Related papers: Nearly Optimal Distinct Elements and Heavy Hitters…

In this work we focus on the problem of finding the heaviest-k and lightest-k hitters in a sliding window data stream. The most recent research endeavours have yielded an epsilon-approximate algorithm with update operations in constant time…

We study algorithms for the sliding-window model, an important variant of the data-stream model, in which the goal is to compute some function of a fixed-length suffix of the stream. We extend the smooth-histogram framework of Braverman and…

We derive new time-space tradeoff lower bounds and algorithms for exactly computing statistics of input data, including frequency moments, element distinctness, and order statistics, that are simple to calculate for sorted data. We develop…

We consider the heavy-hitters and $F_p$ moment estimation problems in the sliding window model. For $F_p$ moment estimation with $1<p\leq 2$, we show that it is possible to give a $(1\pm \epsilon)$ multiplicative approximation to the $F_p$…

Given a stream $x_1,x_2,\dots,x_n$ of items from a Universe $U$ of size poly$(n)$, and a parameter $\epsilon>0$, an item $i\in U$ is said to be an $\ell_2$ heavy hitter if its frequency $f_i$ in the stream is at least $\sqrt{\epsilon F_2}$,…

In turnstile $\ell_p$ $\varepsilon$-heavy hitters, one maintains a high-dimensional $x\in\mathbb{R}^n$ subject to $\texttt{update}(i,\Delta)$ causing $x_i\leftarrow x_i + \Delta$, where $i\in[n]$, $\Delta\in\mathbb{R}$. Upon receiving a…

In the sliding window model, we are required to maintain the target statistics over the most recent $n$ elements of a data stream, which is captured by a window of size $n$ sliding over the data stream. Exact computation usually requires…

Let $p$ be an unknown and arbitrary probability distribution over $[0,1)$. We consider the problem of {\em density estimation}, in which a learning algorithm is given i.i.d. draws from $p$ and must (with high probability) output a…

The distinct elements problem is one of the fundamental problems in streaming algorithms --- given a stream of integers in the range $\{1,\ldots,n\}$, we wish to provide a $(1+\varepsilon)$ approximation to the number of distinct elements…

The ability to detect, in real-time, heavy hitters is beneficial to many network applications, such as DoS and anomaly detection. Through programmable languages as P4, heavy hitter detection can be implemented directly in the data-plane,…

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…

We consider the problems of distributed heavy hitters and frequency moments in both the coordinator model and the distributed tracking model (also known as the distributed functional monitoring model). We present simple and optimal (up to…

We give the first optimal bounds for returning the $\ell_1$-heavy hitters in a data stream of insertions, together with their approximate frequencies, closing a long line of work on this problem. For a stream of $m$ items in $\{1, 2, \dots,…

The sliding window model generalizes the standard streaming model and often performs better in applications where recent data is more important or more accurate than data that arrived prior to a certain time. We study the problem of…

We initiate the study of numerical linear algebra in the sliding window model, where only the most recent $W$ updates in a stream form the underlying data set. We first introduce a unified row-sampling based framework that gives randomized…

The sliding window model of computation captures scenarios in which data are continually arriving in the form of a stream, and only the most recent $w$ items are used for analysis. In this setting, an algorithm needs to accurately track…

Given a data stream $\mathcal{A} = \langle a_1, a_2, \ldots, a_m \rangle$ of $m$ elements where each $a_i \in [n]$, the Distinct Elements problem is to estimate the number of distinct elements in $\mathcal{A}$.Distinct Elements has been a…

We study the problem of distributed distinct element estimation, where $\alpha$ servers each receive a subset of a universe $[n]$ and aim to compute a $(1+\varepsilon)$-approximation to the number of distinct elements using minimal…

Maximizing submodular functions under cardinality constraints lies at the core of numerous data mining and machine learning applications, including data diversification, data summarization, and coverage problems. In this work, we study this…

We study the problem of robustly learning multi-dimensional histograms. A $d$-dimensional function $h: D \rightarrow \mathbb{R}$ is called a $k$-histogram if there exists a partition of the domain $D \subseteq \mathbb{R}^d$ into $k$…