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Count distinct or cardinality estimates are widely used in network monitoring for security. They can be used, for example, to detect the malware spread, network scans, or a denial of service attack. There are many algorithms to estimate…

Cryptography and Security · Computer Science 2023-03-07 Pedro Reviriego , Daniel Ting

Cardinality estimators like HyperLogLog are sketching algorithms that estimate the number of distinct elements in a large multiset. Their use in privacy-sensitive contexts raises the question of whether they leak private information. In…

Cryptography and Security · Computer Science 2018-12-20 Damien Desfontaines , Andreas Lochbihler , David Basin

Cardinality estimation - calculating the number of distinct elements in a stream - is a longstanding problem with applications from networking to bioinformatics. HyperLogLog (HLL), the prevailing standard, has a well-known error spike in…

Data Structures and Algorithms · Computer Science 2026-05-14 Brian Bushnell

Flow cardinality estimation is the problem of estimating the number of distinct elements in a data flow, often with a stringent memory constraint. It has wide applications in network traffic measurement and in database systems. The virtual…

Information Theory · Computer Science 2018-12-10 Zeyu Zhou

We discuss the problem of counting distinct elements in a stream. A stream is usually considered as a sequence of elements that come one at a time. An exact solution to the problem requires memory space of the size of the stream. For many…

Data Structures and Algorithms · Computer Science 2021-06-18 Tal Ohayon

We present HyperLogLogLog, a practical compression of the HyperLogLog sketch that compresses the sketch from $O(m\log\log n)$ bits down to $m \log_2\log_2\log_2 m + O(m+\log\log n)$ bits for estimating the number of distinct elements~$n$…

Data Structures and Algorithms · Computer Science 2022-05-24 Matti Karppa , Rasmus Pagh

The information presented in this paper defines LogLog-Beta. LogLog-Beta is a new algorithm for estimating cardinalities based on LogLog counting. The new algorithm uses only one formula and needs no additional bias corrections for the…

Data Structures and Algorithms · Computer Science 2020-12-22 Jason Qin , Denys Kim , Yumei Tung

Data sketches are a set of widely used approximated data summarizing techniques. Their fundamental property is sub-linear memory complexity on the input cardinality, an important aspect when processing streams or data sets with a vast base…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-10-21 Amit Kulkarni , Monica Chiosa , Thomas B. Preußer , Kaan Kara , David Sidler , Gustavo Alonso

This work presents new cardinality estimation methods for data sets recorded by HyperLogLog sketches. A simple derivation of the original estimator was found, that also gives insight how to correct its deficiencies. The result is an…

Data Structures and Algorithms · Computer Science 2017-06-23 Otmar Ertl

Accurately detecting super host that establishes connections to a large number of distinct peers is significant for mitigating web attacks and ensuring high quality of web service. Existing sketch-based approaches estimate the number of…

Networking and Internet Architecture · Computer Science 2026-04-06 Yilin Zhao , Jiawei Huang , Xianshi Su , Weihe Li , Xin Li , Yan Liu , Jiacheng Xie , Qichen Su , Jin Ye , Wanchun Jiang , Jianxin Wang

Cardinalities estimation is an important research topic in network management and security. How to solve this problem under sliding time window is a hot topic. HyperLogLog is a memory efficient algorithm work under a fixed time window. A…

Networking and Internet Architecture · Computer Science 2018-11-01 Jie Xu

Since its invention HyperLogLog has become the standard algorithm for approximate distinct counting. Due to its space efficiency and suitability for distributed systems, it is widely used and also implemented in numerous databases. This…

Data Structures and Algorithms · Computer Science 2024-06-11 Otmar Ertl

Modern software systems generate massive volumes of runtime logs, necessitating efficient and accurate log parsing to enable critical downstream tasks such as anomaly detection and root cause analysis. Recently, large language models (LLMs)…

Software Engineering · Computer Science 2025-09-17 Yilun Wang , Pengfei Chen , Haiyu Huang , Zilong He , Gou Tan , Chuanfu Zhang , Jingkai He , Zibin Zheng

Keyloggers remain a serious threat in modern cybersecurity, silently capturing user keystrokes to steal credentials and sensitive information. Traditional defenses focus mainly on detection and removal, which can halt malicious activity but…

Cryptography and Security · Computer Science 2025-08-07 Md Sajidul Islam Sajid , Shihab Ahmed , Ryan Sosnoski

Intrusion Detection and Prevention Systems (IDS/IPS) in large enterprises can generate hundreds of thousands of alerts per hour, overwhelming analysts with logs requiring rapidly evolving expertise. Conventional machine-learning detectors…

Cryptography and Security · Computer Science 2026-02-10 Francesco Blefari , Cristian Cosentino , Francesco Aurelio Pironti , Angelo Furfaro , Fabrizio Marozzo

Hyperdimensional Computing (HDC) is facing infringement issues due to straightforward computations. This work, for the first time, raises a critical vulnerability of HDC, an attacker can reverse engineer the entire model, only requiring the…

Cryptography and Security · Computer Science 2022-03-21 Shijin Duan , Shaolei Ren , Xiaolin Xu

Online monitoring user cardinalities (or degrees) in graph streams is fundamental for many applications. For example in a bipartite graph representing user-website visiting activities, user cardinalities (the number of distinct visited…

Data Structures and Algorithms · Computer Science 2018-11-27 Pinghui Wang , Peng Jia , Xiangliang Zhang , Jing Tao , Xiaohong Guan , Don Towsley

Several applications require counting the number of distinct items in the data, which is known as the cardinality counting problem. Example applications include health applications such as rare disease patients counting for adequate…

Cryptography and Security · Computer Science 2023-01-11 Nan Wu , Dinusha Vatsalan , Mohamed Ali Kaafar , Sanath Kumar Ramesh

Cardinality estimation algorithms receive a stream of elements, with possible repetitions, and return the number of distinct elements in the stream. Such algorithms seek to minimize the required memory and CPU resource consumption at the…

Networking and Internet Architecture · Computer Science 2019-03-15 Reuven Cohen , Yuval Nezri

This paper introduces a novel algorithm for cardinality, i.e., the number of nodes, estimation in large scale anonymous graphs using statistical inference methods. Applications of this work include estimating the number of sensor devices,…

Information Theory · Computer Science 2015-08-21 Ahmed Douik , Salah A. Aly , Tareq Y. Al-Naffouri , Mohamed-Slim Alouini
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