Bloom-Filters

JavaScript/TypeScript implementation of probabilistic data structures: Bloom Filter (and its derived), HyperLogLog, Count-Min Sketch, Top-K and MinHash. This package rely on non-cryptographic hash functions.

📕Online documentation

Keywords: bloom filter, cuckoo filter, KyperLogLog, MinHash, Top-K, probabilistic data-structures.

add(element: string) -> void: add an element into the filter.
has(element: string) -> boolean: Test an element for membership, returning False if the element is definitively not in the filter and True is the element might be in the filter.
equals(other: BloomFilter) -> boolean: Test if two filters are equals.
rate() -> number: compute the filter's false positive rate (or error rate).

const { BloomFilter } = require('bloom-filters')
// create a Bloom Filter with a size of 10 and 4 hash functions
let filter = new BloomFilter(10, 4)
// insert data
filter.add('alice')
filter.add('bob')

// lookup for some data
console.log(filter.has('bob')) // output: true
console.log(filter.has('daniel')) // output: false

// print the error rate
console.log(filter.rate())

// alternatively, create a bloom filter optimal for a number of items and a desired error rate
const items = ['alice', 'bob']
const errorRate = 0.04 // 4 % error rate
filter = BloomFilter.create(items.length, errorRate)

// or create a bloom filter optimal for a collections of items and a desired error rate
filter = BloomFilter.from(items, errorRate)

Partitioned Bloom Filter

A Partitioned Bloom Filter is a variation of a classic Bloom Filter.

This filter works by partitioning the M-sized bit array into k slices of size m = M/k bits, k = nb of hash functions in the filter. Each hash function produces an index over m for its respective slice. Thus, each element is described by exactly k bits, meaning the distribution of false positives is uniform across all elements.

Be careful, as a Partitioned Bloom Filter have much higher collison risks that a classic Bloom Filter on small sets of data.

Reference: Chang, F., Feng, W. C., & Li, K. (2004, March). Approximate caches for packet classification. In INFOCOM 2004. Twenty-third AnnualJoint Conference of the IEEE Computer and Communications Societies (Vol. 4, pp. 2196-2207). IEEE. (Full text article)

Methods

add(element: string) -> void: add an element into the filter.
has(element: string) -> boolean: Test an element for membership, returning False if the element is definitively not in the filter and True is the element might be in the filter.
equals(other: PartitionedBloomFilter) -> boolean: Test if two filters are equals.
rate() -> number: compute the filter's false positive rate (or error rate).

const { PartitionedBloomFilter } = require('bloom-filters')

// create a PartitionedBloomFilter of size 10, with 5 hash functions and a load factor of 0.5
const filter = new PartitionedBloomFilter(10, 5, 0.5)

// add some value in the filter
filter.add('alice')
filter.add('bob')

// lookup for some data
console.log(filter.has('bob')) // output: true
console.log(filter.has('daniel')) // output: false

// now use it like a classic bloom filter!
// ...

// alternatively, create a PartitionedBloomFilter optimal for a number of items and a desired error rate
const items = ['alice', 'bob']
const errorRate = 0.04 // 4 % error rate
filter = PartitionedBloomFilter.create(items.length, errorRate)

// or create a PartitionedBloomFilter optimal for a collections of items and a desired error rate
filter = PartitionedBloomFilter.from(items, errorRate)

Cuckoo Filter

Cuckoo filters improve on Bloom filters by supporting deletion, limited counting, and bounded False positive rate with similar storage efficiency as a standard Bloom Filter.

Reference: Fan, B., Andersen, D. G., Kaminsky, M., & Mitzenmacher, M. D. (2014, December). Cuckoo filter: Practically better than bloom. In Proceedings of the 10th ACM International on Conference on emerging Networking Experiments and Technologies (pp. 75-88). ACM. (Full text article)

Methods

add(element: string) -> void: add an element into the filter.
remove(element: string) -> boolean: delete an element from the filter, returning True if the deletion was a success and False otherwise.
has(element: string) -> boolean: Test an element for membership, returning False if the element is definitively not in the filter and True is the element might be in the filter.
equals(other: CuckooFilter) -> boolean: Test if two filters are equals.
rate() -> number: compute the filter's false positive rate (or error rate).

const { CuckooFilter } = require('bloom-filters')

// create a Cuckoo Filter with size = 15, fingerprint length = 3 and bucket size = 2
const filter = new CuckooFilter(15, 3, 2)
filter.add('alice')
filter.add('bob')

