Boom Filters

Boom Filters are probabilistic data structures for processing continuous, unbounded streams. This includes Stable Bloom Filters, Scalable Bloom Filters, Counting Bloom Filters, Inverse Bloom Filters, Cuckoo Filters, several variants of traditional Bloom filters, HyperLogLog, Count-Min Sketch, and MinHash.

Classic Bloom filters generally require a priori knowledge of the data set in order to allocate an appropriately sized bit array. This works well for offline processing, but online processing typically involves unbounded data streams. With enough data, a traditional Bloom filter "fills up", after which it has a false-positive probability of 1.

Boom Filters are useful for situations where the size of the data set isn't known ahead of time. For example, a Stable Bloom Filter can be used to deduplicate events from an unbounded event stream with a specified upper bound on false positives and minimal false negatives. Alternatively, an Inverse Bloom Filter is ideal for deduplicating a stream where duplicate events are relatively close together. This results in no false positives and, depending on how close together duplicates are, a small probability of false negatives. Scalable Bloom Filters place a tight upper bound on false positives while avoiding false negatives but require allocating memory proportional to the size of the data set. Counting Bloom Filters and Cuckoo Filters are useful for cases which require adding and removing elements to and from a set.

For large or unbounded data sets, calculating the exact cardinality is impractical. HyperLogLog uses a fraction of the memory while providing an accurate approximation. Similarly, Count-Min Sketch provides an efficient way to estimate event frequency for data streams, while Top-K tracks the top-k most frequent elements.

MinHash is a probabilistic algorithm to approximate the similarity between two sets. This can be used to cluster or compare documents by splitting the corpus into a bag of words.

Installation

$ go get github.com/tylertreat/BoomFilters

Stable Bloom Filter

This is an implementation of Stable Bloom Filters as described by Deng and Rafiei in Approximately Detecting Duplicates for Streaming Data using Stable Bloom Filters.

A Stable Bloom Filter (SBF) continuously evicts stale information so that it has room for more recent elements. Like traditional Bloom filters, an SBF has a non-zero probability of false positives, which is controlled by several parameters. Unlike the classic Bloom filter, an SBF has a tight upper bound on the rate of false positives while introducing a non-zero rate of false negatives. The false-positive rate of a classic Bloom filter eventually reaches 1, after which all queries result in a false positive. The stable-point property of an SBF means the false-positive rate asymptotically approaches a configurable fixed constant. A classic Bloom filter is actually a special case of SBF where the eviction rate is zero and the cell size is one, so this provides support for them as well (in addition to bitset-based Bloom filters).

Stable Bloom Filters are useful for cases where the size of the data set isn't known a priori and memory is bounded. For example, an SBF can be used to deduplicate events from an unbounded event stream with a specified upper bound on false positives and minimal false negatives.

Usage

package main

import (
    "fmt"
    "github.com/tylertreat/BoomFilters"
)

func main() {
    sbf := boom.NewDefaultStableBloomFilter(10000, 0.01)
    fmt.Println("stable point", sbf.StablePoint())
    
    sbf.Add([]byte(`a`))
    if sbf.Test([]byte(`a`)) {
        fmt.Println("contains a")
    }
    
    if !sbf.TestAndAdd([]byte(`b`)) {
        fmt.Println("doesn't contain b")
    }
    
    if sbf.Test([]byte(`b`)) {
        fmt.Println("now it contains b!")
    }
    
    // Restore to initial state.
    sbf.Reset()
}

Scalable Bloom Filter

This is an implementation of a Scalable Bloom Filter as described by Almeida, Baquero, Preguica, and Hutchison in Scalable Bloom Filters.

A Scalable Bloom Filter (SBF) dynamically adapts to the size of the data set while enforcing a tight upper bound on the rate of false positives and a false-negative probability of zero. This works by adding Bloom filters with geometrically decreasing false-positive rates as filters become full. A tightening ratio, r, controls the filter growth. The compounded probability over the whole series converges to a target value, even accounting for an infinite series.

Scalable Bloom Filters are useful for cases where the size of the data set isn't known a priori and memory constraints aren't of particular concern. For situations where memory is bounded, consider using Inverse or Stable Bloom Filters.

The core parts of this implementation were originally written by Jian Zhen as discussed in Benchmarking Bloom Filters and Hash Functions in Go.

