2 primary keys in a table - database

Making a primary key in a table in database is fine. Making a Composite Primary is also fine. But why cant I have 2 primary keys in a table? What kind of problems may occur if we have 2 primary keys.
Suppose I have a Students table. I don't want Roll No. and Names of each student to be unique. Then why can't I create 2 primary keys in a table? I don't see any logical problem in it now. But definitely I am missing a serious issue that's the reason it does not exist.
I am new in databases, so don't have much idea. It may also create a technical issue rather. Will be happy if someone can educate me on this.
Thanks.

You can create a UNIQUE constraint for both columns UNIQUE(roll,name).

The PK is unique by definition, cause it is used to identify a row from the others, for example, when a foreign key references that table, it is referencing the PK.
If you need another column to 'act' like a PK, give it the attributes unique and not null.

Well, this is simply by definition. There can not be two "primary" conditions, just like there can not be two "latest" versions.
Every table can contain more than one unique keys, but if you decide to have a primary key, this is just one of these unique keys, the "one" you deem the "most important", which identifies every record uniquely.
If you have a table and come to the conclusion that your primary key does not uniquely identify each record (also meaning that there can't be two records with the same values for the primary key), you have chosen the wrong primary key, as by definition, the fields of the primary key must uniquely define each record.
That, however, does not mean there can be no other combination of fields uniquely identifying the record! This is where a second feature kicks in: referential integrity.
You can "link" tables using their primary key. For example: If you have a Customer table and an Orders table, where the Customers table has a primary key on the customer number and the Orders table has a primary key on the order number and the customer number, that means:
Every customer can be identified uniquely by his customer number
Every order is uniquely identified by the order number and the customer number
You can then link the two tables on the customer number. The DB system then ensures several things, among which is the fact that you can not remove a customer who has orders in your database without first removing the orders. Otherwise, you would have orders without being able to find out the customer data, which would violate your database's referential integrity.
If you had two primary keys, the system would not know on which to ensure referential integrity, so you'd have to tell the system which key to use - which would make one of the primary keys more important, which would make it the "primary key" (!) of the primary keys.

You can have multiple candidate keys in a table but by convention only one key per table is called "primary". That's just a convention though and it doesn't make any real difference to the function of the keys. A primary key is no different to any other candidate key. If you find it convenient to call more than one key "primary" then I suggest you do so. In my opinion (I'm not the only one) the idea of designating a "primary" key at all is essentially an outdated concept of very little importance in database design.
You might be interested to know that early papers on the relational database model (e.g. by E.F.Codd, the relational model's inventor) actually used the term "primary key" to describe all the keys of a relation and not just one. So there is a perfectly good precedent for multiple primary keys per table. The idea of designating exactly one primary key is more recent and probably came into common use through the popularity of ER modelling techniques.

Create an unique index on the 2nd attribute (Names), it's almost the same as primary key with another name.
From Wikipedia (http://en.wikipedia.org/wiki/Unique_key):
A table can have at most one primary key, but more than one unique
key. A primary key is a combination of columns which uniquely specify
a row. It is a special case of unique keys. One difference is that
primary keys have an implicit NOT NULL constraint while unique keys do
not. Thus, the values in unique key columns may or may not be NULL,
and in fact such a column may contain at most one NULL fields.
Another difference is that primary keys must be defined using another
syntax.

Related

Why does my database table need a primary key?

