Assignment 1: Entity-Relationship Model Solution

Transcription

1 Data odelling and Databases Exercise dates: arch /arch 2, 208 Ce Zhang, Gustavo Alonso Last update: arch 08, 208 Spring Semester 208 Head TA: Ingo üller Assignment : Entity-Relationship odel Solution This assignment will be discussed during the exercise slots indicated above. If you want feedback for your copy, hand it in during the lecture on the Wednesday before (preferably stapled and with your address). You can also annotate your copy with questions you think should be discussed during the exercise session. If you have questions that are not answered by the solution we provide, send them to Ingo (ingo.mueller@inf.ethz.ch). Understanding Entity-Relationship odels Consider the following entity-relationship (ER) model. passport number person has address name is_a man father mother woman father son daughter mother isson isdaughter For each of the following groups of statements, pick the one that coincides best with the model.

2 . A. Each person has at least one address. B. Each person has at most one address. C. Each person has exactly one address. D. one of the above is true. Explanation: A relation, even of type :, optionally connects entities. If it is weak, only the weak entity needs to participate in such a relation. Since person is not the weak entity here, a person may not have an address. However, due to the cardinalities, each person may have at most one address. 2. A. Each address belongs to at least one person. B. Each address belongs to at most one person. C. Each address belongs to exactly one person. D. one of the above is true. Explanation: The entity is the weak entity of the has relationship, so it must participate in this relationship. Furthermore, the cardinalities restrict it to participate at most once (as with any weak entity). 3. A. Each person has at least one passport number. B. Each person has at most one passport number. C. Each person has exactly one passport number. D. one of the above is true. Explanation: Each entity has exactly one value for each attribute. 4. A. Each man has at least one father. B. Each man has at most one father. C. Each man has exactly one father. D. one of the above is true. Explanation: Entities may or may not participate in relationships, so a man may not have a father. Furthermore, the same man entity can participate several times as son in the isson relationship as long as it is with a different father and a different mother. This is because the :: cardinality of the isson relationship only limits the number of man entities in the role of father to, given a man entity in the son role and a woman entity.

3 For each of the following statements, say whether it is true or false in the model. 5. Each passport number belongs to at most one person. True False Explanation: Passport number is the key of the person entity, so each passport number is unique and used only by one person. 6. There are no two persons with the same name. True False Explanation: ame is not a key of the person entity, so it s values are not restricted and can occur multiple times. 7. Each person who is not a man is a woman. True False Explanation: In this ER model, a person can be neither a man nor a woman. general, there may be entities of the general entity type of a generalization. In 8. Each person who is a man is not a woman. True False Explanation: In this ER model, a person can be both a man and a woman at the same time. In general, an entity of the general entity type of a generalization may also be an entity of multiple different specializations. In other words, the definition of generalization in ER says that the set of entities of each special type (here: man and woman ) is a subset of the entities of the general type (here: person ), but it does not say anything about whether the subset of the special types overlap or not. (It also does not require that each entity of the general type is an entity of one of the special types.) 9. Each woman is a person. True False Explanation: By definition of is-a. 0. A man can be his own father. True False Explanation: There is no constraint that prevents the same man entity to participate both in the man role and in the son role in the isson relationship.. If a woman has a father, she also has a mother. True False Explanation: In an isdaughter relationship, there is always exactly one woman entity in the mother role, one woman entity in the daughter role, and one man entity in the father role.

4 2. Each man is a father. True False Explanation: A man entity may or may not participate in the isson relationship (in either role). 3. Each father is a man. True False Explanation: Only man entities can take the father role of the isson relationship. 4. Each son is a man. True False Explanation: Only man entities can take the son role of the isson relationship. 5. Each woman has at least one daughter. True False Explanation: A woman entity may or may not participate in the isdaughter relationship (in either role). 6. Each woman has at most one daughter. True False Explanation: The :: relationship allows a woman entity arbitrarily many participations in the mother role, for example each time with a different woman entity in the daughter role (or with the same daughter, but a different father). 2 Cardinalities in in/ax otation Consider the following ER model where the two notations of cardinalities from the lecture are superposed: F and F 2 represent numbers in the notation of cardinalities whereas (min i, max i ) follows the (min, max) notation. F E R E 2 (min, max ) (min 2, max 2 ) F 2 For the given cardinality in the form F : F 2, give the equivalent cardinality in the min/max notation by completing the following table.

