Normalization

Boyce-Codd normal form From Wikipedia, the free encyclopedia Boyce-Codd normal form (or BCNF) is a normal form used in database normalization. It is a slightly stronger version of the third normal form (3NF). A table is in Boyce-Codd normal form if and only if, for every one of its non-trivial functional dependencies X → Y, X is a superkey— that is, X is either a candidate key or a superset thereof. BCNF was developed in 1974 by Raymond F. Boyce and Edgar F. Codd to address certain types of anomaly not dealt with by 3NF as originally defined.[1] Chris Date has pointed out that a definition of what we now know as BCNF appeared in a paper by Ian Heath in 1971.[2] Date writes: "Since that definition predated Boyce and Codd's own definition by some three years, it seems to me that BCNF ought by rights to be called Heath normal form. But it isn't."[3] •

3NF tables not meeting BCNF Only in rare cases does a 3NF table not meet the requirements of BCNF. A 3NF table which does not have multiple overlapping candidate keys is guaranteed to be in BCNF. [4] Depending on what its functional dependencies are, a 3NF table with two or more overlapping candidate keys may or may not be in BCNF. An example of a 3NF table that does not meet BCNF is: Today's Court Bookings Court Start Time End Time 1 09:30 10:30 1 11:00 12:00 1 14:00 15:30 2 10:00 11:30 2 11:30 13:30 2 15:00 16:30

Rate Type SAVER SAVER STANDARD PREMIUM-B PREMIUM-B PREMIUM-A

•

Each row in the table represents a court booking at a tennis club that has one hard court (Court 1) and one grass court (Court 2)

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A booking is defined by its Court and the period for which the Court is reserved

•

Additionally, each booking has a Rate Type associated with it. There are four distinct rate types: •

SAVER, for Court 1 bookings made by members

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STANDARD, for Court 1 bookings made by non-members

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PREMIUM-A, for Court 2 bookings made by members

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PREMIUM-B, for Court 2 bookings made by non-members

The table's candidate keys are: •

{Court, Start Time}

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{Court, End Time}

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{Rate Type, Start Time}

•

{Rate Type, End Time}

Recall that 2NF prohibits partial functional dependencies of non-prime attributes on candidate keys, and that 3NF prohibits transitive functional dependencies of non-prime attributes on candidate keys. In the Today's Court Bookings table, there are no non-prime attributes: that is, all attributes belong to candidate keys. Therefore the table adheres to both 2NF and 3NF. The table does not adhere to BCNF. This is because of the dependency Rate Type → Court, in which the determining attribute (Rate Type) is neither a candidate key nor a superset of a candidate key. Any table that falls short of BCNF will be vulnerable to logical inconsistencies. In this example, enforcing the candidate keys will not ensure that the dependency Rate Type → Court is respected. There is, for instance, nothing to stop us from assigning a PREMIUM A Rate Type to a Court 1 booking as well as a Court 2 booking—a clear contradiction, as a Rate Type should only ever apply to a single Court. The design can be amended so that it meets BCNF: Rate Types Rate Type SAVER STANDARD PREMIUMA PREMIUMB

Court 1 1 2 2

Today's Bookings Court Start Time 1 09:30 1 11:00 1 14:00 2 10:00 2 11:30 2 15:00

The candidate keys for the Rate Types table are {Rate Type} and {Court, Member Flag}; the candidate keys for the Today's Bookings table are {Court, Start Time} and {Court, End Time}. Both tables are in BCNF. Having one Rate Type associated with two different Courts is now impossible, so the anomaly affecting the original table has been eliminated.