In my database I have a list of users with information about them, and I also have a feature which allows a user to add other users to a shortlist. My user information is stored in one table with a primary key of the user id, and I have another table for the shortlist. The shortlist table is designed so that it has two columns and is basically just a list of pairs of names. So to find the shortlist for a particular user you retrieve all names from the second column where the id in the first column is a particular value.
The issue is that according to many sources such as this Should each and every table have a primary key? you should have a primary key in every table of the database.
According to this source http://www.w3schools.com/sql/sql_primarykey.asp - a primary key in one which uniquely identifies an entry in a database. So my question is:
What is wrong with the table in my database? Why does it need a primary key?
How should I give it a primary key? Just create a new auto-incrementing column so that each entry has a unique id? There doesn't seem much point for this. Or would I somehow encapsulate the multiple entries that represent a shortlist into another entity in another table and link that in? I'm really confused.
If the rows are unique, you can have a two-column primary key, although maybe that's database dependent. Here's an example:
CREATE TABLE my_table
(
col_1 int NOT NULL,
col_2 varchar(255) NOT NULL,
CONSTRAINT pk_cols12 PRIMARY KEY (col_1,col_2)
)
If you already have the table, the example would be:
ALTER TABLE my_table
ADD CONSTRAINT pk_cols12 PRIMARY KEY (col_1,col_2)
Primary keys must identify each record uniquely and as it was mentioned before, primary keys can consist of multiple attributes (1 or more columns). First, I'd recommend making sure each record is really unique in your table. Secondly, as I understand you left the table without primary key and that's disallowed so yes, you will need to set the key for it.
In this particular case, there is no purpose in same pair of user IDs being stored more than once in the shortlist table. After all, that table models a set, and an element is either in the set or isn't. Having an element "twice" in the set makes no sense1. To prevent that, create a composite key, consisting of these two user ID fields.
Whether this composite key will also be primary, or you'll have another key (that would act as surrogate primary key) is another matter, but either way you'll need this composite key.
Please note that under databases that support clustering (aka. index-organized tables), PK is often also a clustering key, which may have significant repercussions on performance.
1 Unlike in mutiset.
A table with duplicate rows is not an adequate representation of a relation. It's a bag of rows, not a set of rows. If you let this happen, you'll eventually find that your counts will be off, your sums will be off, and your averages will be off. In short, you'll get confusing errors out of your data when you go to use it.
Declaring a primary key is a convenient way of preventing duplicate rows from getting into the database, even if one of the application programs makes a mistake. The index you obtain is a side effect.
Foreign key references to a single row in a table could be made by referencing any candidate key. However, it's much more convenient if you declare one of those candidate keys as a primary key, and then make all foreign key references refer to the primary key. It's just careful data management.
The one-to-one correspondence between entities in the real world and corresponding rows in the table for that entity is beyond the realm of the DBMS. It's up to your applications and even your data providers to maintain that correspondence by not inventing new rows for existing entities and not letting some new entities slip through the cracks.
Well since you are asking, it's good practice but in a few instances (no joins needed to the data) it may not be absolutely required. The biggest problem though is you never really know if requirements will change and so you really want one now so you aren't adding one to a 10m record table after the fact.....
In addition to a primary key (which can span multiple columns btw) I think it is good practice to have a secondary candidate key which is a single field. This makes joins easier.
First some theory. You may remember the definition of a function from HS or college algebra is that y = f(x) where f is a function if and only if for every x there is exactly one y. In this case, in relational math we would say that y is functionally dependent on x on this case.
The same is true of your data. Suppose we are storing check numbers, checking account numbers, and amounts. Assuming that we may have several checking accounts and that for each checking account duplicate check numbers are not allowed, then amount is functionally dependent on (account, check_number). In general you want to store data together which is functionally dependent on the same thing, with no transitive dependencies. A primary key will typically be the functional dependency you specify as the primary one. This then identifies the rest of the data in the row (because it is tied to that identifier). Think of this as the natural primary key. Where possible (i.e. not using MySQL) I like to declare the primary key to be the natural one, even if it spans across columns. This gets complicated sometimes where you may have multiple interchangeable candidate keys. For example, consider:
CREATE TABLE country (
id serial not null unique,
name text primary key,
short_name text not null unique
);
This table really could have any column be the primary key. All three are perfectly acceptable candidate keys. Suppose we have a country record (232, 'United States', 'US'). Each of these fields uniquely identifies the record so if we know one we can know the others. Each one could be defined as the primary key.
I also recommend having a second, artificial candidate key which is just a machine identifier used for linking for joins. In the above example country.id does this. This can be useful for linking other records to the country table.
An exception to needing a candidate key might be where duplicate records really are possible. For example, suppose we are tracking invoices. We may have a case where someone is invoiced independently for two items with one showing on each of two line items. These could be identical. In this case you probably want to add an artificial primary key because it allows you to join things to that record later. You might not have a need to do so now but you may in the future!
Create a composite primary key.
To read more about what a composite primary key is, visit
http://www.relationaldbdesign.com/relational-database-analysis/module2/concatenated-primary-keys.php

Is it fine to have foreign key as primary key?

