A Bloom Filter is a space-efficient probablistic data structure, to test whether an element is a member of a set. This algorithm for data representation ensures the element is in the dataset or not. This may have false positive matches but not false negative result.

The most common use of Bloom Filter Algorithm is to see if an elements is in the disk before performing any operations. This reduces the I/O for lookups dramatically over large datasets.

Consider we have to check a email address to search from large dataset of emails of millions. Searching all the emails in memory definitely is very inefficient and takes lots of time. We can create bloom filter bitarray, which is very small compared to the original dataset and has almost same required result. This is what used in Yahoo Mail. When you log into Yahoo mail, the browser page requests a bloom filter representing your contact list from Yahoo servers. The Bloom Filter is compact and easily fits in your browser cache. In Yahoo, email is verified if it is in existed in your contact list.

Another scenario, consider we have to get unique counts in the dataset, then we can use bloom filter to test if certain pattern or element has already been seen or not in the dataset. Of course this creates some false positives, but this might be much efficient than to compare everything from the memory.

Apache HBase uses bloom filter to boost read speed by filtering out unnecessary disk reads of HFile blocks which do not contain a particular row or column.

Quora implemented a sharded bloom filter in the feed backend to filter out stories that people have seen before. It is much faster and more memory efficient than previous solutions (Redis, Tokyo Cabinet and DB) and saves hundreds of ms on certain types of requests.(Tao Xu, Engineer at Quora)

Transactional Memory (TM) has recently applied Bloom filters to detect memory access conflicts among threads.(Mark Jeffrey, modeled Bloom filters for concurrency conflict detection).

Not to mention Facebook ( Typeahead Search Tech Talk (6/15/2010) ),, LinkedIn ( Cleo: the open source technology behind LinkedIn’s typeahead search | LinkedIn Engineering),  Bit.ly (dablooms – an open source, scalable, counting bloom filter library ) have implemented their own Bloom Filter.

More examples ? Go here https://en.wikipedia.org/wiki/Bloom_filter#Examples

Ok then, enough of the usage of Bloom Filter. We will be developing our own for searching email address from a list in Python.

import numpy as np
from bitarray import bitarray
import random


# The coefficients coff_a and coff_b are randomly chosen integers less than the maximum value of value.
# hashtable_size is a prime number slightly bigger than the maximum value of value.

# @param coff_a,coff_b: hashing coefficients
# @param val: value to be hashed
# @param prime: size of hash table
# @return: hash
def hash_function(coff_a, coff_b, value, hashtable_size):
    return (coff_a * value + coff_b) % hashtable_size


# set True to @position in @bitar:bitarray
def update_bloom(position, bitarr):
    bitarr[position] = 1


# find next prime number
def next_prime(n):
    return prime_range(n, 2 * n)


def prime_range(a, b):
    for p in range(a, b):
        for i in range(2, p):
            if p % i == 0:
                break
        else:
            return p
    return None


def check_for_email(email):
 return bloom_filter[hash_function(a, b, sum([ord(char) for char in email]), hashtable_size)]

email_list = ["trustgeek1@gmail.com", "trustgeek2@gmail.com",
              "trustgeek3@outlook.com", "thisisnewemail@gmail.com",
              "thiswebsite@hotmail.com", "registeredemail@yahoo.com"]

# calculate ordinal sum of characters for every email-address - ascii code sum of characters
email_ascii_sum_list = [sum([ord(char) for char in email]) for email in email_list]

# since we have fixed size of input, the hashtable could have 1.0 load factor
# yet, 0.75 load has much less colisions choose next prime number from the number
# of elements in email list to avoid collisions
hashtable_size = next_prime(int(round(len(email_ascii_sum_list) * 1.25)))
print("Hashtable Size: " + str(hashtable_size))


# generate two random numbers as hashing coefficients
a = random.randint(1, max(email_ascii_sum_list) - 1)
b = random.randint(2, max(email_ascii_sum_list) - 1)

print ("Coefficient a: " + str(a) + ", b: " + str(b))

# hash emails with the hashing function
hash_list = [hash_function(a, b, unicode_sum, hashtable_size) for unicode_sum in email_ascii_sum_list]

# assign hash_values & unicode-sums to emails
print([(email, "->", unicode_sum, "->", hashp) for email, unicode_sum, hashp in
       zip(email_list, email_ascii_sum_list, hash_list)])

# initialise bloom filter
bloom_filter = bitarray(hashtable_size)

# set all bits to 0
bloom_filter[:] = False

print ("Bloom Filter: ", bloom_filter)

# update bloom filter
[update_bloom(index, bloom_filter) for index in hash_list]

# for every email in the list check if it has already been seen by bloom filter
if check_for_email("trustgeek@hotmail.com"):
    print ("Exists")
else:
    print("Not Exists")

if check_for_email("trustgeek1@gmail.com"):
    print("Exists")
else:
    print("Not Exists")

# todo dynamic update new email added to list