what does a B-tree index on more than 1 column look like?

Question

So I was reading up on indexes and their implementation, and I stumbled upon this website that has a brief explanation of b-tree indexes:

http://20bits.com/articles/interview-questions-database-indexes/

The b-tree index makes perfect sense for indexes that are only on a single column, but let's say I create an index with multiple columns, how then does the b-tree work? What is the value of each node in the b-tree?

For example, if I have this table:

table customer: id    number name   varchar phone_number   varchar city   varchar 

and I create an index on: (id, name, city)

and then run the following query:

SELECT id, name    FROM customer  WHERE city = 'My City'; 

how does this query utilize the multiple column index, or does it not utilize it unless the index is created as (city, id, name) or (city, name, id) instead?

Answer 1

With most implementations, the key is simply a longer key that includes all of the key values, with a separator. No magic there ;-)

In your example the key values could look something like

 "123499|John Doe|Conway, NH" "32144|Bill Gates| Seattle, WA" 

One of the characteristics of these indexes with composite keys is that the intermediate tree nodes can be used in some cases to "cover" the query.

For example, if the query is to find the Name and City given the ID, since the ID is first in the index, the index can search by this efficiently. Once in the intermediate node, it can "parse" the Name and City, from the key, and doesn't need to go to the leaf node to read the same.

If however the query wanted also to display the phone number, then the logic would follow down the leaf when the full record is found.

Answer 2

Imagine that the key is represented by a Python tuple (col1, col2, col3) ... the indexing operation involves comparing tuple_a with tuple_b ... if you have don't know which value of col1 and col2 that you are interested in, but only col3, then it would have to read the whole index ("full index scan"), which is not as efficient.

If you have an index on (col1, col2, col3), then you can expect that any RDBMS will use the index (in a direct manner) when the WHERE clause contains reference to (1) all 3 columns (2) both col1 and col2 (3) only col1.

Otherwise (e.g. only col3 in the WHERE clause), either the RDBMS will not use that index at all (e.g. SQLite), or will do a full index scan (e.g. Oracle) [if no other index is better].

In your specific example, presuming that id is a unique identifier of a customer, it is pointless to have it appear in an index (other than the index that your DBMS should set up for a primary key or column noted as UNIQUE).