Related papers: Breaking the Quadratic Barrier: Robust Cardinality…
Cardinality sketches are compact data structures for representing sets or vectors. These sketches are space-efficient, typically requiring only logarithmic storage in the input size, and enable approximation of cardinality (or the number of…
Cardinality sketches are popular data structures that enhance the efficiency of working with large data sets. The sketches are randomized representations of sets that are only of logarithmic size but can support set merges and approximate…
CountSketch is a popular dimensionality reduction technique that maps vectors to a lower dimension using randomized linear measurements. The sketch supports recovering $\ell_2$-heavy hitters of a vector (entries with $v[i]^2 \geq…
Estimating cardinality, i.e., the number of distinct elements, of a data stream is a fundamental problem in areas like databases, computer networks, and information retrieval. This study delves into a broader scenario where each element…
Structured high-cardinality data arises in many domains, and poses a major challenge for both modeling and inference. Graphical models are a popular approach to modeling structured data but they are unsuitable for high-cardinality…
Linear bandits have become a cornerstone of online learning and sequential decision-making, providing solid theoretical foundations for balancing exploration and exploitation. Within this domain, matrix sketching serves as a critical…
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…
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 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…
Dimensionality reduction via linear sketching is a powerful and widely used technique, but it is known to be vulnerable to adversarial inputs. We study the black-box adversarial setting, where a fixed, hidden sketching matrix $A \in R^{k…
We introduce a novel technique for ``lifting'' dimension lower bounds for linear sketches in the real-valued setting to dimension lower bounds for linear sketches with polynomially-bounded integer entries when the input is a…
In this paper we address cardinality estimation problem which is an important subproblem in query optimization. Query optimization is a part of every relational DBMS responsible for finding the best way of the execution for the given query.…
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…
Quantile summaries provide a scalable way to estimate the distribution of individual attributes in large datasets that are often distributed across multiple machines or generated by sensor networks. ReqSketch (arXiv:2004.01668) is currently…
Interactive analytics increasingly involves querying for quantiles over sub-populations of high cardinality datasets. Data processing engines such as Druid and Spark use mergeable summaries to estimate quantiles, but summary merge times can…
The majority of streaming problems are defined and analyzed in a static setting, where the data stream is any worst-case sequence of insertions and deletions that is fixed in advance. However, many real-world applications require a more…
We propose a randomized algorithm with quadratic convergence rate for convex optimization problems with a self-concordant, composite, strongly convex objective function. Our method is based on performing an approximate Newton step using a…
Given a persistence diagram with $n$ points, we give an algorithm that produces a sequence of $n$ persistence diagrams converging in bottleneck distance to the input diagram, the $i$th of which has $i$ distinct (weighted) points and is a…
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.…
Graph sketching has emerged as a powerful technique for processing massive graphs that change over time (i.e., are presented as a dynamic stream of edge updates) over the past few years, starting with the work of Ahn, Guha and McGregor…