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  1. Home > Articles & Issues >
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  3. HyperLogLog: the ana ...
Conference paper

HyperLogLog: the analysis of a near-optimal cardinality estimation algorithm

Philippe Flajolet (1), Éric Fusy (1), Olivier Gandouet (2), Frédéric Meunier (1)
(1) Algorithms
(2) Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
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May 10, 2017
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December 31, 2006
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March 31, 2025
Volume
DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07)
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10.46298/dmtcs.3545
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HyperLogLog: the analysis of a near-optimal cardinality estimation algorithm

Philippe Flajolet (1), Éric Fusy (1), Olivier Gandouet (2), Frédéric Meunier (1)
(1) Algorithms
(2) Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract
This extended abstract describes and analyses a near-optimal probabilistic algorithm, HYPERLOGLOG, dedicated to estimating the number of \emphdistinct elements (the cardinality) of very large data ensembles. Using an auxiliary memory of m units (typically, "short bytes''), HYPERLOGLOG performs a single pass over the data and produces an estimate of the cardinality such that the relative accuracy (the standard error) is typically about $1.04/\sqrt{m}$. This improves on the best previously known cardinality estimator, LOGLOG, whose accuracy can be matched by consuming only 64% of the original memory. For instance, the new algorithm makes it possible to estimate cardinalities well beyond $10^9$ with a typical accuracy of 2% while using a memory of only 1.5 kilobytes. The algorithm parallelizes optimally and adapts to the sliding window model.
Keywords
  • [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS]
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
  • [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG]
  • cardinality estimation
  • Probabilistic algorithm
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    IEEE Transactions on Knowledge and Data Engineering

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    e-Archivo (Carlos III University of Madrid)

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    IEEE Embedded Systems Letters

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    IEEE Transactions on Knowledge and Data Engineering

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    Proceedings of the VLDB Endowment

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    Infoscience (Ecole Polytechnique Fédérale de Lausanne)

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    bioRxiv (Cold Spring Harbor Laboratory)

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    arXiv (Cornell University)

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    bioRxiv (Cold Spring Harbor Laboratory)

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    2022 IEEE 11th IFIP International Conference on Performance Evaluation and Modeling in Wireless and Wired Networks (PEMWN)

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    Research at the University of Copenhagen (University of Copenhagen)

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    Queen Mary Research Online (Queen Mary University of London)

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    Proceedings of the VLDB Endowment

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    IEEE/ACM Transactions on Networking

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    Lecture notes in computer science

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    Lecture notes in computer science

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    Infoscience (Ecole Polytechnique Fédérale de Lausanne)

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    IEEE Transactions on Knowledge and Data Engineering

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    Communications in computer and information science

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    IEEE Embedded Systems Letters

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    bioRxiv (Cold Spring Harbor Laboratory)

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    Proceedings of the ACM on Networking

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    Lecture notes in computer science

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    bioRxiv (Cold Spring Harbor Laboratory)

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    IEEE Transactions on Knowledge and Data Engineering

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    arXiv (Cornell University)

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    Zenodo (CERN European Organization for Nuclear Research)

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    bioRxiv (Cold Spring Harbor Laboratory)

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    arXiv (Cornell University)

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    Proceedings of the VLDB Endowment

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    IEEE/ACM Transactions on Networking

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    bioRxiv (Cold Spring Harbor Laboratory)

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    Aaltodoc (Aalto University)

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    IEEE Transactions on Network Science and Engineering

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    2024 IEEE 40th International Conference on Data Engineering (ICDE)

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    Lecture notes in computer science

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    The VLDB Journal

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    AMS Dottorato Institutional Doctoral Theses Repository (University of Bologna)

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    VBN Forskningsportal (Aalborg Universitet)

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    Datenkompetenz

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    arXiv (Cornell University)

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    IEEE Transactions on Network and Service Management

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    IEEE Transactions on Network Science and Engineering

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    Lecture notes in computer science

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    arXiv (Cornell University)

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    2025 IEEE 25th International Symposium on Cluster, Cloud and Internet Computing (CCGrid)

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    Polish Cartographical Review

