Related papers: Unmasking Vulnerabilities: Cardinality Sketches un…
Sketches have shown high accuracy in multi-way join cardinality estimation, a critical problem in cost-based query optimization. Accurately estimating the cardinality of a join operation -- analogous to its computational cost -- allows the…
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…
Join ordering is a key factor in query performance, yet traditional cost-based optimizers often produce sub-optimal plans due to inaccurate cardinality estimates in multi-predicate, multi-join queries. Existing alternatives such as…
Sketch-based streaming algorithms allow efficient processing of big data. These algorithms use small fixed-size storage to store a summary ("sketch") of the input data, and use probabilistic algorithms to estimate the desired quantity.…
We consider least-squares problems with quadratic regularization and propose novel sketching-based iterative methods with an adaptive sketch size. The sketch size can be as small as the effective dimension of the data matrix to guarantee…
Graph Neural Networks (GNNs) are widely applied to graph learning problems such as node classification. When scaling up the underlying graphs of GNNs to a larger size, we are forced to either train on the complete graph and keep the full…
With the increasing rate of data generated by critical systems, estimating functions on streaming data has become essential. This demand has driven numerous advancements in algorithms designed to efficiently query and analyze one or more…
Linear sketches are powerful algorithmic tools that turn an n-dimensional input into a concise lower-dimensional representation via a linear transformation. Such sketches have seen a wide range of applications including norm estimation over…
Anomaly detection in dynamic graphs is essential for identifying malicious activities, fraud, and unexpected behaviors in real-world systems such as cybersecurity and power grids. However, existing approaches struggle with scalability,…
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…
With the exponentially growing Internet traffic, sketch data structure with a probabilistic algorithm has been expected to be an alternative solution for non-compromised (non-selective) security monitoring. While facilitating counting…
Matrix trace estimation is ubiquitous in machine learning applications and has traditionally relied on Hutchinson's method, which requires $O(\log(1/\delta)/\epsilon^2)$ matrix-vector product queries to achieve a $(1 \pm…
Large, distributed data streams are now ubiquitous. High-accuracy sketches with low memory overhead have become the de facto method for analyzing this data. For instance, if we wish to group data by some label and report the largest counts…
In all state-of-the-art sketching and coreset techniques for clustering, as well as in the best known fixed-parameter tractable approximation algorithms, randomness plays a key role. For the classic $k$-median and $k$-means problems, there…
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…
Motivated by the study of matrix elimination orderings in combinatorial scientific computing, we utilize graph sketching and local sampling to give a data structure that provides access to approximate fill degrees of a matrix undergoing…
Sketched gradient algorithms have been recently introduced for efficiently solving the large-scale constrained Least-squares regressions. In this paper we provide novel convergence analysis for the basic method {\it Gradient Projection…
Recent work has explored transforming data sets into smaller, approximate summaries in order to scale Bayesian inference. We examine a related problem in which the parameters of a Bayesian model are very large and expensive to store in…
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.…
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,…