// lookup for some data
console.log(filter.has('bob')) // output: true
console.log(filter.has('daniel')) // output: false

// remove something
filter.remove('bob')
console.log(filter.has('bob')) // output: false

// alternatively, create a Cuckoo Filter optimal for a number of items and a desired error rate
const items = ['alice', 'bob']
const errorRate = 0.04 // 4 % error rate
filter = CuckooFilter.create(items.length, errorRate)

// or create a Cuckoo Filter optimal for a collections of items and a desired error rate
filter = CuckooFilter.from(items, errorRate)

WARNING: The error rate cannot be higher than 1 * 10^-18. Above this value, you will get an exception stating that the fingerprint length is higher than the hash length.

Counting Bloom Filter

A Counting Bloom filter works in a similar manner as a regular Bloom filter; however, it is able to keep track of insertions and deletions. In a counting Bloom filter, each entry in the Bloom filter is a small counter associated with a basic Bloom filter bit.

Reference: F. Bonomi, M. Mitzenmacher, R. Panigrahy, S. Singh, and G. Varghese, “An Improved Construction for Counting Bloom Filters,” in 14th Annual European Symposium on Algorithms, LNCS 4168, 2006

Methods

add(element: string) -> void: add an element into the filter.
remove(element: string) -> boolean: delete an element from the filter, returning True if the deletion was a success and False otherwise.
has(element: string) -> boolean: Test an element for membership, returning False if the element is definitively not in the filter and True is the element might be in the filter.
equals(other: CountingBloomFilter) -> boolean: Test if two filters are equals.
rate() -> number: compute the filter's false positive rate (or error rate).

const CountingBloomFilter = require('bloom-filters').CountingBloomFilter;

// create a Bloom Filter with capacity = 15 and 4 hash functions
let filter = new CountingBloomFilter(15, 4);

// add some value in the filter
filter.add('alice');
filter.add('bob');
filter.add('carole');

// remove some value
filter.remove('carole');

// lookup for some data
console.log(filter.has('bob')); // output: true
console.log(filter.has('carole')); // output: false
console.log(filter.has('daniel')); // output: false

// print false positive rate (around 0.1)
console.log(filter.rate());

// alternatively, create a Counting Bloom Filter optimal for a number of items and a desired error rate
const items = ['alice', 'bob']
const errorRate = 0.04 // 4 % error rate
filter = CountingBloomFilter.create(items.length, errorRate)

// or create a Counting Bloom Filter optimal for a collections of items and a desired error rate
filter = CountingBloomFilter.from(items, errorRate)

Count Min Sketch

The Count Min Sketch (CM sketch) is a probabilistic data structure that serves as a frequency table of events in a stream of data. It uses hash functions to map events to frequencies, but unlike a hash table uses only sub-linear space, at the expense of overcounting some events due to collisions.

Reference: Cormode, G., & Muthukrishnan, S. (2005). An improved data stream summary: the count-min sketch and its applications. Journal of Algorithms, 55(1), 58-75. (Full text article)

Methods

update(element: string, count = 1) -> void: add count occurences of an element into the sketch.
count(element: string) -> number: estimate the number of occurences of an element.
merge(other: CountMinSketch) -> CountMinSketch: merge occurences of two sketches.
equals(other: CountMinSketch) -> boolean: Test if two sketchs are equals.
clone(): CountMinSketch: Clone the sketch.

const { CountMinSketch } = require('bloom-filters')

// create a new Count Min sketch with 2048 columns and 1 row
const sketch = new CountMinSketch(2048, 1)

// push some occurrences in the sketch
sketch.update('alice')
sketch.update('alice')
sketch.update('bob')

// count occurrences
console.log(sketch.count('alice')) // output: 2
console.log(sketch.count('bob')) // output: 1
console.log(sketch.count('daniel')) // output: 0

// alternatively, create a Count Min sketch optimal for a target error rate and probability of accuracy
const items = ['alice', 'bob']
const errorRate = 0.04 // 4 % error rate
const accuracy = 0.99 // 99% accuracy
sketch = CountMinSketch.create(errorRate, accuracy)

// or create a Count Min Sketch optimal for a collections of items, 
// a target error rate and probability of accuracy
sketch = CountMinSketch.from(items, errorRate, accuracy)

HyperLogLog

HyperLogLog is an algorithm for the count-distinct problem, approximating the number of distinct elements in a multiset. Calculating the exact cardinality of a multiset requires an amount of memory proportional to the cardinality, which is impractical for very large data sets. Probabilistic cardinality estimators, such as the HyperLogLog algorithm, use significantly less memory than this, at the cost of obtaining only an approximation of the cardinality. The HyperLogLog algorithm is able to estimate cardinalities greather than 10e9 with a typical accuracy (standard error) of 2%, using around 1.5 kB of memory (see reference).