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    bioRxiv (Cold Spring Harbor Laboratory)

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    IEEE/ACM Transactions on Networking

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    Lecture notes in business information processing

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    bioRxiv (Cold Spring Harbor Laboratory)

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    IEEE Transactions on Network and Service Management

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    The VLDB Journal

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    arXiv (Cornell University)

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    ACM Transactions on Algorithms

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    2025 IEEE 33rd International Conference on Network Protocols (ICNP)

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    Çukurova Üniversitesi Mühendislik Fakültesi Dergisi

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    IEEE Transactions on Knowledge and Data Engineering

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    IEEE Transactions on Knowledge and Data Engineering

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    Genome biology

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    2025 IEEE Symposium on Computers and Communications (ISCC)

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    DROPS (Schloss Dagstuhl – Leibniz Center for Informatics)

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    Lecture notes in computer science

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    2024 57th IEEE/ACM International Symposium on Microarchitecture (MICRO)

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    Lecture notes in computer science

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    2023 8th International Conference on Data Science in Cyberspace (DSC)

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    2025 IEEE/ACM 33rd International Symposium on Quality of Service (IWQoS)

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    2023 IEEE 31st International Conference on Network Protocols (ICNP)

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    arXiv (Cornell University)

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    IEEE Transactions on Computers

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    arXiv (Cornell University)

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    IEEE INFOCOM 2023 - IEEE Conference on Computer Communications

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    arXiv (Cornell University)

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    2025 34th International Conference on Parallel Architectures and Compilation Techniques (PACT)

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    IEEE Transactions on Network and Service Management

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    IEEE Transactions on Services Computing

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    2021 IEEE Conference on Network Function Virtualization and Software Defined Networks (NFV-SDN)

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    ARCA (Università Ca' Foscari Venezia)

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    arXiv (Cornell University)

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    bioRxiv (Cold Spring Harbor Laboratory)

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    NOMS 2024-2024 IEEE Network Operations and Management Symposium

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    IEEE Access

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    IEEE/ACM Transactions on Networking

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    Scuola Normale Superiore di Pisa

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    IEEE/ACM Transactions on Networking

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    arXiv (Cornell University)

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    Lecture notes in computer science

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    bioRxiv (Cold Spring Harbor Laboratory)

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    IEEE Access

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    e-Archivo (Carlos III University of Madrid)

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  • Routing-Oblivious Network-Wide Measurements

    UCL Discovery (University College London)

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  • SuperFE: A Scalable and Flexible Feature Extractor for ML-based Traffic Analysis Applications

    Proceedings of the Twentieth European Conference on Computer Systems

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    Proceedings of the VLDB Endowment

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    Applied Sciences

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    IEEE/ACM Transactions on Networking

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    bioRxiv (Cold Spring Harbor Laboratory)

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    Encyclopedia of Big Data Technologies

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    Communications in computer and information science

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  • P2Sketch: Finding Persistent Items in Data Streams Based on Periodic Arrival

    2024 IEEE International Performance, Computing, and Communications Conference (IPCCC)

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  • SPAC: Scalable Pattern Approximate Counting in Graph Mining

    Lecture notes in computer science

    Authors : Ruini Xue ORCID, Yijun Wang ORCID, Shengbo Liu ORCID, Yunxiang Li ORCID, Wenhong Tian ORCID, Weimin Zheng ORCID

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  • TTLs Matter: Efficient Cache Sizing with TTL-Aware Miss Ratio Curves and Working Set Sizes

    Proceedings of the Nineteenth European Conference on Computer Systems

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    IEEE INFOCOM 2022 - IEEE Conference on Computer Communications

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    IEEE Transactions on Dependable and Secure Computing

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    Proceedings of the ACM on Management of Data

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    Proceedings of the ACM Special Interest Group on Data Communication

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    Lecture notes on data engineering and communications technologies

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    IEEE Access

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  • Data-Independent Space Partitionings for Summaries

    Warwick Research Archive Portal (University of Warwick)

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    Lecture notes in computer science

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    2023 Third International Conference on Secure Cyber Computing and Communication (ICSCCC)

