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Approximating the length of the longest increasing sequence (LIS) of an array is a well-studied problem. We study this problem in the data stream model, where the algorithm is allowed to make a single left-to-right pass through the array…

Data Structures and Algorithms · Computer Science 2013-04-16 Michael Saks , C. Seshadhri

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

We revisit the classic basic counting problem in the distributed streaming model that was studied by Gibbons and Tirthapura (GT). In the solution for maintaining an $(\epsilon,\delta)$-estimate, as what GT's method does, we make the…

Data Structures and Algorithms · Computer Science 2013-12-03 Bojian Xu

Consider the following distance query for an $n$-node graph $G$ undergoing edge insertions and deletions: given two sets of nodes $I$ and $J$, return the distances between every pair of nodes in $I\times J$. This query is rather general and…

Data Structures and Algorithms · Computer Science 2019-10-18 Jan van den Brand , Danupon Nanongkai

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 consider computing a longest palindrome in the streaming model, where the symbols arrive one-by-one and we do not have random access to the input. While computing the answer exactly using sublinear space is not possible in such a…

Data Structures and Algorithms · Computer Science 2016-10-12 Paweł Gawrychowski , Oleg Merkurev , Arseny M. Shur , Przemysław Uznański

The seminal work of Ahn, Guha, and McGregor in 2012 introduced the graph sketching technique and used it to present the first streaming algorithms for various graph problems over dynamic streams with both insertions and deletions of edges.…

Data Structures and Algorithms · Computer Science 2023-12-11 Sepehr Assadi , Gillat Kol , Zhijun Zhang

In the maximum coverage problem we are given $d$ subsets from a universe $[n]$, and the goal is to output $k$ subsets such that their union covers the largest possible number of distinct items. We present the first algorithm for maximum…

Data Structures and Algorithms · Computer Science 2025-05-08 Alina Ene , Alessandro Epasto , Vahab Mirrokni , Hoai-An Nguyen , Huy L. Nguyen , David P. Woodruff , Peilin Zhong

Streaming analytics are essential in a large range of applications, including databases, networking, and machine learning. To optimize performance, practitioners are increasingly offloading such analytics to network nodes such as switches.…

Networking and Internet Architecture · Computer Science 2025-03-19 Jonatan Langlet , Peiqing Chen , Michael Mitzenmacher , Ran Ben Basat , Zaoxing Liu , Gianni Antichi

Imagine a large graph that is being processed by a cluster of computers, e.g., described by the $k$-machine model or the Massively Parallel Computation Model. The graph, however, is not static; instead it is receiving a constant stream of…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-02-18 Seth Gilbert , Lawrence Li

Graph streams represent data interactions in real applications. The mining of graph streams plays an important role in network security, social network analysis, and traffic control, among others. However, the sheer volume and high dynamics…

Databases · Computer Science 2023-04-07 Yiling Zeng , Chunyao Song , Yuhan Li , Tingjian Ge

We develop a new algorithmic technique that allows to transfer some constant time approximation algorithms for general graphs into random order streaming algorithms. We illustrate our technique by proving that in random order streams with…

Data Structures and Algorithms · Computer Science 2017-11-15 Pan Peng , Christian Sohler

Time-evolving stream datasets exist ubiquitously in many real-world applications where their inherent hot keys often evolve over times. Nevertheless, few existing solutions can provide efficient load balance on these time-evolving datasets…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-06-05 Yu Huang

The turnstile continual release model of differential privacy captures scenarios where a privacy-preserving real-time analysis is sought for a dataset evolving through additions and deletions. In typical applications of real-time data…

Data Structures and Algorithms · Computer Science 2025-05-30 Rachel Cummings , Alessandro Epasto , Jieming Mao , Tamalika Mukherjee , Tingting Ou , Peilin Zhong

An $\alpha$-spanner of a graph $ G $ is a subgraph $ H $ such that $ H $ preserves all distances of $ G $ within a factor of $ \alpha $. In this paper, we give fully dynamic algorithms for maintaining a spanner $ H $ of a graph $ G $…

Data Structures and Algorithms · Computer Science 2018-03-02 Greg Bodwin , Sebastian Krinninger

Sketches are probabilistic data structures that can provide approximate results within mathematically proven error bounds while using orders of magnitude less memory than traditional approaches. They are tailored for streaming data analysis…

Data Structures and Algorithms · Computer Science 2019-03-05 Fatih Taşyaran , Kerem Yıldırır , Kamer Kaya , Mustafa Kemal Taş

In a sequence of recent results (PODC 2015 and PODC 2016), the running time of the fastest algorithm for the \emph{minimum spanning tree (MST)} problem in the \emph{Congested Clique} model was first improved to $O(\log \log \log n)$ from…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-10-19 Sriram V. Pemmaraju , Vivek B. Sardeshmukh

Mini-batch optimization has proven to be a powerful paradigm for large-scale learning. However, the state of the art parallel mini-batch algorithms assume synchronous operation or cyclic update orders. When worker nodes are heterogeneous…

Optimization and Control · Mathematics 2015-05-20 Hamid Reza Feyzmahdavian , Arda Aytekin , Mikael Johansson

One of the oldest problems in the data stream model is to approximate the $p$-th moment $\|\mathcal{X}\|_p^p = \sum_{i=1}^n |\mathcal{X}_i|^p$ of an underlying vector $\mathcal{X} \in \mathbb{R}^n$, which is presented as a sequence of…

Data Structures and Algorithms · Computer Science 2019-07-15 Rajesh Jayaram , David P. Woodruff

Modern data stream applications demand memory-efficient solutions for accurately tracking frequent items, such as heavy hitters and heavy changers, under strict resource constraints. Traditional sketches face inherent accuracy-memory…

Databases · Computer Science 2025-05-20 Zicang Xu , Yuxuan Tian , Yuhan Wu , Tong Yang