Achievability of BCNF In some cases, a non-BCNF table cannot be decomposed into tables that satisfy BCNF and preserve the dependencies that held in the original table. Beeri and Bernstein showed in 1979

that, for example, a set of functional dependencies {AB → C, C → B} cannot be represented by a BCNF schema.[5] Thus, unlike the first three normal forms, BCNF is not always achievable. Consider the following non-BCNF table whose functional dependencies follow the {AB → C, C → B} pattern: Nearest Shops P S Ne ers hop are on Typ st e Sho p Da Opti E vid cian agl son e Eye Da Hair S vid dres nip son ser pets W B Me righ ooks rlin t hop Bo oks Full B Do er aker ugh y y's Full Hair Sw er dres een ser ey Tod d's Full Opti E er cian agl e Eye For each Person / Shop Type combination, the table tells us which shop of this type is geographically nearest to the person's home. The candidate keys of the table are: •

{Person, Shop Type}

•

{Person, Nearest Shop}

Because all three attributes are prime attributes (i.e. belong to candidate keys), the table is in 3NF. The table is not in BCNF, however, as the Shop Type attribute is functionally dependent on a non-superkey: Nearest Shop.

The violation of BCNF means that the table is subject to anomalies. For example, Eagle Eye might have its Shop Type changed to "Optometrist" on its "Fuller" record while retaining the Shop Type "Optician" on its "Davidson" record. This would imply contradictory answers to the question: "What is Eagle Eye's Shop Type?" Holding each shop's Shop Type only once would seem preferable, as doing so would prevent such anomalies from occurring: Shop Near Person Person Shop Davidson Eagle Eye Davidson Snippets Wright Merlin Books Fuller Doughy' s Fuller Sweeney Todd's Fuller Eagle Eye

Shop Shop Eagle Eye Snippets Merlin Books Doughy' s Sweeney Todd's

Shop Type Optician Hairdresser Bookshop Bakery Hairdresser

In this revised design, the "Shop Near Person" table has a candidate key of {Person, Shop}, and the "Shop" table has a candidate key of {Shop}. Unfortunately, although this design adheres to BCNF, it is unacceptable on different grounds: it allows us to record multiple shops of the same type against the same person. In other words, its candidate keys do not guarantee that the functional dependency {Person, Shop Type} → {Shop} will be respected. A design that eliminates all of these anomalies (but does not conform to BCNF) is possible. [6] This design consists of the original "Nearest Shops" table supplemented by the "Shop" table described above. Shop Nearest Shops Shop Person Shop Type Nearest Eagle Shop Eye Davidson Optician Eagle Snippets EyeMerlin Davidson Hairdresser Snippets Books Wright Bookshop Merlin Doughy' Books s Fuller Bakery Doughy' Sweeney s Todd's Fuller Hairdresser Sweeney Todd's Fuller Optician Eagle Eye

Shop Type Optician Hairdresser Bookshop Bakery Hairdresser

If a referential integrity constraint is defined to the effect that {Shop Type, Nearest Shop} from the first table must refer to a {Shop Type, Shop} from the second table, then the data anomalies described previously are prevented. Fourth normal form (4NF) is a normal form used in database normalization. Introduced by Ronald Fagin in 1977, 4NF is the next level of normalization after Boyce-Codd normal form (BCNF). Whereas the second, third, and Boyce-Codd normal forms are concerned with functional dependencies, 4NF is concerned with a more general type of dependency known as a multivalued dependency. A table is in 4NF if and only if, for every one of its non-trivial multivalued dependencies X →→ Y, X is a superkey—that is, X is either a candidate key or a superset thereof.[1] •

Multitivalued dependencies If the column headings in a relational database table are divided into three disjoint groupings X, Y, and Z, then, in the context of a particular row, we can refer to the data beneath each group of headings as x, y, and z respectively. A multivalued dependency X →→ Y signifies that if we choose any x actually occurring in the table (call this choice xc), and compile a list of all the xcyz combinations that occur in the table, we will find that xc is associated with the same y entries regardless of z. A trivial multivalued dependency X →→ Y is one in which Y consists of all columns not belonging to X. That is, a subset of attributes in a table has a trivial multivalued dependency on the remaining subset of attributes. A functional dependency is a special case of multivalued dependency. In a functional dependency X → Y, every x determines exactly one y, never more than one.