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    2024 International Scientific and Technical Conference Modern Computer Network Technologies (MoNeTeC)

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    ISPRS International Journal of Geo-Information

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    Encyclopedia of Big Data Technologies

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  • QSketch: An Efficient Sketch for Weighted Cardinality Estimation in Streams

    Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining

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    Lecture notes on data engineering and communications technologies

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  • PS-Sketch: Fast and Accurate Detection of Persistent-Spreaders in High-Speed Networks

    IEEE Transactions on Networking

    Authors : Zhaohui Wang ORCID, Ye Tian ORCID, Yiwen Wu, Wei Chen ORCID, Xinyu Zhang ORCID, Xinming Zhang ORCID

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    Genome biology

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    IEEE Journal on Selected Areas in Information Theory

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    Proceedings of the 2015 ACM on Conference on Online Social Networks

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    2025 World Skills Conference on Universal Data Analytics and Sciences (WorldSUAS)

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    Proceedings of the VLDB Endowment

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    IEEE Transactions on Networking

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    Lecture notes in computer science

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    Computer Communications

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  • The SpaceSaving± Family of Algorithms for Data Streams with Bounded Deletions

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  • A Synopses Data Engine for Interactive Extreme-Scale Analytics

    Zenodo (CERN European Organization for Nuclear Research)

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    LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas)

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    Proceedings of the 8th Asia-Pacific Workshop on Networking

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    IEEE Transactions on Knowledge and Data Engineering

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    Computer Networks

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    ISPRS International Journal of Geo-Information

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  • Scube: Efficient Summarization for Skewed Graph Streams

    2022 IEEE 42nd International Conference on Distributed Computing Systems (ICDCS)

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    Computer Communications

    Authors : Yaime Fernández ORCID, Javier E. Soto ORCID, Carolina Gallardo-Pavesi, Yasmany Prieto ORCID, Cecilia Hernández, Miguel Figueroa

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    Computer Networks

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    Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

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    ACM Transactions on Architecture and Code Optimization

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    Information Systems

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    Lecture notes in computer science

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  • SP-Sketch: Persistent Flow Detection with Sliding Windows on Programmable Switches

    Computers, materials & continua/Computers, materials & continua (Print)

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  • Generalized Measure-Biased Sampling and Priority Sampling

    IEEE Transactions on Knowledge and Data Engineering

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    Wireless networks

    Authors : Shigang Chen ORCID, Min Chen ORCID, Qingjun Xiao ORCID

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    Proceedings of the 26th Annual International Conference on Mobile Computing and Networking

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  • CardSketch: Shift Attention for Network-wide Cardinality Telemetry

    2024 IEEE 49th Conference on Local Computer Networks (LCN)

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    2023 IEEE 39th International Conference on Data Engineering (ICDE)

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    Proceedings of the fifth ACM/IEEE Workshop on Hot Topics in Web Systems and Technologies

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    Proceedings of the 2017 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining 2017

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    ACM Transactions on Sensor Networks

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    Proceedings on Privacy Enhancing Technologies

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  • Path-Centric Cardinality Estimation for Subgraph Matching

    Proceedings of the VLDB Endowment

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    bioRxiv (Cold Spring Harbor Laboratory)

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  • Information theoretic limits of cardinality estimation: Fisher meets Shannon

    Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing

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  • And synopses for all: A synopses data engine for extreme scale analytics-as-a-service

    Dépôt institutionnel de l'Université libre de Bruxelles (Université Libre de Bruxelles)

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  • Differentially-Private Multi-Party Sketching for Large-Scale Statistics

    Proceedings on Privacy Enhancing Technologies

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  • Compact Frequency Estimators in Adversarial Environments

    Repository for Publications and Research Data (ETH Zurich)

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    Data Science and Engineering

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  • Carrera: Enabling High-Performance eBPF-based Sketches in Network Measurement

    2025 IEEE 33rd International Conference on Network Protocols (ICNP)

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    PubMed Central

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  • Online Anomaly Detection over Big Data Streams

    Applied Data Science

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    bioRxiv (Cold Spring Harbor Laboratory)

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    IEEE Transactions on Knowledge and Data Engineering