5 F : F 2 (min, max ) (min 2, max 2 ) : (0, ) (0, ) : (0, ) (0, ) : (0, ) (0, ) : (0, ) (0, ) Explanation: This table makes it clear that the two notations have to be read the opposite way. Let us look closely at what the means in the case of :. In the notation of the cardinalities, it means that there is one E for each entity E 2. We write the on the side of E (and not on the side of E 2 ). This is because, in relationships with more than two entities, a means that there is one E for each set of the other entities (see discussion of next question). In order to express the in the min/max notation, we can only limit the number of occurences of each entity in isolation. In the example of the exercise, we have to say that E 2 can occur at most once, which implies the fact that there can be at most one E for that E 2. This is written as (min 2, max 2 ) = (0, ) on the side of E 2 (since it is the entity we put the limit on). Can you establish such an equivalence for ternary relationships? Solution: o, you cannot. Consider the seminar example from the lecture: the entity types student, professor, and topic are in a :: relationship supervise. The for the topic entity type means that, given an entity of type professor and an entity of type student, there is at most one entity of type topic (i.e., a student can only take one topic with a professor). You may be tempted to express this as (0, ) in the min/max notation, which would mean that each topic can be supervised at most once. However, in the :: relationship supervise, each topic entity may participate several times just not with the same student. In the min/max notation, there is no way to epxress a :: relationship exactly. At the same time, other situations may only be expressable using the min/max notation, so we may need both depending on what we want to do. 3 Cardinalities on Ternary Relationships Consider the following entity-relationship (ER) model, where the cardinalities of relationship R are given as variables A, B, and C. For example, if A = B = C =, then R is a :: relationship.

6 A A B B R C C The table below shows entities of type A, B, and C respectively that are connected through relationship R. For example, the first tuple m, o, x indicates that entity m of type A, entity o of type B, and entity x of type C are connected through R. We are now interested in the question which are valid sets of tuples for R with different cardinalities A, B, and C. For each assignment of cardinalities in the table, select a maximal subset of tuples that form a valid set R. Select a tuple by adding a checkmark ( ) to the corresponding cell. If a tuple cannot be in R, write down the number of the tuple with which it conflicts. For example, if R is a :: relationship and n of type A, o of type B, and z of type C participate together in R (this is Tuple 2), then no other entity of type B can participate in R together with n and z. In particular, Tuple 4 ( n, p, z ) cannot be in R as well, so it conflicts with Tuple 2. tuple number tuple A B C A, B, C R for given cardinality? A = B = C = O A = B = C = A = B = C = A = B = C = m o x 2 n o z 3 m q y 4 n p z n o x 6 m q z 3

7 Explanation: We fill the table column by column: A =, B =, C = O: If we take two entities out of the three entity types A, B, or C, there can be tuples in R with these two entities. This means that any set of tuples is allowed for R (but it must be a set), so we select all tuples. A =, B =, C = : For any two entities of types B and C respectively, there may only be a single entity of type A; and there are no other constraints. However, entity o of type B and entity x of type C participate in R with entities m and n of type A, so we can only select one of the two (we select tuple ). A =, B =, C = : We have the same constraint on entities of type A as before, so we can only select the tuples that we selected previously. Additionally, for any two entities of types A and C respectively, there may only be a single entity of type B. Since entity n of type A and entity z of type C participate in R with entities o and p of type B, we can only select one of them (we select tuple 2). A =, B =, C = : We have the same constraint on entities of types A and B as before, so we can only select the tuples that we selected previously. Additionally, for any two entities of types A and B respectively, there may only be a single entity of type C. Since entity m of type A and entity q of type B participate in R with entities y and z of type C, we can only select one of them (we select tuple 3). 4 odelling ini-worlds: Getting Started odel the following relationships in ER.. An apartment is located in a house in a street in a city in a country. Example solution: Apartement Copy Located Availablein House Copy Located Availablein Country Located Availablein Copy City Located Availablein Street Copy

