#### PostgreSQL

##### Indexes in PostgreSQL — 10 (Bloom)

In the previous articles we discussed PostgreSQL indexing engine and the interface of access methods, as well as B-trees, GiST, SP-GiST, GIN, RUM, and BRIN. But we still need to look at Bloom indexes.

## Bloom

### General concept

A classical Bloom filter is a data structure that enables us to quickly check membership of an element in a set. The filter is highly compact, but allows false positives: it can mistakenly consider an element to be a member of a set (false positive), but it is not permitted to consider an element of a set not to be a member (false negative).

The filter is an array of *m* bits (also called a *signature*) that is initially filled with zeros. *k* different hash functions are chosen that map any element of the set to *k* bits of the signature. To add an element to the set, we need to set each of these bits in the signature to one. Consequently, if all the bits corresponding to an element are set to one, the element can be a member of the set, but if at least one bit equals zero, the element is not in the set for sure.

In the case of a DBMS, we actually have *N* separate filters built for each index row. As a rule, several fields are included in the index, and it's values of these fields that compose the set of elements for each row.

By choosing the length of the signature *m*, we can find a trade-off between the index size and the probability of false positives. The application area for Bloom index is large, considerably "wide" tables to be queried using filters on each of the fields. This access method, like BRIN, can be regarded as an accelerator of sequential scan: all the matches found by the index must be rechecked with the table, but there is a chance to avoid considering most of the rows at all.

##### Indexes in PostgreSQL — 9 (BRIN)

In the previous articles we discussed PostgreSQL indexing engine, the interface of access methods, and the following methods: B-trees, GiST, SP-GiST, GIN, and RUM. The topic of this article is BRIN indexes.

## BRIN

### General concept

Unlike indexes with which we've already got acquainted, the idea of BRIN is to avoid looking through definitely unsuited rows rather than quickly find the matching ones. This is always an inaccurate index: it does not contain TIDs of table rows at all.

Simplistically, BRIN works fine for columns where values correlate with their physical location in the table. In other words, if a query without ORDER BY clause returns the column values virtually in the increasing or decreasing order (and there are no indexes on that column).

This access method was created in scope of Axle, the European project for extremely large analytical databases, with an eye on tables that are several terabyte or dozens of terabytes large. An important feature of BRIN that enables us to create indexes on such tables is a small size and minimal overhead costs of maintenance.

This works as follows. The table is split into *ranges* that are several pages large (or several blocks large, which is the same) - hence the name: Block Range Index, BRIN. The index stores *summary information* on the data in each range. As a rule, this is the minimal and maximal values, but it happens to be different, as shown further. Assume that a query is performed that contains the condition for a column; if the sought values do not get into the interval, the whole range can be skipped; but if they do get, all rows in all blocks will have to be looked through to choose the matching ones among them.

It will not be a mistake to treat BRIN not as an index, but as an accelerator of sequential scan. We can regard BRIN as an alternative to partitioning if we consider each range as a "virtual" partition.

Now let's discuss the structure of the index in more detail.

##### Indexes in PostgreSQL — 6 (SP-GiST)

We've already discussed PostgreSQL indexing engine, the interface of access methods, and three methods: hash index, B-tree, and GiST. In this article, we will describe SP-GiST.

## SP-GiST

First, a few words about this name. The "GiST" part alludes to some similarity with the same-name access method. The similarity does exist: both are generalized search trees that provide a framework for building various access methods.

"SP" stands for space partitioning. The space here is often just what we are used to call a space, for example, a two-dimensional plane. But we will see that any search space is meant, that is, actually any value domain.

SP-GiST is suitable for structures where the space can be recursively split into *non-intersecting* areas. This class comprises quadtrees, k-dimensional trees (k-D trees), and radix trees.

### Structure

So, the idea of SP-GiST access method is to split the value domain into *non-overlapping* subdomains each of which, in turn, can also be split. Partitioning like this induces *non-balanced* trees (unlike B-trees and regular GiST).

The trait of being non-intersecting simplifies decision-making during insertion and search. On the other hand, as a rule, the trees induced are of low branching. For example, a node of a quadtree usually has four child nodes (unlike B-trees, where the nodes amount to hundreds) and larger depth. Trees like these well suit the work in RAM, but the index is stored on a disk and therefore, to reduce the number of I/O operations, nodes have to be packed into pages, and it is not easy to do this efficiently. Besides, the time it takes to find different values in the index, may vary because of differences in branch depths.

##### Indexes in PostgreSQL — 5 (GiST)

In the previous articles, we discussed PostgreSQL indexing engine, the interface of access methods, and two access methods: hash index and B-tree. In this article, we will describe GiST indexes.

## GiST

GiST is an abbreviation of "generalized search tree". This is a balanced search tree, just like "b-tree" discussed earlier.

What is the difference? "btree" index is strictly connected to the comparison semantics: support of "greater", "less", and "equal" operators is all it is capable of (but very capable!) However, modern databases store data types for which these operators just make no sense: geodata, text documents, images, ...

GiST index method comes to our aid for these data types. It permits defining a rule to distribute data of an arbitrary type across a balanced tree and a method to use this representation for access by some operator. For example, GiST index can "accommodate" R-tree for spatial data with support of relative position operators (located on the left, on the right, contains, etc.) or RD-tree for sets with support of intersection or inclusion operators.

Thanks to extensibility, a totally new method can be created from scratch in PostgreSQL: to this end, an interface with the indexing engine must be implemented. But this requires premeditation of not only the indexing logic, but also mapping data structures to pages, efficient implementation of locks, and support of a write-ahead log. All this assumes high developer skills and a large human effort. GiST simplifies the task by taking over low-level problems and offering its own interface: several functions pertaining not to techniques, but to the application domain. In this sense, we can regard GiST as a framework for building new access methods.