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    Oxford University Research Archive (ORA) (University of Oxford)

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    Proceedings of the 51st International Conference on Parallel Processing

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    Proceedings of the 16th International Conference on emerging Networking EXperiments and Technologies

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    Lecture notes in computer science

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    Formal Methods in System Design

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  • On Cardinality Estimation Protocols for Wireless Sensor Networks

    Lecture notes in computer science

    Authors : Jacek Cichoń ORCID, Jakub Lemiesz ORCID, Marcin Zawada ORCID

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  • Low-Latency Sliding-Window Aggregation in Worst-Case Constant Time

    Proceedings of the 11th ACM International Conference on Distributed and Event-based Systems

    Authors : Kanat Tangwongsan ORCID, Martin Hirzel ORCID, Scott Schneider

    Journal reference : Volume , 2017, pp. 66-77

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  • Hierarchical Interleaved Bloom Filter: enabling ultrafast, approximate sequence queries

    Genome biology

    Authors : Svenja Mehringer, Enrico Seiler ORCID, Felix Droop, Mitra Darvish ORCID, René Rahn, Martin Vingron ORCID, Knut Reinert ORCID

    Journal reference : Volume 24, 2023, pp. 131

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  • Multiscale Sketch: Finding Heavy Spread Changes in High-Speed Networks Over Sliding Windows

    Lecture notes in computer science

    Authors : Dan Wang, Yang Du, He Huang, Yu-E. Sun, Guoju Gao

    Journal reference : Volume , 2025, pp. 199-210

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  • An Accurate and Invertible Sketch for Super Spread Detection

    Electronics

    Authors : Zheng Zhang ORCID, Jie Lu ORCID, Quan Ren, Ziyong Li ORCID, Yuxiang Hu ORCID, Hongchang Chen ORCID

    Journal reference : Volume 13, 2024, pp. 222

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  • FUS: FPGA-based Universal Sketch with homogeneous and heterogeneous memory architectures

    CCF Transactions on High Performance Computing

    Authors : Yunkun Liao ORCID, Jingya Wu ORCID, Wenyan Lu, Huawei Li ORCID, Xiaowei Li ORCID, Guihai Yan

    Journal reference : Volume 7, 2025, pp. 275-290

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  • Online and Scalable Adaptive Cyber Defense

    Lecture notes in computer science

    Authors : Benjamin W. Priest ORCID, George Cybenko ORCID, Satinder Singh ORCID, Massimiliano Albanese ORCID, Peng Liu ORCID

    Journal reference : Volume , 2019, pp. 232-261

    DOI : 10.1007/978-3-030-30719-6_10

  • Current Trends in Data Summaries

    ACM SIGMOD Record

    Authors : Graham Cormode ORCID

    Journal reference : Volume 50, 2022, pp. 6-15

    DOI : 10.1145/3516431.3516433

  • Half-Xor: A Fully-Dynamic Sketch for Estimating the Number of Distinct Values in Big Tables

    IEEE Transactions on Knowledge and Data Engineering

    Authors : Pinghui Wang ORCID, Dongdong Xie ORCID, Junzhou Zhao ORCID, Jinsong Li ORCID, Zhicheng Li ORCID, Rundong Li ORCID, Yang Ren ORCID, Jia Di ORCID

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  • Bamdam: a post-mapping authentication toolkit for ancient metagenomics

    Genome biology

    Authors : Bianca De Sanctis ORCID, Cade Mirchandani ORCID, Haoran Dong ORCID, Ruairidh Macleod ORCID, Russell Corbett-Detig ORCID, Yucheng Wang ORCID

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  • HSS: A Memory-Efficient, Accurate, and Fast Network Measurement Framework in Sliding Windows

    IEEE Transactions on Network and Service Management

    Authors : Zijun Hang ORCID, Yongjie Wang ORCID, Yuliang Lu ORCID

    Journal reference : Volume 21, 2024, pp. 5958-5976

    DOI : 10.1109/tnsm.2024.3460751

  • Improved metagenomic analysis with Kraken 2

    Genome biology

    Authors : Derrick E. Wood ORCID, Jennifer Lu ORCID, Ben Langmead ORCID

    Journal reference : Volume 20, 2019, pp. 257

    DOI : 10.1186/s13059-019-1891-0

  • CoVnita, an end-to-end privacy-preserving framework for SARS-CoV-2 classification