Example Consider the following example: Pizza Delivery Permutations Restaurant Pizza Variety A1 Pizza Thick Crust A1 Pizza Thick Crust A1 Pizza Thick Crust A1 Pizza Stuffed Crust A1 Pizza Stuffed Crust A1 Pizza Stuffed Crust Elite Pizza Thin Crust Elite Pizza Stuffed Crust Vincenzo's Pizza Thick Crust Vincenzo's Pizza Thick Crust Vincenzo's Pizza Thin Crust Vincenzo's Pizza Thin Crust

Delivery Area Springfield Shelbyville Capital City Springfield Shelbyville Capital City Capital City Capital City Springfield Shelbyville Springfield Shelbyville

Each row indicates that a given restaurant can deliver a given variety of pizza to a given area. The table has no non-key attributes because its only key is {Restaurant, Pizza Variety, Delivery Area}. Therefore it meets all normal forms up to BCNF. It does not, however, meet 4NF. The

problem is that the table features two non-trivial multivalued dependencies on the {Restaurant} attribute (which is not a superkey). The dependencies are: •

{Restaurant} →→ {Pizza Variety}

•

{Restaurant} →→ {Delivery Area}

These non-trivial multivalued dependencies on a non-superkey reflect the fact that the varieties of pizza a restaurant offers are independent from the areas to which the restaurant delivers. This state of affairs leads to redundancy in the table: for example, we are told three times that A1 Pizza offers Stuffed Crust, and if A1 Pizza start producing Cheese Crust pizzas then we will need to add multiple rows, one for each of A1 Pizza's delivery areas. There is, moreover, nothing to prevent us from doing this incorrectly: we might add Cheese Crust rows for all but one of A1 Pizza's delivery areas, thereby failing to respect the multivalued dependency {Restaurant} →→ {Pizza Variety}. To eliminate the possibility of these anomalies, we must place the facts about varieties offered into a different table from the facts about delivery areas, yielding two tables that are both in 4NF: Varieties By Restaurant Restaurant Pizza Variety A1 Pizza Thick Crust A1 Pizza Stuffed Crust Elite Pizza Thin Crust Elite Pizza Stuffed Crust Vincenzo's Thick Pizza Crust Vincenzo's Thin Pizza Crust

Delivery Areas By Restaurant Restaurant Delivery Area A1 Pizza Springfield A1 Pizza Shelbyville A1 Pizza Capital City Elite Pizza Capital City Vincenzo's Springfield Pizza Vincenzo's Shelbyville Pizza

In contrast, if the pizza varieties offered by a restaurant sometimes did legitimately vary from one delivery area to another, the original three-column table would satisfy 4NF. Ronald Fagin demonstrated[2] that it is always possible to achieve 4NF. Rissanen's theorem is also applicable on multivalued dependencies.

4NF in practice A 1992 paper by Margaret S. Wu notes that the teaching of database normalization typically stops short of 4NF, perhaps because of a belief that tables violating 4NF (but meeting all lower normal forms) are rarely encountered in business applications. This belief may not be accurate,

however. Wu reports that in a study of forty organizational databases, over 20% contained one or more tables that violated 4NF while meeting all lower normal forms

Fifth normal form From Wikipedia, the free encyclopedia Jump to: navigation, search Fifth normal form (5NF), also known as Project-join normal form (PJ/NF) is a level of database normalization, designed to reduce redundancy in relational databases recording multivalued facts by isolating semantically related multiple relationships. A table is said to be in the 5NF if and only if it is in 4NF and every join dependency in it is implied by the candidate keys. •

