for BCNF Projecting FD s is easy here For Drinkersi name addr favBeer relevant FD s are name addr and name favBeer Thus name is the only key and Drinkers1 is in BCNF Example BCNF Decomposition For Drinkers2 name beersLiked manf the only FD is beersLiked manf and the only key is name beersLiked Violation of BCNF beersLiked beersLiked manf so we decompose Drinkers into 1 Drinkers3 beersLiked manf 2 Drinkers4 name beersLiked Example BCNF Decomposition The resulting decomposition of Drinkers PWN i Drinkersi name addr favBeer Drinkers3 beersLiked manf Drinkers4 name beersLiked Notice Drinkers1 tells us about drinkers Drinkers3 tells us about beers and Drinkers4 tells us the relationship between drinkers and the beers they like Compare with running example Drinkers name addr phone Beers name manf Likes drinker beer Third Normal Form Motivation There is one structure of FD s that causes trouble when we decompose AB C and C B Example A street address B city C post code There are two keys A B and A C C B is a BCNF violation so we must
8. Boyce Codd Normal Form We say a relation R is in BCNF if whenever X Y is a nontrivial FD that holds in X is a superkey Remember nontrivial means Y is not contained in X Remember a superkey is any superset of a key not necessarily a proper superset Example Drinkers name addr beersLiked manf favBeer FD s name addr favBeer beersLiked manf Only key is name beersLiked In each FD the left side is not a superkey Any one of these FD s shows Drinkers is not in BCNF Another Example Beers name manf manfAddr FD s name manf manf manfAddr Only key is name Name manf does not violate BCNF but manf manfAddr does Decomposition into BCNF Given relation R with FD s F Look among the given FD s for a BCNF violation X Y If any FD following from F violates BCNF then there will surely be an FD in F itself that violates BCNF Compute X Not all attributes or else X is a superkey Decompose R Using X Y Replace R by relations with schemas 1 R X 2 R R X X Project given FD s F onto the two new relations Decomposition Picture Example BCNF Decomposition Drinkers name addr beersLiked manf favBeer F name addr name favBeers beersLiked manf Pick BCNF violation name addr Close
9. 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 relationship set a set of tuples with one component for each related entity set Example Relationship Set For the relationship Sells we might have a relationship set like Od Cl Erd Wei Od Cl Pilsener Erd Wei 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 Example 3 Way Relationship name addr name manf lt Preference name Gaar A Typical Relationship Set Ch Erd Wei Od Cl Od Cl Pilsener Erd Wei Tuborg Ale 48 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 In Pictures many many 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
10. ame location Logins loginName hostName expiry AtCeginName hostName hostName2 Panne At becomes part of Must be the same Logins Subclasses Three Approaches 1 Object oriented One relation per subset of subclasses with all relevant attributes 2 Use nulls One relation entities have NULL in attributes that don t belong to them 3 E R style One relation for each subclass Key attribute s Attributes of that subclass Example Subclass Relations Object Oriented Odense Classic Beers Ales Good for queries like find the color of ales made by Albani 101 E R Style Odense Classic Albani HC Andersen Albani Beers name color HC Andersen red Ales Good for queries like find all beers including ales made by Albani 102 Using Nulls name manf color Odense Classic Albani NULL HC Andersen Albani red Beers Saves space unless there are ots of attributes that are usually NULL 103 Summary 6 More things you should know Entities Attributes Entity Sets Relationships Multiplicity Keys Roles Subclasses Weak Entity Sets Design guidelines E R diagrams relational model 104 The Project Purpose of the Project To try in practice the process of designing and creating a relational database application This process includes development of an E R model transfer to the relational model normalization of relations
11. anufacturer has exactly one best seller 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 Example Attribute on Relationship 9 price Price is a function of both the bar and the beer not of one alone Equivalent Diagrams Without Attributes on Relationships Create an entity set representing values of the attribute Make that entity set participate in the relationship Example Removing an Attribute from a Relationship Note convention arrow from multiway relationship all other entity sets together determine a unique one of these 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 ro es Example Roles Relationship Set husband wife Example Roles Relationship Set 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 Subclasses in E R Diagrams Assume subclasses form a tree T e no multiple inheritance Isa triangles indicate the subclass relationship Point to the superclass Example Subclasses E
12. del The E R model allows us to sketch database schema designs Includes some constraints but not operations Designs are pictures called entity relationship diagrams Later convert E R designs to relational DB designs Framework for E R Design is a serious business The boss knows they want a database but they don t know what they want in it Sketching the key components is an efficient way to develop a working database 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 not structs sets etc E R Diagrams In an entity relationship diagram Entity set rectangle Attribute oval with a line to the rectangle representing its entity set Example Crame man Entity set Beers has two attributes name and manf manufacturer Each Beers entity has values for these two attributes e g Odense Classic Albani Relationships A relationship connects two or more entity sets It is represented by a diamond with lines to each of the entity sets involved Example Relationships license Drinkers like Freuen tes some beers Note elas 7 Drinkers frequent eer Tull some bars none fam Bars sell some beers 43 Relationship Set
13. get abcd 29 3NF Synthesis Algorithm We can always construct a decomposition into 3NF relations with a lossless join and dependency preservation Need minimal basis for the FD s 1 Right sides are single attributes 2 No FD can be removed 3 No attribute can be removed from a left side Constructing a Minimal Basis 1 Split right sides 2 Repeatedly try to remove an FD and see if the remaining FD s are equivalent to the original 3 Repeatedly try to remove an attribute from a left side and see if the resulting FD s are equivalent to the original 3NF Synthesis 2 One relation for each FD in the minimal basis Schema is the union of the left and right sides If no key is contained in an FD then add one relation whose schema is some key Example 3NF Synthesis Relation R ABCD FD s A B and A gt C Decomposition AB and AC from the FD s plus AD for a key Why It Works Preserves dependencies each FD from a minimal basis is contained in a relation thus preserved Lossless Join use the chase to show that the row for the relation that contains a key can be made all unsubscripted variables 3NF hard part a property of minimal bases Summary 5 More things you should know Functional Dependency Key Superkey Update Anomaly Deletion Anomaly BCNF Closure Decomposition Chase Algorithm 3rd Normal Form Entity Relationship Model Purpose of E R Mo