Reference: Philippe Flajolet, Éric Fusy, Olivier Gandouet and Frédéric Meunier (2007). "Hyperloglog: The analysis of a near-optimal cardinality estimation algorithm". Discrete Mathematics and Theoretical Computer Science Proceedings. (Full text article)

Methods

update(element: string) -> void: add a new occurence of an element to the sketch.
count() -> number: estimate the number of distinct elements in the sketch.
merge(other: HyperLogLog) -> HyperLogLog: merge occurences of two sketches.
equals(other: HyperLogLog) -> boolean: Test if two sketchs are equals.

const { HyperLogLog } = require('bloom-filters')

// create a new HyperLogLog with 100 registers
const sketch = new HyperLogLog(100)

// push some occurrences in the sketch
sketch.update('alice')
sketch.update('alice')
sketch.update('bob')

// count occurrences
console.log(sketch.count())

// print accuracy
console.log(sketch.accuracy())

MinHash

MinHash (or the min-wise independent permutations locality sensitive hashing scheme) is a technique for quickly estimating how similar two sets are. The goal of MinHash is to estimate the Jaccard similarity coefficient, a commonly used indicator of the similarity between two sets, without explicitly computing the intersection and union of the two sets. It does so by computing fixed sized signatures for a set of numbers using randomly generated hash functions.

❗️WARNINGS❗

A MinHash class only accepts numbers (integers and floats) as inputs.
Two MinHash can be compared only if they share the same set of randomly generated hash functions. To ease the creation of MinHash sets, we introduce a MinHashFactory class that is able to create MinHash structures that share the same set of hash functions. We recommend most users to rely on the factory, but the MinHash class remains importable for advanced usage.

Reference: Andrei Z. Broder, "On the resemblance and containment of documents", in Compression and Complexity of Sequences: Proceedings (1997). (Full text article)

`MinHashFactory` methods

create() -> MinHash: create a new empty MinHash structure, using the parameters of the factory.

`MinHash` methods

add(element: number) -> void: add a new element to the set.
bulkLoad(elements: number[]) -> void: efficently add several new elements to the set.
isEmpty() -> boolean: test if the signature of the MinHash is empty.
compareWith(other: MinHash) -> number: estimate the Jaccard similarity coefficient with another MinHash set.

const { MinHashFactory } = require('bloom-filters')

// create the MinHashFactory, to create several comparable MinHash sets
// it uses 10 random hash functions and expect to see a maximum value of 999
const factory = new MinHashFactory(10, 999)

// create two empty MinHash
const fistSet = factory.create()
const secondSet = factory.create()

// push some occurrences in the first set
fistSet.add(1)
fistSet.add(2)

// the MinHash class also supports bulk loading
secondSet.bulkLoad([1, 3, 4])

// estimate the jaccard similarity between the two sets
const jaccardSim = fistSet.compareWith(secondSet)
console.log(`The estimated Jaccard similarity is ${jaccardSim}`)

Top-K

Given a multiset of elements, the Top-K problem is to compute the ranking of these elements (by an arbitrary score) and returns the k results with the highest scores. This package provides an implementation of the Top-K problem that sort items based on their estimated cardinality in the multiset. It is based on a Count Min Sketch, for estimating the cardinality of items, and a MinHeap, for implementing a sliding window over the k results with the highest scores.