Example Consider the following example: Travelling Salesman Product Availability By Brand Travelling Salesman Brand Product Type Jack Schneider Acme Vacuum Cleaner Jack Schneider Acme Breadbox Willy Loman Robusto Pruning Shears Willy Loman Robusto Vacuum Cleaner Willy Loman Robusto Breadbox Willy Loman Robusto Umbrella Stand Louis Ferguson Robusto Vacuum Cleaner Louis Ferguson Robusto Telescope Louis Ferguson Acme Vacuum Cleaner Louis Ferguson Acme Lava Lamp Louis Ferguson Nimbus Tie Rack The table's predicate is: Products of the type designated by Product Type, made by the brand designated by Brand, are available from the travelling salesman designated by Travelling Salesman. In the absence of any rules restricting the valid possible combinations of Travelling Salesman, Brand, and Product Type, the three-attribute table above is necessary in order to model the situation correctly. Suppose, however, that the following rule applies: A Travelling Salesman has certain Brands and certain Product Types in his repertoire. If Brand B is in his repertoire, and Product Type P is in his repertoire, then (assuming Brand B makes Product Type P), the Travelling Salesman must offer products of Product Type P made by Brand B. In that case, it is possible to split the table into three: Product Types Salesman Travelling Salesman

By

Travelling

Product Type

Brands By Salesman Travelling Salesman

Travelling Brand

Product Types By Brand Brand Product Type Acme Vacuum Cleaner

Jack Schneider Jack Schneider Willy Loman Willy Loman Willy Loman Willy Loman Louis Ferguson Louis Ferguson Louis Ferguson Louis Ferguson

Vacuum Cleaner Breadbox Pruning Shears Vacuum Cleaner Breadbox Umbrella Stand Telescope Vacuum Cleaner Lava Lamp Tie Rack

Jack Schneider Willy Loman Louis Ferguson Louis Ferguson Louis Ferguson

Acme Robusto Robusto Acme Nimbus

Acme Breadbox Acme Lava Lamp Robusto Pruning Shears Robusto Vacuum Cleaner Robusto Breadbox Robusto Umbrella Stand Robusto Telescope Nimbus Tie Rack

Note how this setup helps to remove redundancy. Suppose that Jack Schneider starts selling Robusto's products. In the previous setup we would have to add two new entries since Jack Schneider is able to sell two Product Types covered by Robusto: Breadboxes and Vacuum Cleaners. With the new setup we need only add a single entry (in Brands By Travelling Salesman).

Usage Only in rare situations does a 4NF table not conform to 5NF. These are situations in which a complex real-world constraint governing the valid combinations of attribute values in the 4NF table is not implicit in the structure of that table. If such a table is not normalized to 5NF, the burden of maintaining the logical consistency of the data within the table must be carried partly by the application responsible for insertions, deletions, and updates to it; and there is a heightened risk that the data within the table will become inconsistent. In contrast, the 5NF design excludes the possibility of such inconsistencies. Spurious rows in result set may occur unless you re-join ALL of the tables in 5NF.

First normal form From Wikipedia, the free encyclopedia Jump to: navigation, search First normal form (1NF or Minimal Form) is a normal form used in database normalization. A relational database table that adheres to 1NF is one that meets a certain minimum set of criteria. These criteria are basically concerned with ensuring that the table is a faithful representation of a relation[1] and that it is free of repeating groups.[2] The concept of a "repeating group" is, however, understood in different ways by different theorists. As a consequence, there is not universal agreement as to which features would disqualify a table from being in 1NF. Most notably, 1NF as defined by some authors (for example, Ramez Elmasri and Shamkant B. Navathe,[3] following the precedent established by

Edgar F. Codd) excludes relation-valued attributes (tables within tables); whereas 1NF as defined by other authors (for example, Chris Date) permits them.

