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An implementation of the HyperLogLog algorithm backed by Redis
tag: v0.2.0

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This gem is an implementation of the HyperLogLog algorithm for estimating cardinalities of sets observed via a stream of events. A Redis instance is used for storing the counters. A simple example:

require 'redis'
require 'hyperloglog-redis'

redis =
counter =
['john', 'paul', 'george', 'ringo', 'john', 'paul'].each do |beatle|
  counter.add('beatles', beatle)

puts "There are approximately #{counter.count('beatles')} distinct Beatles"

You can also ask for an estimate from multiple counters and you'll get an estimate of the size of their union:

['joe', 'denny', 'linda', 'jimmy', 'paul'].each do |wing_member|
  counter.add('wings', wing_member)

puts "There are approximately #{counter.count('beatles', 'wings')} people who were in the Beatles or Wings"

Each HyperLogLog counter uses a small, fixed amount of space but can estimate the cardinality of any set of up to around a billion values with relative error of about 1.04 / Math.sqrt(2 ** b), where b is a parameter passed to the HyperLogLog initializer that defaults to 10. With b = 10, each counter is represented by a Redis sorted set with 2 ** b = 1024 values (a few KB of space) and we get an expected relative error of 3%. Contrast this with the amount of space needed to compute set cardinality exactly, which is over 100 MB for a even a bit vector representing a set with a billion values.

The basic idea of HyperLogLog (and its predecessors PCSA and LogLog) is to apply a good hash function to each value you see in the stream and record the longest run of zeros that you've seen as a prefix of any hashed value. If the hash function is good, you'd expect that its bits are statistically independent, so seeing a value that starts with exactly X zeros should happen with probability 2 ** -(X + 1). So if you've seen a run of 5 zeros in one of your hash values, you're likely to have around 2 ** 6 = 64 values in the underlying set. The actual implementation and analysis are much more advanced than this, but that's the idea.

The HyperLogLog algorithm is described and analyzed in the paper "HyperLogLog: the analysis of a near-optimal cardinality estimation algorithm" by Flajolet, Fusy, Gandouet, and Meunier. Our implementation closely follows the program described in Section 4 of that paper.


gem install hyperloglog-redis
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