I have two tables:
User (username, password)
Profile (profileId, gender, dateofbirth, ...)
Currently I'm using this approach: each Profile record has a field named "userId" as foreign key which links to the User table. When a user registers, his Profile record is automatically created.
I'm confused with my friend suggestion: to have the "userId" field as the foreign and primary key and delete the "profileId" field. Which approach is better?
Foreign keys are almost always "Allow Duplicates," which would make them unsuitable as Primary Keys.
Instead, find a field that uniquely identifies each record in the table, or add a new field (either an auto-incrementing integer or a GUID) to act as the primary key.
The only exception to this are tables with a one-to-one relationship, where the foreign key and primary key of the linked table are one and the same.
Primary keys always need to be unique, foreign keys need to allow non-unique values if the table is a one-to-many relationship. It is perfectly fine to use a foreign key as the primary key if the table is connected by a one-to-one relationship, not a one-to-many relationship. If you want the same user record to have the possibility of having more than 1 related profile record, go with a separate primary key, otherwise stick with what you have.
Yes, it is legal to have a primary key being a foreign key. This is a rare construct, but it applies for:
a 1:1 relation. The two tables cannot be merged in one because of different permissions and privileges only apply at table level (as of 2017, such a database would be odd).
a 1:0..1 relation. Profile may or may not exist, depending on the user type.
performance is an issue, and the design acts as a partition: the profile table is rarely accessed, hosted on a separate disk or has a different sharding policy as compared to the users table. Would not make sense if the underlining storage is columnar.
Yes, a foreign key can be a primary key in the case of one to one relationship between those tables
I would not do that. I would keep the profileID as primary key of the table Profile
A foreign key is just a referential constraint between two tables
One could argue that a primary key is necessary as the target of any foreign keys which refer to it from other tables. A foreign key is a set of one or more columns in any table (not necessarily a candidate key, let alone the primary key, of that table) which may hold the value(s) found in the primary key column(s) of some other table. So we must have a primary key to match the foreign key.
Or must we? The only purpose of the primary key in the primary key/foreign key pair is to provide an unambiguous join - to maintain referential integrity with respect to the "foreign" table which holds the referenced primary key. This insures that the value to which the foreign key refers will always be valid (or null, if allowed).
http://www.aisintl.com/case/primary_and_foreign_key.html
It is generally considered bad practise to have a one to one relationship. This is because you could just have the data represented in one table and achieve the same result.
However, there are instances where you may not be able to make these changes to the table you are referencing. In this instance there is no problem using the Foreign key as the primary key. It might help to have a composite key consisting of an auto incrementing unique primary key and the foreign key.
I am currently working on a system where users can log in and generate a registration code to use with an app. For reasons I won't go into I am unable to simply add the columns required to the users table. So I am going down a one to one route with the codes table.
It depends on the business and system.
If your userId is unique and will be unique all the time, you can use userId as your primary key. But if you ever want to expand your system, it will make things difficult. I advise you to add a foreign key in table user to make a relationship with table profile instead of adding a foreign key in table profile.
Short answer: DEPENDS.... In this particular case, it might be fine. However, experts will recommend against it just about every time; including your case.
Why?
Keys are seldomly unique in tables when they are foreign (originated in another table) to the table in question. For example, an item ID might be unique in an ITEMS table, but not in an ORDERS table, since the same type of item will most likely exist in another order. Likewise, order IDs might be unique (might) in the ORDERS table, but not in some other table like ORDER_DETAILS where an order with multiple line items can exist and to query against a particular item in a particular order, you need the concatenation of two FK (order_id and item_id) as the PK for this table.
I am not DB expert, but if you can justify logically to have an auto-generated value as your PK, I would do that. If this is not practical, then a concatenation of two (or maybe more) FK could serve as your PK. BUT, I cannot think of any case where a single FK value can be justified as the PK.
It is not totally applied for the question's case, but since I ended up on this question serching for other info and by reading some comments, I can say it is possible to only have a FK in a table and get unique values.
You can use a column that have classes, which can only be assigned 1 time, it works almost like and ID, however it could be done in the case you want to use a unique categorical value that distinguish each record.