Contents [hide] •

1 1NF tables as representations of relations

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2 Repeating groups ○

2.1 Example 1: Domains and values

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2.2 Example 2: Repeating groups across columns

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2.3 Example 3: Repeating groups within columns

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2.4 A design that complies with 1NF

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3 Atomicity

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4 Normalization beyond 1NF

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5 Notes and references

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6 See also

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7 Further reading

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8 External links

[edit] 1NF tables as representations of relations According to Date's definition of 1NF, a table is in 1NF if and only if it is "isomorphic to some relation", which means, specifically, that it satisfies the following five conditions: 1. There's no top-to-bottom ordering to the rows. 2. There's no left-to-right ordering to the columns. 3. There are no duplicate rows. 4. Every row-and-column intersection contains exactly one value from the applicable domain (and nothing else). 5. All columns are regular [i.e. rows have no hidden components such as row IDs, object IDs, or hidden timestamps]. —Chris Date, "What First Normal Form Really Means", pp. 127-8[4] Violation of any of these conditions would mean that the table is not strictly relational, and therefore that it is not in 1NF. Examples of tables (or views) that would not meet this definition of 1NF are: •

A table that lacks a unique key. Such a table would be able to accommodate duplicate rows, in violation of condition 3.

•

A view whose definition mandates that results be returned in a particular order, so that the row-ordering is an intrinsic and meaningful aspect of the view. [5] This violates condition 1. The tuples in true relations are not ordered with respect to each other.

•

A table with at least one nullable attribute. A nullable attribute would be in violation of condition 4, which requires every field to contain exactly one value from its column's

domain. It should be noted, however, that this aspect of condition 4 is controversial. It marks an important departure from Codd's original vision of the relational model, which made explicit provision for nulls.[6]

[edit] Repeating groups Date's fourth condition, which expresses "what most people think of as the defining feature of 1NF",[7] is concerned with repeating groups. The following example illustrates how a database design might incorporate repeating groups, in violation of 1NF.

[edit] Example 1: Domains and values Suppose a novice designer wishes to record the names and telephone numbers of customers. He defines a customer table which looks like this: Customer Customer ID 123 456 789

First Name Surname Telephone Number Robert Ingram 555-861-2025 Jane Wright 555-403-1659 Maria Fernandez 555-808-9633

The designer then becomes aware of a requirement to record multiple telephone numbers for some customers. He reasons that the simplest way of doing this is to allow the "Telephone Number" field in any given record to contain more than one value: Customer Customer ID First Name Surname Telephone Number 123 Robert Ingram 555-861-2025 555-403-1659 456 Jane Wright 555-776-4100 789 Maria Fernandez 555-808-9633 Assuming, however, that the Telephone Number column is defined on some Telephone Numberlike domain (e.g. the domain of strings 12 characters in length), the representation above is not in 1NF. 1NF (and, for that matter, the RDBMS) prohibits a field from containing more than one value from its column's domain.

[edit] Example 2: Repeating groups across columns The designer might attempt to get around this restriction by defining multiple Telephone Number columns: Customer Customer ID 123 456 789

First Name Surname Tel. No. 1 Tel. No. 2 Tel. No. 3 Robert Ingram 555-861-2025 Jane Wright 555-403-1659 555-776-4100 Maria Fernandez 555-808-9633

This representation, however, makes use of nullable columns, and therefore does not conform to Date's definition of 1NF. Even if the view is taken that nullable columns are allowed, the design is not in keeping with the spirit of 1NF. Tel. No. 1, Tel. No. 2., and Tel. No. 3. share exactly the same domain and exactly the same meaning; the splitting of Telephone Number into three headings is artificial and causes logical problems. These problems include:

•

Difficulty in querying the table. Answering such questions as "Which customers have telephone number X?" and "Which pairs of customers share a telephone number?" is awkward.

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Inability to enforce uniqueness of Customer-to-Telephone Number links through the RDBMS. Customer 789 might mistakenly be given a Tel. No. 2 value that is exactly the same as her Tel. No. 1 value.

•

Restriction of the number of telephone numbers per customer to three. If a customer with four telephone numbers comes along, we are constrained to record only three and leave the fourth unrecorded. This means that the database design is imposing constraints on the business process, rather than (as should ideally be the case) vice-versa.

