相关论文: Back to the Future: an Even More Nearly Optimal Ca…
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…
This paper presents new methods to estimate the cardinalities of data sets recorded by HyperLogLog sketches. A theoretically motivated extension to the original estimator is presented that eliminates the bias for small and large…
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~$n$…
Non-monotone constrained submodular maximization plays a crucial role in various machine learning applications. However, existing algorithms often struggle with a trade-off between approximation guarantees and practical efficiency. The…
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…
We introduce the Huffman-Bucket Sketch (HBS), a simple, mergeable data structure that losslessly compresses a HyperLogLog (HLL) sketch with $m$ registers to optimal space $O(m+\log n)$ bits, with amortized constant-time updates, acting as a…
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…
Cardinality estimation is the task of approximating the number of distinct elements in a large dataset with possibly repeating elements. LogLog and HyperLogLog (c.f. Durand and Flajolet [ESA 2003], Flajolet et al. [Discrete Math Theor.…
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…
This paper considers the problem of cardinality estimation in data stream applications. We present a statistical analysis of probabilistic counting algorithms, focusing on two techniques that use pseudo-random variates to form…
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…
In 2020 Blasiok (ACM Trans. Algorithms 16(2) 3:1-3:28) constructed an optimal space streaming algorithm for the cardinality estimation problem with the space complexity of $\mathcal O(\varepsilon^{-2} \ln(\delta^{-1}) + \ln n)$ where…
We propose an advancement in cardinality estimation by augmenting autoregressive models with a traditional grid structure. The novel hybrid estimator addresses the limitations of autoregressive models by creating a smaller representation of…
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…
Extracting cosmological parameters from galaxy/halo catalogues with sub-percent level accuracy is an important aspect of modern cosmology, especially in view of ongoing and upcoming surveys such as Euclid, DESI, and LSST. While traditional…
Cardinality estimation algorithms receive a stream of elements whose order might be arbitrary, with possible repetitions, and return the number of distinct elements. Such algorithms usually seek to minimize the required storage and…
The Harrow-Hassidim-Lloyd (HHL) algorithm is a quantum algorithm for solving systems of linear equations that, in principle, offers an exponential improvement in scaling with the system size compared to classical approaches. In this work,…
We present several novel encodings for cardinality constraints, which use fewer clauses than previous encodings and, more importantly, introduce new generally applicable techniques for constructing compact encodings. First, we present a CNF…
Subgraph counting is a fundamental problem in understanding and analyzing graph structured data, yet computationally challenging. This calls for an accurate and efficient algorithm for Subgraph Cardinality Estimation, which is to estimate…
DB engines produce efficient query execution plans by relying on cost models. Practical implementations estimate cardinality of queries using heuristics, with magic numbers tuned to improve average performance on benchmarks. Empirically,…