Compare commits
15 commits
02b0214eb3
...
763ee444d4
Author | SHA1 | Date | |
---|---|---|---|
Bruno BELANYI | 763ee444d4 | ||
Bruno BELANYI | 5e3ba4fb04 | ||
Bruno BELANYI | 0030310952 | ||
Bruno BELANYI | dda444bdc0 | ||
Bruno BELANYI | aea5587742 | ||
Bruno BELANYI | c13abdc134 | ||
Bruno BELANYI | 987078068f | ||
Bruno BELANYI | f0b3c77862 | ||
Bruno BELANYI | 6a1c074e32 | ||
Bruno BELANYI | c413bb82a4 | ||
Bruno BELANYI | 937cd8e730 | ||
Bruno BELANYI | 3ca80055e2 | ||
Bruno BELANYI | ea9fe25571 | ||
Bruno BELANYI | bbcc1f97ce | ||
Bruno BELANYI | b56078f917 |
97
content/posts/2024-07-14-bloom-filter/index.md
Normal file
97
content/posts/2024-07-14-bloom-filter/index.md
Normal file
|
@ -0,0 +1,97 @@
|
||||||
|
---
|
||||||
|
title: "Bloom Filter"
|
||||||
|
date: 2024-07-14T17:46:40+01:00
|
||||||
|
draft: false # I don't care for draft mode, git has branches for that
|
||||||
|
description: "Probably cool"
|
||||||
|
tags:
|
||||||
|
- algorithms
|
||||||
|
- data structures
|
||||||
|
- python
|
||||||
|
categories:
|
||||||
|
- programming
|
||||||
|
series:
|
||||||
|
- Cool algorithms
|
||||||
|
favorite: false
|
||||||
|
disable_feed: false
|
||||||
|
---
|
||||||
|
|
||||||
|
The [_Bloom Filter_][wiki] is a probabilistic data structure for set membership.
|
||||||
|
|
||||||
|
The filter can be used as an inexpensive first step when querying the actual
|
||||||
|
data is quite costly (e.g: as a first check for expensive cache lookups or large
|
||||||
|
data seeks).
|
||||||
|
|
||||||
|
[wiki]: https://en.wikipedia.org/wiki/Bloom_filter
|
||||||
|
|
||||||
|
<!--more-->
|
||||||
|
|
||||||
|
## What does it do?
|
||||||
|
|
||||||
|
A _Bloom Filter_ can be understood as a hash-set which can either tell you:
|
||||||
|
|
||||||
|
* An element is _not_ part of the set.
|
||||||
|
* An element _may be_ part of the set.
|
||||||
|
|
||||||
|
More specifically, one can tweak the parameters of the filter to make it so that
|
||||||
|
the _false positive_ rate of membership is quite low.
|
||||||
|
|
||||||
|
I won't be going into those calculations here, but they are quite trivial to
|
||||||
|
compute, or one can just look up appropriate values for their use case.
|
||||||
|
|
||||||
|
## Implementation
|
||||||
|
|
||||||
|
I'll be using Python, which has the nifty ability of representing bitsets
|
||||||
|
through its built-in big integers quite easily.
|
||||||
|
|
||||||
|
We'll be assuming a `BIT_COUNT` of 64 here, but the implementation can easily be
|
||||||
|
tweaked to use a different number, or even change it at construction time.
|
||||||
|
|
||||||
|
### Representation
|
||||||
|
|
||||||
|
A `BloomFilter` is just a set of bits and a list of hash functions.
|
||||||
|
|
||||||
|
```python
|
||||||
|
BIT_COUNT = 64
|
||||||
|
|
||||||
|
class BloomFilter[T]:
|
||||||
|
_bits: int
|
||||||
|
_hash_functions: list[Callable[[T], int]]
|
||||||
|
|
||||||
|
def __init__(self, hash_functions: list[Callable[[T], int]]) -> None:
|
||||||
|
# Filter is initially empty
|
||||||
|
self._bits = 0
|
||||||
|
self._hash_functions = hash_functions
|
||||||
|
```
|
||||||
|
|
||||||
|
### Inserting a key
|
||||||
|
|
||||||
|
To add an element to the filter, we take the output from each hash function and
|
||||||
|
use that to set a bit in the filter. This combination of bit will identify the
|
||||||
|
element, which we can use for lookup later.
|
||||||
|
|
||||||
|
```python
|
||||||
|
def insert(self, val: T) -> None:
|
||||||
|
# Iterate over each hash
|
||||||
|
for f in self._hash_functions:
|
||||||
|
n = f(val) % BIT_COUNT
|
||||||
|
# Set the corresponding bit
|
||||||
|
self._bit |= 1 << n
|
||||||
|
```
|
||||||
|
|
||||||
|
### Querying a key
|
||||||
|
|
||||||
|
Because the _Bloom Filter_ does not actually store its elements, but some
|
||||||
|
derived data from hashing them, it can only definitely say if an element _does
|
||||||
|
not_ belong to it. Otherwise, it _may_ be part of the set, and should be checked
|
||||||
|
against the actual underlying store.
|
||||||
|
|
||||||
|
```python
|
||||||
|
def may_contain(self, val: T) -> bool:
|
||||||
|
for f in self._hash_functions:
|
||||||
|
n = f(val) % BIT_COUNT
|
||||||
|
# If one of the bits is unset, the value is definitely not present
|
||||||
|
if not (self._bit & (1 << n)):
|
||||||
|
return False
|
||||||
|
# All bits were matched, `val` is likely to be part of the set
|
||||||
|
return True
|
||||||
|
```
|
Loading…
Reference in a new issue