Usage

package main

import (
    "fmt"
    "github.com/tylertreat/BoomFilters"
)

func main() {
    sbf := boom.NewDefaultScalableBloomFilter(0.01)
    
    sbf.Add([]byte(`a`))
    if sbf.Test([]byte(`a`)) {
        fmt.Println("contains a")
    }
    
    if !sbf.TestAndAdd([]byte(`b`)) {
        fmt.Println("doesn't contain b")
    }
    
    if sbf.Test([]byte(`b`)) {
        fmt.Println("now it contains b!")
    }
    
    // Restore to initial state.
    sbf.Reset()
}

Inverse Bloom Filter

An Inverse Bloom Filter, or "the opposite of a Bloom filter", is a concurrent, probabilistic data structure used to test whether an item has been observed or not. This implementation, originally described and written by Jeff Hodges, replaces the use of MD5 hashing with a non-cryptographic FNV-1 function.

The Inverse Bloom Filter may report a false negative but can never report a false positive. That is, it may report that an item has not been seen when it actually has, but it will never report an item as seen which it hasn't come across. This behaves in a similar manner to a fixed-size hashmap which does not handle conflicts.

This structure is particularly well-suited to streams in which duplicates are relatively close together. It uses a CAS-style approach, which makes it thread-safe.

Usage

package main

import (
    "fmt"
    "github.com/tylertreat/BoomFilters"
)

func main() {
    ibf := boom.NewInverseBloomFilter(10000)
    
    ibf.Add([]byte(`a`))
    if ibf.Test([]byte(`a`)) {
        fmt.Println("contains a")
    }
    
    if !ibf.TestAndAdd([]byte(`b`)) {
        fmt.Println("doesn't contain b")
    }
    
    if ibf.Test([]byte(`b`)) {
        fmt.Println("now it contains b!")
    }
}

Counting Bloom Filter

This is an implementation of a Counting Bloom Filter as described by Fan, Cao, Almeida, and Broder in Summary Cache: A Scalable Wide-Area Web Cache Sharing Protocol.

A Counting Bloom Filter (CBF) provides a way to remove elements by using an array of n-bit buckets. When an element is added, the respective buckets are incremented. To remove an element, the respective buckets are decremented. A query checks that each of the respective buckets are non-zero. Because CBFs allow elements to be removed, they introduce a non-zero probability of false negatives in addition to the possibility of false positives.

Counting Bloom Filters are useful for cases where elements are both added and removed from the data set. Since they use n-bit buckets, CBFs use roughly n-times more memory than traditional Bloom filters.

See Deletable Bloom Filter for an alternative which avoids false negatives.

Usage

package main

import (
    "fmt"
    "github.com/tylertreat/BoomFilters"
)

func main() {
    bf := boom.NewDefaultCountingBloomFilter(1000, 0.01)
    
    bf.Add([]byte(`a`))
    if bf.Test([]byte(`a`)) {
        fmt.Println("contains a")
    }
    
    if !bf.TestAndAdd([]byte(`b`)) {
        fmt.Println("doesn't contain b")
    }
    
    if bf.TestAndRemove([]byte(`b`)) {
        fmt.Println("removed b")
    }
    
    // Restore to initial state.
    bf.Reset()
}

Cuckoo Filter

This is an implementation of a Cuckoo Filter as described by Andersen, Kaminsky, and Mitzenmacher in Cuckoo Filter: Practically Better Than Bloom. The Cuckoo Filter is similar to the Counting Bloom Filter in that it supports adding and removing elements, but it does so in a way that doesn't significantly degrade space and performance.

It works by using a cuckoo hashing scheme for inserting items. Instead of storing the elements themselves, it stores their fingerprints which also allows for item removal without false negatives (if you don't attempt to remove an item not contained in the filter).

For applications that store many items and target moderately low false-positive rates, cuckoo filters have lower space overhead than space-optimized Bloom filters.

Usage

package main

import (
    "fmt"
    "github.com/tylertreat/BoomFilters"
)

func main() {
    cf := boom.NewCuckooFilter(1000, 0.01)
    
    cf.Add([]byte(`a`))
    if cf.Test([]byte(`a`)) {
        fmt.Println("contains a")
    }
    
    if contains, _ := cf.TestAndAdd([]byte(`b`)); !contains {
        fmt.Println("doesn't contain b")
    }
    
    if cf.TestAndRemove([]byte(`b`)) {
        fmt.Println("removed b")
    }
    
    // Rest