Items produced by the TopK class are JavaScript objects with the following content (shown in Typescript notation).

interface TopkElement {
  // The element's value
  value: string,
  // The element's frequency
  frequency: number,
  // The element's rank in the TopK, ranging from 1 to k
  rank: number
}

Methods

add(element: string) -> void: add a new occurence of an element to the sketch.
values() -> Array<TopkElement>: get the top-k values as an array of objects.
iterator() -> Iterator<TopkElement>: get the top-k values as an iterator that yields objects.

const { TopK } = require('bloom-filters')

// create a new TopK with k = 10, an error rate of 0.001 and an accuracy of 0.99
const topk = new TopK(10, 0.001, 0.99)

// push some occurrences in the multiset
topk.add('alice')
topk.add('bob')
topk.add('alice')

// print the top k values
for(let item of topk.values()) {
  console.log(`Item "${item.value}" is in position ${item.rank} with an estimated frequency of ${item.frequency}`)
}
// Output:
// Item "alice" is in position 1 with an estimated frequency of 2
// Item "bob" is in position 2 with an estimated frequency of 1

Invertible Bloom Filters

An Invertible Bloom Filters (IBLT), also called Invertible Bloom Lookup Table, is a space-efficient and probabilistic data-structure for solving the set-difference problem efficiently without the use of logs or other prior context. It computes the set difference with communication proportional to the size of the difference between the sets being compared. They can simultaneously calculate D(A−B) and D(B−A) using O(d) space. This data structure encodes sets in a fashion that is similar in spirit to Tornado codes’ construction, in that it randomly combines elements using the XOR function.

❗️WARNING❗️ An IBLT only accepts Buffer as inputs. If you are using bloom-filters in a Web browser, you might consider using the feros/buffer package, which provides a polyfill for Buffer in a browser.

Reference: Eppstein, D., Goodrich, M. T., Uyeda, F., & Varghese, G. (2011). What's the difference?: efficient set reconciliation without prior context. ACM SIGCOMM Computer Communication Review, 41(4), 218-229. (Full text article)

Methods

add(element: Buffer) -> void: add an element into the filter.
remove(element: Buffer) -> void: delete an element from the filter, returning True if the deletion was a success and False otherwise.
has(element: Buffer) -> boolean: Test an element for membership, returning False if the element is definitively not in the filter and True is the element might be in the filter.
equals(other: InvertibleBloomFilter) -> boolean: Test if two filters are equals.
substract(remote: InvertibleBloomFilter): peform the XOR substraction of two IBLTs.
decode() -> {additional: Buffer[], missing: Buffer[]} : decode an IBLT.
listEntries() -> Generator<Buffer, number, void>: list all entries in the IBLT using a Generator.

const { InvertibleBloomFilter } = require('bloom-filters')

const hashcount = 3
const size = 50
const iblt = new InvertibleBloomFilter(size, hashcount)

// push some data in the IBLT
iblt.add(Buffer.from('alice'))
iblt.add(Buffer.from('42'))
iblt.add(Buffer.from('help'))
iblt.add(Buffer.from('meow'))
iblt.add(Buffer.from('json'))

console.log(ilbt.has(Buffer.from('alice'))) // output: true
console.log(ilbt.has(Buffer.from('daniel'))) // output: false

iblt.remove(Buffer.from('alice'))
console.log(ilbt.has(Buffer.from('alice'))) // output: false

// Now, let's demonstrate the decoding power of IBLT!
const remote = new InvertibleBloomFilter(size, hashcount)
remote.add(Buffer.from('alice'))
remote.add(Buffer.from('car'))
remote.add(Buffer.from('meow'))
remote.add(Buffer.from('help'))

// decode the difference between the two filters
const result = iblt.substract(remote).decode()

console.log(`Did we successfully decode the subtracted iblts? ${result.success}. Why? $${result.reason}`)
console.log(`Elements of iblt missing elements from remote: ${result.additional}`)
console.log(`Elements of remote missing elements from iblt: ${result.missing}`)

// alternatively, create an IBLT optimal for a number of items and a desired error rate
const items = [Buffer.from('alice'), Buffer.from('bob')]
const errorRate = 0.04 // 4 % error rate
filter = InvertibleBloomFilter.create(items.length, errorRate)

// or create an IBLT optimal for a collections of items and a desired error rate
filter = InvertibleBloomFilter.from(items, errorRate)

Tuning the IBLT We recommend to use at least a hashcount of 3 and an alpha of 1.5 for at least 50 differences, which equals to 1.5*50 = 75 cells. Then, if you insert a huge number of values in there, the decoding will work (whatever the number of differences less than 50) but testing the presence of a value is still probabilistic, based on the number of elements inserted (Even for the functions like listEntries). For more details, you should read the seminal research paper on IBLTs (full-text article).