8 Several variants are possible. Above solutions expresses constraints not given in the exercise description, which we know because we are domain experts of this miniworld: We assume that an appartment cannot exist without a house, a house must be located in a street, etc. The model expresses these constraints by making the locatedin relationships weak. Whether or not this is actually the case in the real world is debatable and ER does not provide an answer to this debate. Instead, this kind of knowledge must be provided by domain experts. However, as formal representation of the real world, the resulting ER model is unambiguous. The question does not explicitly say that a house is in a street, a street in a city, and a city in a country. It is thus possible to make all of them attributes of apartment. However, it is not possible make all of them entities and connect them with a big relationship. That model would allow the same apartment to be in two houses as long as the two house are in different streets, cities, or countries. 2. Two teams play football against each other. A referee makes sure the rules are followed. Example solution: Home Team Plays Referee Away Again, many variants are possible. Some models represents certain aspects better than others and there may be no model that represents all of them perfectly. Above solution has the property that it allows a pair of teams to play at most twice: each team once as Home and once as Away team. This would be appropriate for modelling a single season. If we turn the Plays relationship, which is now ::, into a ::K relationship, then a pair of teams can play several times, but only if they change their referee, which may or may not be what we want. Home Team Plays Referee Away Alternatively, we can demote Referee to an attribute, which is very similar to the first solution, but cannot model other aspects of referees.

9 One problem that both solutions have is the fact that the same team can be in the Home role and in the Away role at the same time. Some solutions that are wrong: Two different entities for Team A and Team B : This would imply that the home teams and the away teams are fundamentally different from each other always, not just during a match. Rules as entity or attribute: there are no instances or values of rules, which could potentially be different from one game to the other. A Game entity connected twice with Team : This would mean that many different pairs of teams can play (pairwise) in the same game, which clearly conflicts with reality. 5 ini-world: International Wholesale Supplier odel the following mini-world of an international wholesale supplier in ER. Identify the keys and give the cardinalities of all relationships (e.g., :, :, :) The wholesale supplier has customers that place orders, which are placed on a particular date and have a total price, current status, and an order number (starting from for each customer). In each order, a customer can order several parts (products), each in a different quantity and at a (possibly discounted) price. We also want to model the date on which each of the parts has been sent. The parts are provided by suppliers. Each part may be provided by several suppliers and customers may order the same part of different suppliers in the same order, but in this case, they may have different (retail) prices. Customers and suppliers have a name, an address, a phone number, and a customer/supplier number and they come from a certain nation, which in turn is from a particular region (of the world). Parts have a brand, a size, and a retail price. Solution:

10 address id status date name phone customer places order is from number price quantity name region nation consists of price shipdate is from phone name supplier O provides part price size address id id brand In order to satisfy the requirement that order numers should [start] from for each customer, order must be weak with respect to customer and order number a subkey of order. Weak entity setss do not have an independent key; they inherit the key of their strong entity set and their subkey only identifies weak entities of the same strong entity. It is possible to model customer and supplier as generalizations of person, which has attributes address, name, phone, and id and is connected to nation. consists of may only connect order and part. In this case, the meaning of part must be part from supplier ABC, which means that, for example, iphone X provided by supplier A is different from iphone X provided by supplier B. This is somewhat less elegant. parts must have this meaning because, otherwise, the following statement would not be modelled correctly: Each part may be provided by several suppliers and customers may order the same part of different suppliers in the same order, but in this case, they may have different (retail) prices. It is possible, though less ideal, to model part as lineitem (item on the bill). In this case, quantity and price are attributes of part and part is in a : relationship with order.

11 6 ini-world: Entity-Relationship odel odel ER in ER. Solution: Weak Entity is-a Attribute of Copy Entity Available Has Entity ame Cardinality ame IsPartOfKey Cardinality Role Participate Available Participate Role in in ax ame ax Attribute of Copy Relationship Available Has Relationship ame is-a Relationship of Copy Weak Entity A few aspects are not perfectly expressed in this model: Relationship entities can only exist if they are connected to at least two Entity entities. This is like being weak with respect to two entities. However, as seen in the lecture, weak entities are weak with respect to one entity. Our model thus allows to have dangling relationships. In ER, relationships of weak entity types can only be : or :. In particular, they are binary. Our model does not impose any of these restrictions on Relationship of Weak Entity entities. In ER, for each relationship, the role names of the participating entity types are unique. Our model does not impose this restriction. In ER, an entity can participate several times in the same relationship through different roles. In our model, the Participate relationship allows each Entity entity to be connected to a particular Relationship entity only once.

