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Popular approximate membership query structures such as Bloom filters and cuckoo filters are widely used in databases, security, and networking. These structures represent sets approximately, and support at least two operations - insert and…

Data Structures and Algorithms · Computer Science 2022-01-17 Jim Apple

Filters are fast, small and approximate set membership data structures. They are often used to filter out expensive accesses to a remote set S for negative queries (that is, a query x not in S). Filters have one-sided errors: on a negative…

Data Structures and Algorithms · Computer Science 2021-07-08 David J. Lee , Samuel McCauley , Shikha Singh , Max Stein

Adaptive filters, such as telescoping and adaptive cuckoo filters, update their representation upon detecting a false positive to avoid repeating the same error in the future. Adaptive filters require an auxiliary structure, typically much…

Data Structures and Algorithms · Computer Science 2024-05-17 Richard Wen , Hunter McCoy , David Tench , Guido Tagliavini , Michael A. Bender , Alex Conway , Martin Farach-Colton , Rob Johnson , Prashant Pandey

Probabilistic filters are approximate set membership data structures that represent a set of keys in small space, and answer set membership queries without false negative answers, but with a certain allowed false positive probability. Such…

Databases · Computer Science 2025-08-14 Johanna Elena Schmitz , Jens Zentgraf , Sven Rahmann

We introduce the adaptive cuckoo filter (ACF), a data structure for approximate set membership that extends cuckoo filters by reacting to false positives, removing them for future queries. As an example application, in packet processing…

Data Structures and Algorithms · Computer Science 2017-10-12 Michael Mitzenmacher , Salvatore Pontarelli , Pedro Reviriego

Bloom filters are space-efficient probabilistic data structures that are used to test whether an element is a member of a set, and may return false positives. Recently, variations referred to as learned Bloom filters were developed that can…

Data Structures and Algorithms · Computer Science 2020-10-06 Kapil Vaidya , Eric Knorr , Tim Kraska , Michael Mitzenmacher

In this paper, we present an implementation of a cuckoo filter for membership testing, optimized for distributed data stores operating in high workloads. In large databases, querying becomes inefficient using traditional search methods. To…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-06-30 Aman Khalid

The Bloom filter---or, more generally, an approximate membership query data structure (AMQ)---maintains a compact, probabilistic representation of a set S of keys from a universe U. An AMQ supports lookups, inserts, and (for some AMQs)…

Data Structures and Algorithms · Computer Science 2018-08-28 Michael A. Bender , Martin Farach-Colton , Mayank Goswami , Rob Johnson , Samuel McCauley , Shikha Singh

Many efficient data structures use randomness, allowing them to improve upon deterministic ones. Usually, their efficiency and correctness are analyzed using probabilistic tools under the assumption that the inputs and queries are…

Cryptography and Security · Computer Science 2019-01-30 Moni Naor , Eylon Yogev

A filter is a widely used data structure for storing an approximation of a given set $S$ of elements from some universe $U$ (a countable set).It represents a superset $S'\supseteq S$ that is ''close to $S$'' in the sense that for $x\not\in…

Data Structures and Algorithms · Computer Science 2024-06-18 Ioana O. Bercea , Jakob Bæk Tejs Houen , Rasmus Pagh

Many applications of approximate membership query data structures, or filters, require only an incremental filter that supports insertions but not deletions. However, the design space of incremental filters is missing a "sweet spot" filter…

Data Structures and Algorithms · Computer Science 2022-10-26 Tomer Even , Guy Even , Adam Morrison

A Bloom filter is a simple data structure supporting membership queries on a set. The standard Bloom filter does not support the delete operation, therefore, many applications use a counting Bloom filter to enable deletion. This paper…

Data Structures and Algorithms · Computer Science 2019-08-13 Denis Kleyko , Abbas Rahimi , Ross W. Gayler , Evgeny Osipov

In the last decade, significant efforts have been made to reduce the false positive rate of approximate membership checking structures. This has led to the development of new structures such as cuckoo filters and xor filters. Adaptive…

Data Structures and Algorithms · Computer Science 2021-11-15 Pedro Reviriego , Alfonso Sánchez-Macián , Stefan Walzer , Peter C. Dillinger

There is a plethora of data structures, algorithms, and frameworks dealing with major data-stream problems like estimating the frequency of items, answering set membership, association and multiplicity queries, and several other statistics…

Data Structures and Algorithms · Computer Science 2021-06-24 Anes Abdennebi , Kamer Kaya

Filters are ubiquitous in computer science, enabling space-efficient approximate membership testing. Since Bloom filters were introduced in 1970, decades of work improved their space efficiency and performance. Recently, three new paradigms…

Data Structures and Algorithms · Computer Science 2026-02-17 Diandre Miguel Sabale , Wolfgang Gatterbauer , Prashant Pandey

Bloom Filters are a space-efficient data structure used for the testing of membership in a set that errs only in the False Positive direction. However, the standard analysis that measures this False Positive rate provides a form of worst…

Data Structures and Algorithms · Computer Science 2024-02-06 Kahlil Dozier , Loqman Salamatian , Dan Rubenstein

A Bloom filter is a widely used data-structure for representing a set $S$ and answering queries of the form "Is $x$ in $S$?". By allowing some false positive answers (saying "yes" when the answer is in fact `no') Bloom filters use space…

Data Structures and Algorithms · Computer Science 2016-11-03 Mayank Goswami , Rasmus Pagh , Francesco Silvestri , Johan Sivertsen

Bloom and cuckoo filters provide fast approximate set membership while using little memory. Engineers use them to avoid expensive disk and network accesses. The recently introduced xor filters can be faster and smaller than Bloom and cuckoo…

Data Structures and Algorithms · Computer Science 2022-03-15 Thomas Mueller Graf , Daniel Lemire

With the growing scale of big data, probabilistic structures receive increasing popularity for efficient approximate storage and query processing. For example, Bloom filters (BF) can achieve satisfactory performance for approximate…

Data Structures and Algorithms · Computer Science 2019-12-17 Yue Fu , Rong Du , Haibo Hu , Man Ho Au , Dagang Li

Bloom Filter is a probabilistic membership data structure and it is excessively used data structure for membership query. Bloom Filter becomes the predominant data structure in approximate membership filtering. Bloom Filter extremely…

Data Structures and Algorithms · Computer Science 2019-04-01 Ripon Patgiri , Sabuzima Nayak , Samir Kumar Borgohain
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