What is the difference between Primary Key and unique key constraint?

What is the difference between Primary key And unique Key constraint?
What's the use of it??
Both are used to denote candidate keys for a table.
You can only have one primary key for a table so would just need to pick one if you have multiple candidates.
Either can be used in Foreign Key constraints. In SQL Server the Primary Key columns cannot be nullable. Columns used in Unique Key constraints can be.
By default in SQL Server the Primary Key will become the clustered index if it is created on a heap but it is by no means mandatory that the PK and clustered index should be the same.
A primary key is one which is used to identify the row in question. It might also have some meaning beyond that (if there was already a piece of "real" data that could serve) or it may be purely an implementation artefact (most IDENTITY columns, and equivalent auto-incremented values on other database systems).
A unique key is a more general case, where a key cannot have repeated values. In most cases people cannot have the same social security numbers in relation to the same jurisdiction (an international case could differ). Hence if we were storing social security numbers, then we would want to model them as unique, as any case of them matching an existing number is clearly wrong. Usernames generally must be unique also, so here's another case. External identifiers (identifiers used by another system, standard or protocol) tend to also be unique, e.g. there is only one language that has a given ISO 639 code, so if we were storing ISO 639 codes we would model that as unique.
This uniqueness can also be across more than one column. For example, in most hierarchical categorisation systems (e.g. a folder structure) no item can have both the same parent item and the same name, though there could be other items with the same parent and different names, and others with the same name and different parents. This multi-column capability is also present on primary keys.
A table may also have more than one unique key. E.g. a user may have both an id number and a username, and both will need to be unique.
Any non-nullable unique key can therefore serve as a primary key. Sometimes primary keys that come from the innate data being modelled are referred to as "natural primary keys", because they are a "natural" part of the data, rather than just an implementation artefact. The decision as to which to use depends on a few things:
Likelihood of change of specification. If we modelled a social security number as unique and then had to adapt to allow for multiple jurisdictions where two or more use a similar enough numbering system to allow for collisions, we likely need just remove the uniqueness constraint (other changes may be needed). If it was our primary key, we now also need to use a new primary key, and change any table that was using that primary key as part of a relationship, and any query that joined on it.
Speed of look-up. Key efficiency can be important, as they are used in many WHERE clauses and (more often) in many JOINs. With JOINS in particular, speed of lookup can be vital. The impact will depend on implementation details, and different databases vary according to how they will handle different datatypes (I would have few qualms from a performance perspective in using a large piece of text as a primary key in Postgres where I could specify the use of hash joins, but I'd be very hesitant to do so in SQLServer [Edit: for "large" I'm thinking of perhaps the size of a username, not something the size of the entire Norse Eddas!]).
Frequency of the key being the only interesting data. For example, with a table of languages, and a table of pieces of comments in that language, very often the only reason I would want to join on the language table when dealing with the comments table is either to obtain the language code or to restrict a query to those with a particular language code. Other information about the language is likely to be much more rarely used. In this case while joining on the code is likely to be less efficient than joining on a numeric id set from an IDENTITY column, having the code as the primary key - and hence as what is stored in the foreign key column on the comments table - will remove the need for any JOIN at all, with a considerable efficiency gain. More often though I want more information from the relevant tables than that, so making the JOIN more efficient is more important.
Primary key:
Primary key is nothing but it uniquely identifies each row in a table.
Primary key does not allow duplicate values, nor NULL.
Primary key by default is a clustered index.
A table can have only one primary key.
Unique Key:
Unique key is nothing but it uniquely identifies each row in a table.
Unique key does not allow duplicate values, but it allows (at most one) NULL.
Unique key by default is a non-clustered index.
This is a fruit full link to understand the Primary Key Database Keys.
Keep in mind we have only one clustered index in a table [Talking about SQL Server 2005].
Now if we want to add another unique column then we will use Unique Key column, because
Unique Key column can be added more than one.
A primary key is just any one candidate key. In principle primary keys are not different from any other candidate key because all keys are equal in the relational model.
SQL however has two different syntax for implementing candidate keys: the PRIMARY KEY constraint and the UNIQUE constraint (on non-nullable columns of course). In practice they achieve exactly the same thing except for the essentially useless restriction that a PRIMARY KEY can only be used once per table whereas a UNIQUE constraint can be used multiple times.
So there is no fundamental "use" for the PRIMARY KEY constraint. It is redundant and could easily be ignored or dropped from the language altogether. However, many people find it convenient to single out one particular key per table as having special significance. There is a very widely observed convention that keys designated with PRIMARY KEY are used for foreign key references, although this is entirely optional.
Short version:
From the point of view of database theory, there is none. Both are simply candidate keys.
In practice, most DMBS like to have one "standard key", which can be used for e.g. deciding how to store data, and to tell tools and DB clients which is the best way to identify a record.
So distinguishing one unique key as the "primary key" is just an implementation convenience (but an important one).