    Scientific Reports

    Authors : Jun Jie Sim ORCID, Weizhuang Zhou ORCID, Fook Mun Chan, Meenatchi Sundaram Muthu Selva Annamalai ORCID, Xiaoxia Deng, Benjamin Hong Meng Tan ORCID, Khin Mi Mi Aung ORCID

    Journal reference : Volume 13, 2023, pp. 7461

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  • SetSketch

    arXiv (Cornell University)

    Authors : Otmar Ertl

    Journal reference : Volume 14, 2021, pp. 2244-2257

    DOI : 10.14778/3476249.3476276

  • SpaceSaving$^\pm$: An Optimal Algorithm for Frequency Estimation and Frequent items in the Bounded Deletion Model

    arXiv (Cornell University)

    Authors : Zhao, Agrawal, Abbadi, Metwally

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    DOI : 10.14778/3514061.3514068

  • Enhanced Machine Learning Sketches for Network Measurements

    IEEE Transactions on Computers

    Authors : Hengrui Wang ORCID, Huiping Lin ORCID, Zheng Zhong, Tong Yang ORCID, Muhammad Shahzad ORCID

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  • An LDP Compatible Sketch for Securely Approximating Set Intersection Cardinalities

    Proceedings of the ACM on Management of Data

    Authors : Pinghui Wang ORCID, Yitong Liu ORCID, Zhicheng Li ORCID, Rundong Li ORCID

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  • Scotch

    Proceedings of the VLDB Endowment

    Authors : Martin Kiefer ORCID, Ilias Poulakis, Sebastian Breß, Volker Markl ORCID

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  • Protecting Privacy in Volunteered Geographic Information Processing

    Volunteered Geographic Information

    Authors : Marc Löchner ORCID, Alexander Dunkel ORCID, Dirk Burghardt ORCID

    Journal reference : Volume , 2023, pp. 277-297

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  • Expected 10-anonymity of HyperLogLog sketches for federated queries of clinical data repositories

    bioRxiv (Cold Spring Harbor Laboratory)

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  • Secure federated Boolean count queries using fully-homomorphic cryptography

    bioRxiv (Cold Spring Harbor Laboratory)

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    Naučnyj servis v seti internet

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    Proceedings of the 2017 ACM International Conference on Management of Data

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  • Timely Semantics: A Study of a Stream-Based Ranking System for Entity Relationships

    Lecture notes in computer science

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  • ByteCard: Enhancing ByteDance's Data Warehouse with Learned Cardinality Estimation

    Companion of the 2024 International Conference on Management of Data

    Authors : Yuxing Han ORCID, Haoyu Wang, Lixiang Chen ORCID, Yifeng Dong, Xing Chen ORCID, Benquan Yu ORCID, Chengcheng Yang ORCID, Weining Qian ORCID

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  • BeauCoup

    Proceedings of the Annual conference of the ACM Special Interest Group on Data Communication on the applications, technologies, architectures, and protocols for computer communication

    Authors : Xiaoqi Chen ORCID, Shir Landau-Feibish, Mark Braverman ORCID, Jennifer Rexford ORCID

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    Discrete Applied Mathematics

    Authors : Frédéric Giroire ORCID

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  • Learned Bloom Filter for Multi-key Membership Testing

    Lecture notes in computer science

    Authors : Yunchuan Li ORCID, Ziwei Wang ORCID, Ruixin Yang ORCID, Yan Zhao ORCID, Rui Zhou ORCID, Kai Zheng ORCID

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  • CARBINE: Exploring Additional Properties of HyperLogLog for Secure and Robust Flow Cardinality Estimation

    IEEE INFOCOM 2024 - IEEE Conference on Computer Communications

    Authors : Damu Ding ORCID

    Journal reference : Volume , 2024, pp. 471-480

    DOI : 10.1109/infocom52122.2024.10621185
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