12 Our model does not express generalizations ( is-a ) and aggregations ( part-of ). Common mistakes: A ternary relationship between the entity Entity, which participates twice (as Entity A and Entity B ), and the entity Relationship : This means that there can only be binary relationships (which is ironic you used a ternary relationship to express that!). A binary relationship between the entity Entity participating as Entity A and Entity B without entity for Relationship : Same problem, plus attributes of relationships are not expressed. Attribute as weak entity with respect to both Entity and Relationship : This does not exist a weak enity is weak with respect to exactly one strong entity. 7 ini-world: Olympics Olympic games happen in a certain year at a certain place. Each year, there is at most one instance of Olympic games. In each discipline of an olympic game, there is exactly one gold medalist, one silver medalist, and one bronze medalist. All these medalists are athletes. Give an ER model for this mini-world. Identify the keys and give the cardinalities of all relationships. Solution:

13 Year Place ame Discipline Game won-gold Athlete Same relationship for: won-silver won-bronze Some remarks: ote that if the key of Game would be based on year and place, the requirement that there is at most one event per year would be violated. The way the medalists are modeled is by creating three ternary relationships for Gold, Silver, and Bronze medals each (from which we pictured only one). While this solution fulfills the requirements, it also allows for the same athlete to win three medals in the same discipline. Can you find a more elegant solution without losing any constraints? It is not correct to have a single relation wins where athlete participates three times in the roles gold, silver, and bronze, as well as discipline. The problem is that for the same discipline we can only limit the number of athletes winning gold to one given the discipline and the athletes for silver and bronze. This means that several athletes could win gold in the same discipline. It is possible to interprete discipline as competition, i.e., discipline this year. In this case, 00m Sprint 206 would be a different discipline than 00m Sprint 202. In this case, discipline would be in a : relationship with Game and in one : relationship with Athlete per medal kind (gold, silver, bronze). If Year is modelled as entity, Game should be a weak entity with respect to Year as, otherwise, there could be a game without year.

14 8 ini-world: Travelling Consider the following mini-world. A person has a name and an age. Cities have a name and are located in a country. Every year, persons can form groups in order to travel together to a city. A person may be part of the same or a different group in different years, but may be part of at most one group in any given year. Furthermore, a group travels to the same or different city in different years, but travels to exactly one city in any given year. Give an ER model for this mini-world. Identify the keys and give the cardinalities of all relationships (e.g., :, :, :). Solution: ame Person Group Country Age Belongs-to Is-in Year Travels-to Copy City ame ote that Group, Year, and Country have a single attribute name that is their primary key. This has been omitted from the figure for simplicity. Also note that the model makes the following compromise: On the one hand side, it limits the number of groups each person can belong to in a given year by making Year a separate entity type and using cardinalities for belongs-to. On the other side, it does not model the fact that each group travels to exactly one city in any given year. We could model exactly one with the min/max notation, but then the constraint above (a person can belong to at most one group per year) could not be enforced anymore. It is not correct to have a cardinality of next to Year for either Belongs-to or Travelsto. The first would mean that a person can belong to a group only for one year, which contradicts A person may be part of the same [... ] group in different years. The second would mean that a group can travel to a city only during one year, which contradicts a group travels to [a] different city in different years. It is also not correct to connect Year, Group, City, and Person with one big Travel relationship, as this would allow a person to travel with several groups each year, provided they travel to different cities.

15 9 ini-world: Library System Assume there is a library system with the following properties. The library contains one or several copies of the same book. Every copy of a book has a copy number and is located at a specific location in a shelf. A copy is identified by the copy number and the ISB number of the book. Every book has a unique ISB, a publication year, a title, an author, and a number of pages. Books are published by publishers. A publisher has a name as well as a location. Within the library system, books are assigned to one or several categories. A category can be a subcategory of exactly one other category. A category has a name and no further properties. Each reader needs to provide his/her family name, his/her first name, his/her city, and his/her date of birth to register at the library. Each reader gets a unique reader number. Readers borrow copies of books. Upon borrowing the return date is stored. Create an ER diagram of this library system. Solution: Familyame Readerr ReturnDate Shelf Position Firstname Reader Borrows Copy Copyr City Birthdate Available Parent Catname ISB Contains Category InCat Book PubYear Sub Title Publisher Publishes umpages Author Pubname Pubcity

16 Alternative solutions: Borrows as entity (what is the key of this entity?) Author as its own entity Shelf as its own entity Publishes relationship as : (books are published by several publishers) Borrows as : (a copy can be borrowed only once). Then we model Borrows as Borrows currently instead of Has borrowed at some point. Both solutions are correct interpreations of the text, but model something slightly different.