Are there any good reasons to have a database table without an integer primary key?

Although I'm guilty of this crime, it seems to me there can't be any good reason for a table to not have an identity field primary key.
Pros:
- whether you want to or not, you can now uniquely identify every row in your table which previously you could not do
- you can't do sql replication without a primary key on your table
Cons:
- an extra 32 bits for each row of your table
Consider for example the case where you need to store user settings in a table in your database. You have a column for the setting name and a column for the setting value. No primary key is necessary, but having an integer identity column and using it as your primary key seems like a best practice for any table you ever create.
Are there other reasons besides size that every table shouldn't just have an integer identity field?
Sure, an example in a single-database solution is if you have a table of countries, it probably makes more sense to use the ISO 3166-1-alpha-2 country code as the primary key as this is an international standard, and makes queries much more readable (e.g. CountryCode = 'GB' as opposed to CountryCode = 28). A similar argument could be applied to ISO 4217 currency codes.
In a SQL Server database solution using replication, a UNIQUEIDENTIFIER key would make more sense as GUIDs are required for some types of replication (and also make it much easier to avoid key conflicts if there are multiple source databases!).
The most clear example of a table that doesn't need a surrogate key is a many-to-many relation:
CREATE TABLE Authorship (
author_id INT NOT NULL,
book_id INT NOT NULL,
PRIMARY KEY (author_id, book_id),
FOREIGN KEY (author_id) REFERENCES Authors (author_id),
FOREIGN KEY (book_id) REFERENCES Books (book_id)
);
I also prefer a natural key when I design a tagging system:
CREATE TABLE Tags (
tag VARCHAR(20) PRIMARY KEY
);
CREATE TABLE ArticlesTagged (
article_id INT NOT NULL,
tag VARCHAR(20) NOT NULL,
PRIMARY KEY (article_id, tag),
FOREIGN KEY (article_id) REFERENCES Articles (article_id),
FOREIGN KEY (tag) REFERENCES Tags (tag)
);
This has some advantages over using a surrogate "tag_id" key:
You can ensure tags are unique, without adding a superfluous UNIQUE constraint.
You prevent two distinct tags from having the exact same spelling.
Dependent tables that reference the tag already have the tag text; they don't need to join to Tags to get the text.
Every table should have a primary key. It doesn't matter if it's an integer, GUID, or the "setting name" column. The type depends on the requirements of the application. Ideally, if you are going to join the table to another, it would be best to use a GUID or integer as your primary key.
Yes, there are good reasons. You can have semantically meaningful true keys, rather than articificial identity keys. Also, it is not a good idea to have a seperate autoincrementing primary key for a Many-Many table. There are some reasons you might want to choose a GUID.
That being said, I typically use autoincrementing 64bit integers for primary keys.
Every table should have a primary key. But it doesn't need to be a single field identifier. Take for example in a finance system, you may have the primary key on a journal table being the Journal ID and Line No. This will produce a unique combination for each row (and the Journal ID will be a primary key in its own table)
Your primary key needs to be defined on how you are going to link the table to other tables.
I don't think every table needs a primary key. Sometimes you only want to "connect" the contents of two tables - via their primary key.
