https://www.postgresql.org/docs/9.5/brin-intro.html :
BRIN stands for Block Range Index. BRIN is designed for handling very
large tables in which certain columns have some natural correlation
with their physical location within the table. A block range is a
group of pages that are physically adjacent in the table; for each
block range, some summary info is stored by the index. For example, a
table storing a store's sale orders might have a date column on which
each order was placed, and most of the time the entries for earlier
orders will appear earlier in the table as well; a table storing a ZIP
code column might have all codes for a city grouped together
naturally.
BRIN indexes can satisfy queries via regular bitmap index scans, and
will return all tuples in all pages within each range if the summary
info stored by the index is consistent with the query conditions. The
query executor is in charge of rechecking these tuples and discarding
those that do not match the query conditions — in other words, these
indexes are lossy. Because a BRIN index is very small, scanning the
index adds little overhead compared to a sequential scan, but may
avoid scanning large parts of the table that are known not to contain
matching tuples.
The specific data that a BRIN index will store, as well as the
specific queries that the index will be able to satisfy, depend on the
operator class selected for each column of the index. Data types
having a linear sort order can have operator classes that store the
minimum and maximum value within each block range, for instance;
geometrical types might store the bounding box for all the objects in
the block range.
The size of the block range is determined at index creation time by
the pages_per_range storage parameter. The number of index entries
will be equal to the size of the relation in pages divided by the
selected value for pages_per_range. Therefore, the smaller the number,
the larger the index becomes (because of the need to store more index
entries), but at the same time the summary data stored can be more
precise and more data blocks can be skipped during an index scan.
See this post for some benchmarks:
https://www.percona.com/blog/2019/07/16/brin-index-for-postgresql-dont-forget-the-benefits/
They genereated a 1.3 GB table of naturally ordered data (timestamps incemented). Then they generated a BRIN index (with pages_per_range = 32) and a B-Tree index on this database. Then they compared the SELECT execution time and the size of the indices. What they got:
B-Tree:
Planning Time: 22.225 ms Execution Time: 2.657 ms
public | testtab_date_idx | index | postgres | testtab | 171 MB
BRIN:
Planning Time: 0.272 ms Execution Time: 87.703 ms
public | testtab_date_brin_idx | index | postgres | testtab | 64 kB
meanwhile with no-index it would be:
Planning Time: 0.296 ms Execution Time: 1766.454 ms
Just to give a sense of orders.
What is important to discuss furthermore is the complexity of INSERT of the two. While for BRIN it is O(1), since you write sequentially on the next free space on the memory, however for B-Tree as we well know it is O(logN) (B-Trees) (higher the tree longer it takes).
