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To approximate sums of values in key-value data streams, sketches are widely used in databases and networking systems. They offer high-confidence approximations for any given key while ensuring low time and space overhead. While existing…

Data Structures and Algorithms · Computer Science 2024-06-04 Yuhan Wu , Hanbo Wu , Xilai Liu , Yikai Zhao , Tong Yang , Kaicheng Yang , Sha Wang , Lihua Miao , Gaogang Xie

Sketching and streaming algorithms are in the forefront of current research directions for cut problems in graphs. In the streaming model, we show that $(1-\epsilon)$-approximation for Max-Cut must use $n^{1-O(\epsilon)}$ space; moreover,…

Data Structures and Algorithms · Computer Science 2026-02-23 Dmitry Kogan , Robert Krauthgamer

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…

Data Structures and Algorithms · Computer Science 2023-04-11 Matthew Fahrbach , Gary L. Miller , Richard Peng , Saurabh Sawlani , Junxing Wang , Shen Chen Xu

We initiate the study of the Interval Selection problem in the (streaming) sliding window model of computation. In this problem, an algorithm receives a potentially infinite stream of intervals on the line, and the objective is to maintain…

Data Structures and Algorithms · Computer Science 2024-11-13 Cezar-Mihail Alexandru , Christian Konrad

Algorithms in the data stream model use $O(polylog(N))$ space to compute some property of an input of size $N$, and many of these algorithms are implemented and used in practice. However, sketching algorithms in the graph semi-streaming…

Data Structures and Algorithms · Computer Science 2025-04-25 Michael A. Bender , Martín Farach-Colton , Riko Jacob , Hanna Komlós , David Tench , Evan West

We consider the problem of selecting non-zero entries of a matrix $A$ in order to produce a sparse sketch of it, $B$, that minimizes $\|A-B\|_2$. For large $m \times n$ matrices, such that $n \gg m$ (for example, representing $n$…

Machine Learning · Computer Science 2013-11-20 Dimitris Achlioptas , Zohar Karnin , Edo Liberty

We study the problem of partitioning integer sequences in the one-pass data streaming model. Given is an input stream of integers $X \in \{0, 1, \dots, m \}^n$ of length $n$ with maximum element $m$, and a parameter $p$. The goal is to…

Data Structures and Algorithms · Computer Science 2014-07-08 Christian Konrad , László Kozma

We propose two one-pass streaming algorithms for the $\mathcal{NP}$-hard hypergraph matching problem. The first algorithm stores a small subset of potential matching edges in a stack using dual variables to select edges. It has an…

Data Structures and Algorithms · Computer Science 2025-07-09 Henrik Reinstädtler , S M Ferdous , Alex Pothen , Bora Uçar , Christian Schulz

Network stream mining is fundamental to many network operations. Sketches, as compact data structures that offer low memory overhead with bounded accuracy, have emerged as a promising solution for network stream mining. Recent studies…

Networking and Internet Architecture · Computer Science 2025-02-12 Yuanpeng Li , Zhen Xu , Zongwei Lv , Yannan Hu , Yong Cui , Tong Yang

A semi-streaming algorithm in dynamic graph streams processes any $n$-vertex graph by making one or multiple passes over a stream of insertions and deletions to edges of the graph and using $O(n \cdot \mbox{polylog}(n))$ space.…

Data Structures and Algorithms · Computer Science 2024-07-31 Sepehr Assadi , Soheil Behnezhad , Christian Konrad , Kheeran K. Naidu , Janani Sundaresan

We explore the use of local algorithms in the design of streaming algorithms for the Maximum Directed Cut problem. Specifically, building on the local algorithm of Buchbinder et al. (FOCS'12) and Censor-Hillel et al. (ALGOSENSORS'17), we…

Data Structures and Algorithms · Computer Science 2024-12-02 Raghuvansh R. Saxena , Noah G. Singer , Madhu Sudan , Santhoshini Velusamy

Given a matrix $A\in \mathbb{R}^{n\times d}$ and a vector $b\in \mathbb{R}^n$, we consider the regression problem with $\ell_\infty$ guarantees: finding a vector $x'\in \mathbb{R}^d$ such that $ \|x'-x^*\|_\infty \leq…

Data Structures and Algorithms · Computer Science 2023-02-02 Zhao Song , Mingquan Ye , Junze Yin , Lichen Zhang

We study the relation between streaming algorithms and linear sketching algorithms, in the context of binary updates. We show that for inputs in $n$ dimensions, the existence of efficient streaming algorithms which can process $\Omega(n^2)$…

Computational Complexity · Computer Science 2018-09-25 Kaave Hosseini , Shachar Lovett , Grigory Yaroslavtsev

We study the Multiple Cluster Scheduling problem and the Multiple Strip Packing problem. For both problems, there is no algorithm with approximation ratio better than $2$ unless $P = NP$. In this paper, we present an algorithm with…

Data Structures and Algorithms · Computer Science 2019-02-12 Klaus Jansen , Malin Rau

Randomized algorithms in numerical linear algebra can be fast, scalable and robust. This paper examines the effect of sketching on the right singular vectors corresponding to the smallest singular values of a tall-skinny matrix. We analyze…

Numerical Analysis · Mathematics 2023-05-29 Yuji Nakatsukasa , Taejun Park

We investigate the scheduling of $n$ jobs divided into $c$ classes on $m$ identical parallel machines. For every class there is a setup time which is required whenever a machine switches from the processing of one class to another class.…

Data Structures and Algorithms · Computer Science 2019-05-02 Max A. Deppert , Klaus Jansen

In the numerical linear algebra community, it was suggested that to obtain nearly optimal bounds for various problems such as rank computation, finding a maximal linearly independent subset of columns (a basis), regression, or low-rank…

Data Structures and Algorithms · Computer Science 2021-11-04 Nadiia Chepurko , Kenneth L. Clarkson , Praneeth Kacham , David P. Woodruff

We study classic streaming and sparse recovery problems using deterministic linear sketches, including l1/l1 and linf/l1 sparse recovery problems (the latter also being known as l1-heavy hitters), norm estimation, and approximate inner…

Data Structures and Algorithms · Computer Science 2012-12-12 Jelani Nelson , Huy Nguyen , David P. Woodruff

Linear sketching algorithms have been widely used for processing large-scale distributed and streaming datasets. Their popularity is largely due to the fact that linear sketches can be naturally composed in the distributed model and be…

Data Structures and Algorithms · Computer Science 2017-03-28 Jiecao Chen , Qin Zhang

We consider statistical and algorithmic aspects of solving large-scale least-squares (LS) problems using randomized sketching algorithms. Prior results show that, from an \emph{algorithmic perspective}, when using sketching matrices…

Machine Learning · Statistics 2015-05-26 Garvesh Raskutti , Michael Mahoney