So you have a table like users and one table like groups (each with primary keys) and you have a third table called users_groups with only two colums (user and group) where users and groups are connected with each other.
For example a row with user = 3 and group = 6 would link the user with primary key 3 to the group with primary key 6.
One reason not to have primary key defined as identity is having primary key defined as GUIDs or populated with externally generated values.
In general, every table that is semantically meaningful by itself should have primary key and such key should have no semantic meaning. A join table that realizes many-to-many relationship is not meaningful by itself and so it doesn't need such primary key (it already has one via its values).
To be a properly normalised table, each row should only have a single identifiable key. Many tables will already have natural keys, such a unique invoice number. I agree, especially with storage being so cheap, there is little overhead in having an autonumber/identity key on all tables, but in this instance which is the real key.
Another area where I personally don't use this approach if for reference data, where typically we have a Description and a Value
Code, Description
'L', 'Live'
'O', 'Old'
'P', 'Pending'
In this situation making code a primary key ensures no duplicates, and is more human readable.
The key difference (sorry) between a natural primary key and a surrogate primary key is that the value of the natural key contains information whereas the value of a surrogate key doesn't.
Why is this important? Well a natural primary key is by definition guaranteed to be unique, but its value is not usually guaranteed to stay the same. When it changes, you have to update it in multiple places.
A surrogate key's value has no real meaning and simply serves to identify that row, so it never needs to be changed. It is a feature of the model rather than the domain itself.
So the only place I would say a surrogate key isn't appropriate is in an association table which only contains columns referring to rows in other tables (most many-to-many relations). The only information this table carries is the association between two (or more) rows, and it already consists solely of surrogate key values. In this case I would choose a composite primary key.
If such a table had bag semantics, or carried additional information about the association, I would add a surrogate key.
A primary key is ALWAYS a good idea. It allows for very fast and easy joining of tables. It aides external tools that can read system tables to make join allowing less skilled people to create their own queries by drag-and-drop. It also makes the implementation of referential integrity a breeze and that is a good idea from the get go.
I know for sure that some very smart people working for web giants do this. While I don't know why their own reasons, I know 2 cases where PK-less tables make sense:
Importing data. The table is temporary. Insertions and whole table scans need to be as fast as possible. Also, we need to accept duplicate records. Later we will clean the data, but the import process needs to work.
Analytics in a DBMS. Identifying a row is not useful - if we need to do it, it is not analytics. We just need a non-relational, redundant, horrible blob that looks like a table. We will build summary tables or materialized views by writing proper SQL queries.
Note that these cases have good reasons to be non-relational. But normally your tables should be relational, so... yes, they need a primary key.