Export and import

All data structures exposed by this package can be exported and imported to/from JSON:

Use the method saveAsJSON() to export any data structures into a JSON object.
Use the static method fromJSON(json) to load a data structure from a JSON object.

const { BloomFilter } = require('bloom-filters')

const filter = new BloomFilter(15, 0.01)
filter.add('alice')

// export a bloom filter to JSON
const exported = filter.saveAsJSON()

// do something with the JSON object (save it as file, send it to a server, etc)
// ...

// import the same filter from its JSON export
const importedFilter = BloomFilter.fromJSON(exported)
console.log(filter.has('alice')) // output: true
console.log(filter.has('bob')) // output: false

Every hash function is seeded

By default every hash function is seeded with an internal seed which is equal to 0x1234567890. If you want to change it:

const { BloomFilter } = require('bloom-filter')
const bl = new BloomFilter(...)
console.log(bl.seed) // 78187493520
bl.seed = 0xABCD
console.log(bl.seed) // 43981

Documentation

See documentation online or generate it in directory doc/ with: npm run doc

Tests

Running with Mocha + Chai

# run tests
npm test

References

Classic Bloom Filter: Bloom, B. H. (1970). Space/time trade-offs in hash coding with allowable errors. Communications of the ACM, 13(7), 422-426.
Partitioned Bloom Filter: Chang, F., Feng, W. C., & Li, K. (2004, March). Approximate caches for packet classification. In INFOCOM 2004. Twenty-third AnnualJoint Conference of the IEEE Computer and Communications Societies (Vol. 4, pp. 2196-2207). IEEE.
Cuckoo Filter: Fan, B., Andersen, D. G., Kaminsky, M., & Mitzenmacher, M. D. (2014, December). Cuckoo filter: Practically better than bloom. In Proceedings of the 10th ACM International on Conference on emerging Networking Experiments and Technologies (pp. 75-88). ACM.
Counting Bloom Filter: F. Bonomi, M. Mitzenmacher, R. Panigrahy, S. Singh, and G. Varghese, An Improved Construction for Counting Bloom Filters, in 14th Annual European Symposium on Algorithms, LNCS 4168, 2006, pp.
Count Min Sketch: Cormode, G., & Muthukrishnan, S. (2005). An improved data stream summary: the count-min sketch and its applications. Journal of Algorithms, 55(1), 58-75.
HyperLogLog: Philippe Flajolet, Éric Fusy, Olivier Gandouet and Frédéric Meunier (2007). "Hyperloglog: The analysis of a near-optimal cardinality estimation algorithm". Discrete Mathematics and Theoretical Computer Science Proceedings.
MinHash: Andrei Z. Broder, "On the resemblance and containment of documents", in Compression and Complexity of Sequences: Proceedings (1997).
Invertible Bloom Filters: Eppstein, D., Goodrich, M. T., Uyeda, F., & Varghese, G. (2011). What's the difference?: efficient set reconciliation without prior context. ACM SIGCOMM Computer Communication Review, 41(4), 218-229.

Changelog

Version	Release date	Major changes
`v1.3.0`	10/04/2020	Added the MinHash set
`v1.2.0`	08/04/2020	Add the TopK class
`v1.1.0`	03/04/2020	Add the HyperLogLog sketch
`v1.0.0`	23/03/2020	Rework the whole library using TypeScript, unify the API and fix the documentation
`v0.8.0`	11/11/2019	Fix some issues with the cuckoo filter (performances). Fix the global API. It allows now to customize each Filter. If you want to use the old API, use the `.create()` or `.from()` functions to match the old api.
`v0.7.1`	11/09/2019	Add the Counting Bloom Filter
`v0.7.0`	01/07/2019	Move to XXHASH for hashing elements in the library. One property has been added into the exported json `_seed` which is used to seed every hash of every elements. Update Invertible Bloom Filters with #add, #has, #delete, #listEntries, #substract, #Static.decode methods. Updated the way to get distinct indices which could have collisions in many cases.
`v0.6.1`	18/06/2019	Add Invertible Bloom Filters (only #encode/#substract/#Static.decode methods)

License

MIT License

Name		Name	Last commit message	Last commit date
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src		src
test		test
.gitignore		.gitignore
.travis.yml		.travis.yml
LICENSE		LICENSE
README.md		README.md
package.json		package.json
tsconfig.json		tsconfig.json
yarn.lock		yarn.lock

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Bloom-Filters

Table of contents

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Classic Bloom Filter

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Partitioned Bloom Filter

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MinHash

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