[edit] Example 3: Repeating groups within columns The designer might, alternatively, retain the single Telephone Number column but alter its domain, making it a string of sufficient length to accommodate multiple telephone numbers: Customer Customer ID 123 456 789

First Name Surname Telephone Number Robert Ingram 555-861-2025 Jane Wright 555-403-1659, 555-776-4100 Maria Fernandez 555-808-9633

This design is not consistent with 1NF, and presents several design issues. The Telephone Number heading becomes semantically woolly, as it can now represent either a telephone number, a list of telephone numbers, or indeed anything at all. A query such as "Which pairs of customers share a telephone number?" is more difficult to formulate, given the necessity to cater for lists of telephone numbers as well as individual telephone numbers. Meaningful constraints on telephone numbers are also very difficult to define in the RDBMS with this design.

[edit] A design that complies with 1NF A design that is unambiguously in 1NF makes use of two tables: a Customer Name table and a Customer Telephone Number table. Customer Name Customer Number Customer First Surname ID Name Customer 123 Robert Ingram ID 456 Jane Wright 123 789 Maria Fernandez 456 456 789

Telephone Telephone Number 555-8612025 555-4031659 555-7764100 555-8089633

Repeating groups of telephone numbers do not occur in this design. Instead, each Customer-toTelephone Number link appears on its own record.

[edit] Atomicity Some definitions of 1NF, most notably that of Edgar F. Codd, make reference to the concept of atomicity. Codd states that the "values in the domains on which each relation is defined are required to be atomic with respect to the DBMS." [8] Codd defines an atomic value as one that "cannot be decomposed into smaller pieces by the DBMS (excluding certain special functions)."[9] Hugh Darwen and Chris Date have suggested that Codd's concept of an "atomic value" is ambiguous, and that this ambiguity has led to widespread confusion about how 1NF should be understood.[10][11] In particular, the notion of a "value that cannot be decomposed" is problematic, as it would seem to imply that few, if any, data types are atomic: •

A character string would seem not be atomic, as the RDBMS typically provides operators to decompose it into substrings.

•

A date would seem not to be atomic, as the RDBMS typically provides operators to decompose it into day, month, and year components.

•

A fixed-point number would seem not to be atomic, as the RDBMS typically provides operators to decompose it into integer and fractional components.

Date suggests that "the notion of atomicity has no absolute meaning":[12] a value may be considered atomic for some purposes, but may be considered an assemblage of more basic elements for other purposes. If this position is accepted, 1NF cannot be defined with reference to atomicity. Columns of any conceivable data type (from string types and numeric types to array types and table types) are then acceptable in a 1NF table—although perhaps not always desirable. Date argues that relation-valued attributes, by means of which a field within a table can contain a table, are useful in rare cases.[13]

[edit] Normalization beyond 1NF Any table that is in second normal form (2NF) or higher is, by definition, also in 1NF (each normal form has more stringent criteria than its predecessor). On the other hand, a table that is in 1NF may or may not be in 2NF; if it is in 2NF, it may or may not be in 3NF, and so on. Normal forms higher than 1NF are intended to deal with situations in which a table suffers from design problems that may compromise the integrity of the data within it. For example, the following table is in 1NF, but is not in 2NF and therefore is vulnerable to logical inconsistencies: Customer Names and Telephone Numbers Customer ID First Name Surname Telephone Number 123 Robert Ingram 555-861-2025 456 Jane Wright 555-403-1659 456 Jane Wright 555-776-4100 789 Maria Fernandez 555-808-9633 The table's key is {Customer ID, Telephone Number}. If Jane Wright changes her surname by marriage, the change must be applied to two rows. If the change is only applied to one row, a contradiction results: the question "What is Customer 456's name?" has two conflicting answers. 2NF addresses this problem.

Second normal form From Wikipedia, the free encyclopedia Jump to: navigation, search Second normal form (2NF) is a normal form used in database normalization. 2NF was originally defined by E.F. Codd[1] in 1971. A table that is in first normal form (1NF) must meet additional criteria if it is to qualify for second normal form. Specifically: a 1NF table is in 2NF if and only if, given any candidate key and any attribute that is not a constituent of a candidate key, the non-key attribute depends upon the whole of the candidate key rather than just a part of it. In slightly more formal terms: a 1NF table is in 2NF if and only if none of its non-prime attributes are functionally dependent on a part (proper subset) of a candidate key. (A non-prime attribute is one that does not belong to any candidate key.) Note that when a 1NF table has no composite candidate keys (candidate keys consisting of more than one attribute), the table is automatically in 2NF.