14. he 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 In E R Diagrams Note must be rounded because each player needs a team to help with the key e Double diamond for supporting many one relationship e Double rectangle for the weak entity set 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 But supporting relationships must have a rounded arrow entity at the one end is guaranteed Weak Entity Set Rules 2 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 Design Techniques Avoid redundancy Limit the use of weak entity sets Don t use an entity set when an attribute will do Avoiding Redundancy Redundancy saying the same thing in two or more different ways Wastes space and more importantly encourages inconsistency Two representations of the same fact become inconsistent if we change one and forget to change the other Recall anomalies due to FD s Example Good This design gives the address of each manufacturer exactly once Example Bad
15. implementation in a DBMS programming of an application 106 Project as part of The Exam Part of the exam and grading The project must be done individually No cooperation is allowed beyond what is explicitly stated in the description 107 Subject of the Project To create an electronic inventory for a computer store Keep information about complete computer systems and components System should be able to calculate prices for components and computer systems make lists of components to order from the distributor 108 Objects of the System component name kind price kind is one of CPU RAM graphics card mainboard case CPU socket bus speed RAM type bus speed mainboard CPU socket RAM type on board graphics form factor case form factor 109 Objects of the System computer system catchy name list of components requires a case a mainboard a CPU RAM optionally a graphics card sockets bus speed RAM type and form factor must match if there is no on board graphics a graphics card must be included 110 Objects of the System current stock list of components and their current amount minimum inventory list of components their allowed minimum amount and their preferred amount after restocking 111 Intended Use of the System Print a daily price list for components and computer systems Give quotes for custom orders Print out
16. iolated by the database as a whole 17 3NF Let s Us Avoid This Problem 3rd Normal Form 3NF modifies the BCNF condition so we do not have to decompose in this problem situation An attribute is prime if it is a member of any key X A violates 3NF if and only if X is not a superkey and also A is not prime Example 3NF In our problem situation with FD s AB C and C B we have keys AB and AC Thus A B and C are each prime Although C B violates BCNF it does not violate 3NF What 3NF and BCNF Give You There are two important properties of a decomposition 1 Lossless Join it should be possible to project the original relations onto the decomposed schema and then reconstruct the original 2 Dependency Preservation it should be possible to check in the projected relations whether all the given FD s are satisfied 3NF and BCNF Continued We can get 1 with a BCNF decomposition We can get both 1 and 2 with a 3NF decomposition But we can t always get 1 and 2 witha BCNF decomposition street city post is an example time track train is another example Testing for a Lossless Join If we project R onto R R Rg can we recover R by rejoining Any tuple in R can be recovered from its projected fragments So the only question is when we rejoin do we ever get back something we didn t have originally The Chase Test Suppose tuple t comes back
17. o facilities for updating are required except for the Selling mentioned explicitly Only a simple command line based interface for user interaction is required Choices by the user can be input by showing a numbered list of alternatives or by prompting for component names etc You are welcome to include update facilities or make a better user interface but this will not influence the final grade Tasks Develop an appropriate E R model 2 Transfer to a relational model Ensure that all relations are in 3NF decompose and refine the E R model Implement in PostgreSQL DBMS ensuring the constraints hold Program in Java or Python an application for the user interaction providing all functionality from above 18 Test Data Can be made up as you need it At least in the order of 8 computer systems and 30 components Sharing data with other participants in the course is explicitly allowed and encouraged 119 Formalities Printed report of approx 10 pages design choices and reasoning structure of the final solution Must include A diagram of your E R model Schemas of your relations Arguments showing that these are in 3NF Central parts of your SQL code explanation A very short user manual for the application Documentation of testing 120 Milestones There are two stages 1 Tasks 1 3 deadline March 11 Preliminary report describing design choices E R model resul
18. one or many entities of the first set In Pictures VA many one Example Many One Relationship Favorite from Drinkers to Beers is many one A drinker has at most one favorite beer But a beer can be the favorite of any number of drinkers including zero 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 In Pictures yt one one Representing Multiplicity Show a many one relationship by an arrow entering the one side Remember Like a functional dependency 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 Example Many One Relationship Notice two relationships connect the same entity sets but are different 57 Example One One Relationship 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 In the E R Diagram A beer is the best seller for O or 1 manufacturer s A m
19. ting relational model will be commented on and handed back 2 Tasks 4 5 deadline March 25 Final report as correction and extension of the preliminary report Grade for the project will be based both on the preliminary and on the final report Implementation Java with fx JDBC as DB interface Python with fx psycopg2 as DB interface SQL and Java Python code handed in electronically with report in Blackboard Database for testing must be available on the PostgreSQL server Testing during grading will use your program and the data on that server 122
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