One or Two Primary Keys in Many-to-Many Table?

I have the following tables in my database that have a many-to-many relationship, which is expressed by a connecting table that has foreign keys to the primary keys of each of the main tables:
Widget: WidgetID (PK), Title, Price
User: UserID (PK), FirstName, LastName
Assume that each User-Widget combination is unique. I can see two options for how to structure the connecting table that defines the data relationship:
UserWidgets1: UserWidgetID (PK), WidgetID (FK), UserID (FK)
UserWidgets2: WidgetID (PK, FK), UserID (PK, FK)
Option 1 has a single column for the Primary Key. However, this seems unnecessary since the only data being stored in the table is the relationship between the two primary tables, and this relationship itself can form a unique key. Thus leading to option 2, which has a two-column primary key, but loses the one-column unique identifier that option 1 has. I could also optionally add a two-column unique index (WidgetID, UserID) to the first table.
Is there any real difference between the two performance-wise, or any reason to prefer one approach over the other for structuring the UserWidgets many-to-many table?
You only have one primary key in either case. The second one is what's called a compound key. There's no good reason for introducing a new column. In practise, you will have to keep a unique index on all candidate keys. Adding a new column buys you nothing but maintenance overhead.
Go with option 2.
Personally, I would have the synthetic/surrogate key column in many-to-many tables for the following reasons:
If you've used numeric synthetic keys in your entity tables then having the same on the relationship tables maintains consistency in design and naming convention.
It may be the case in the future that the many-to-many table itself becomes a parent entity to a subordinate entity that needs a unique reference to an individual row.
It's not really going to use that much additional disk space.
The synthetic key is not a replacement to the natural/compound key nor becomes the PRIMARY KEY for that table just because it's the first column in the table, so I partially agree with the Josh Berkus article. However, I don't agree that natural keys are always good candidates for PRIMARY KEY's and certainly should not be used if they are to be used as foreign keys in other tables.
Option 2 uses a simple compund key, option 1 uses a surrogate key. Option 2 is preferred in most scenarios and is close to the relational model in that it is a good candidate key.
There are situations where you may want to use a surrogate key (Option 1)
You are not certain that the compound key is a good candidate key over time. Particularly with temporal data (data that changes over time). What if you wanted to add another row to the UserWidget table with the same UserId and WidgetId? Think of Employment(EmployeeId,EmployeeId) - it would work in most cases except if someone went back to work for the same employer at a later date
If you are creating messages/business transactions or something similar that requires an easier key to use for integration. Replication maybe?
If you want to create your own auditing mechanisms (or similar) and don't want keys to get too long.
As a rule of thumb, when modeling data you will find that most associative entities (many to many) are the result of an event. Person takes up employment, item is added to basket etc. Most events have a temporal dependency on the event, where the date or time is relevant - in which case a surrogate key may be the best alternative.
So, take option 2, but make sure that you have the complete model.
I agree with the previous answers but I have one remark to add.
If you want to add more information to the relation and allow more relations between the same two entities you need option one.
For example if you want to track all the times user 1 has used widget 664 in the userwidget table the userid and widgetid isn't unique anymore.
What is the benefit of a primary key in this scenario? Consider the option of no primary key:
UserWidgets3: WidgetID (FK), UserID (FK)
If you want uniqueness then use either the compound key (UserWidgets2) or a uniqueness constraint.
The usual performance advantage of having a primary key is that you often query the table by the primary key, which is fast. In the case of many-to-many tables you don't usually query by the primary key so there is no performance benefit. Many-to-many tables are queried by their foreign keys, so you should consider adding indexes on WidgetID and UserID.
Option 2 is the correct answer, unless you have a really good reason to add a surrogate numeric key (which you have done in option 1).
Surrogate numeric key columns are not 'primary keys'. Primary keys are technically one of the combination of columns that uniquely identify a record within a table.
Anyone building a database should read this article http://it.toolbox.com/blogs/database-soup/primary-keyvil-part-i-7327 by Josh Berkus to understand the difference between surrogate numeric key columns and primary keys.
In my experience the only real reason to add a surrogate numeric key to your table is if your primary key is a compound key and needs to be used as a foreign key reference in another table. Only then should you even think to add an extra column to the table.
Whenever I see a database structure where every table has an 'id' column the chances are it has been designed by someone who doesn't appreciate the relational model and it will invariably display one or more of the problems identified in Josh's article.
I would go with both.
Hear me out:
The compound key is obviously the nice, correct way to go in so far as reflecting the meaning of your data goes. No question.
However: I have had all sorts of trouble making hibernate work properly unless you use a single generated primary key - a surrogate key.
So I would use a logical and physical data model. The logical one has the compound key. The physical model - which implements the logical model - has the surrogate key and foreign keys.
Since each User-Widget combination is unique, you should represent that in your table by making the combination unique. In other words, go with option 2. Otherwise you may have two entries with the same widget and user IDs but different user-widget IDs.
The userwidgetid in the first table is not needed, as like you said the uniqueness comes from the combination of the widgetid and the userid.
I would use the second table, keep the foriegn keys and add a unique index on widgetid and userid.
So:
userwidgets( widgetid(fk), userid(fk),
unique_index(widgetid, userid)
)
There is some preformance gain in not having the extra primary key, as the database would not need to calculate the index for the key. In the above model though this index (through the unique_index) is still calculated, but I believe that this is easier to understand.

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