Contents [hide] •

1 Example

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2 2NF and candidate keys

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3 References

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4 See also

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5 Further reading

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6 External links

[edit] Example Consider a table describing employees' skills: Employees' Skills Employee Skill Current Work Location Jones Typing 114 Main Street Jones Shorthand 114 Main Street Jones Whittling 114 Main Street Roberts Light Cleaning 73 Industrial Way Ellis Alchemy 73 Industrial Way Ellis Juggling 73 Industrial Way Harrison Light Cleaning 73 Industrial Way The table's only candidate key is {Employee, Skill}.

The remaining attribute, Current Work Location, is dependent on only part of the candidate key, namely Employee. Therefore the table is not in 2NF. Note the redundancy in the way Current Work Locations are represented: we are told three times that Jones works at 114 Main Street, and twice that Ellis works at 73 Industrial Way. This redundancy makes the table vulnerable to update anomalies: it is, for example, possible to update Jones' work location on his "Typing" and "Shorthand" records and not update his "Whittling" record. The resulting data would imply contradictory answers to the question "What is Jones' current work location?" A 2NF alternative to this design would represent the same information in two tables: Employees

Employees' Skills Current Employee Skill Employee Work Jones Typing Location Jones Shorthand 114 Main Jones Whittling Jones Street Light Roberts 73 Cleaning Roberts Industrial Ellis Alchemy Way Ellis Juggling 73 Light Ellis Industrial Harrison Cleaning Way 73 Harrison Industrial Way Update anomalies cannot occur in these tables, which are both in 2NF. Not all 2NF tables are free from update anomalies, however. An example of a 2NF table which suffers from update anomalies is: Tournament Winners Tournament Year Des Moines Masters 1998 Indiana Invitational 1998 Cleveland Open 1999 Des Moines Masters 1999 Indiana Invitational 1999

Winner Winner Date of Birth Chip Masterson 14 March 1977 Al Fredrickson 21 July 1975 Bob Albertson 28 September 1968 Al Fredrickson 21 July 1975 Chip Masterson 14 March 1977

Even though Winner and Winner Date of Birth are determined by the whole key {Tournament, Year} and not part of it, particular Winner / Winner Date of Birth combinations are shown redundantly on multiple records. This problem is addressed by third normal form (3NF).

[edit] 2NF and candidate keys A table for which there are no partial functional dependencies on the primary key is typically, but not always, in 2NF. In addition to the primary key, the table may contain other candidate keys; it is necessary to establish that no non-prime attributes have part-key dependencies on any of these candidate keys.

Multiple candidate keys occur in the following table: Electric Toothbrush Models Manufacturer Model Forte X-Prime Forte Ultraclean Dent-o-Fresh EZBrush Kobayashi ST-60 Hoch Toothmaster Hoch Contender

Model Full Name Manufacturer Country Forte X-Prime Italy Forte Ultraclean Italy Dent-o-Fresh EZBrush USA Kobayashi ST-60 Japan Hoch Toothmaster Germany Hoch Contender Germany

Even if the designer has specified the primary key as {Model Full Name}, the table is not in 2NF. {Manufacturer, Model} is also a candidate key, and Manufacturer Country is dependent on a proper subset of it: Manufacturer.

Third normal form From Wikipedia, the free encyclopedia Jump to: navigation, search

The third normal form (3NF) is a normal form used in database normalization. 3NF was originally defined by E.F. Codd[1] in 1971. Codd's definition states that a table is in 3NF if and only if both of the following conditions hold: •

The relation R (table) is in second normal form (2NF)

•

Every non-prime attribute of R is non-transitively dependent (i.e. directly dependent) on every key of R.

A non-prime attribute of R is an attribute that does not belong to any candidate key of R. [2] A transitive dependency is a functional dependency in which X → Z (X determines Z) indirectly, by virtue of X → Y and Y → Z (where it is not the case that Y → X).[3]

A 3NF definition that is equivalent to Codd's, but expressed differently, was given by Carlo Zaniolo in 1982. This definition states that a table is in 3NF if and only if, for each of its functional dependencies X → A, at least one of the following conditions holds: •

X contains A (that is, X → A is trivial functional dependency), or

•

X is a superkey, or

•

A is a prime attribute (i.e., A is contained within a candidate key)[4]

Zaniolo's definition gives a clear sense of the difference between 3NF and the more stringent Boyce-Codd normal form (BCNF). BCNF simply eliminates the third alternative ("A is a prime attribute").

[edit] "Nothing but the key" A memorable summary of Codd's definition of 3NF, paralleling the traditional pledge to give true evidence in a court of law, was given by Bill Kent: every non-key attribute "must provide a fact about the key, the whole key, and nothing but the key."[5] A common variation supplements this definition with the oath: "so help me Codd".[6] Requiring that non-key attributes be dependent on "the whole key" ensures that a table is in 2NF; further requiring that non-key attributes be dependent on "nothing but the key" ensures that the table is in 3NF. Chris Date refers to Kent's summary as "an intuitively attractive characterization" of 3NF, and notes that with slight adaptation it may serve as a definition of the slightly-stronger Boyce-Codd normal form: "Each attribute must represent a fact about the key, the whole key, and nothing but the key."[7] Here the requirement is concerned with every attribute in the table, not just non-key attributes.

[edit] Example An example of a 2NF table that fails to meet the requirements of 3NF is: Tournament Winners Tournament Year Indiana Invitational 1998 Cleveland Open 1999 Des Moines Masters 1999 Indiana Invitational 1999

Winner Winner Date of Birth Al Fredrickson 21 July 1975 Bob Albertson 28 September 1968 Al Fredrickson 21 July 1975 Chip Masterson 14 March 1977

The only candidate key is {Tournament, Year}. The breach of 3NF occurs because the non-prime attribute Winner Date of Birth is transitively dependent on {Tournament, Year} via the non-prime attribute Winner. The fact that Winner Date of Birth is functionally dependent on Winner makes the table vulnerable to logical inconsistencies, as there is nothing to stop the same person from being shown with different dates of birth on different records. In order to express the same facts without violating 3NF, it is necessary to split the table into two: Tournament Winners

Player Dates of Birth Player Date of

Tournament Year Indiana 1998 Invitational Cleveland 1999 Open Des Moines 1999 Masters Indiana 1999 Invitational

Winner Al Fredrickson Bob Albertson Al Fredrickson Chip Masterson

Birth Chip 14 March Masterson 1977 Al 21 July Fredrickson 1975 28 Bob September Albertson 1968

Update anomalies cannot occur in these tables, which are both in 3NF.

[edit] Derivation of Zaniolo's conditions A lemma proved by Zaniolo states that a table is in 3NF if and only if, for each of its functional dependencies X → A, at least one of the following conditions holds: •

X contains A, or

•

X is a superkey, or

•

A is a prime attribute (i.e., A is contained within a candidate key)

The lemma is proved in the following way: Let X → A be a nontrivial FD (i.e. one where X does not contain A) and let A be a non-key attribute. Also let Y be a key of R. Then Y → X. Therefore A is not transitively dependent on Y if and only if X → Y, that is, if and only if X is a superkey.[8]

[edit] Normalization beyond 3NF Most 3NF tables are free of update, insertion, and deletion anomalies. Certain types of 3NF tables, rarely met with in practice, are affected by such anomalies; these are tables which either fall short of Boyce-Codd normal form (BCNF) or, if they meet BCNF, fall short of the higher normal forms 4NF or 5NF.