Related papers: An Optimal Algorithm for l1-Heavy Hitters in Inser…
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 $\sqrt{\epsilon F_2}$,…
Given a stream $p_1, \ldots, p_m$ of items from a universe $\mathcal{U}$, which, without loss of generality we identify with the set of integers $\{1, 2, \ldots, n\}$, we consider the problem of returning all $\ell_2$-heavy hitters, i.e.,…
An old and fundamental problem in databases and data streams is that of finding the heavy hitters, also known as the top-$k$, most popular items, frequent items, elephants, or iceberg queries. There are several variants of this problem,…
The task of finding heavy hitters is one of the best known and well studied problems in the area of data streams. One is given a list $i_1,i_2,\ldots,i_m\in[n]$ and the goal is to identify the items among $[n]$ that appear frequently in the…
Detecting frequent elements is among the oldest and most-studied problems in the area of data streams. Given a stream of $m$ data items in $\{1, 2, \dots, n\}$, the objective is to output items that appear at least $d$ times, for some…
For each $p \in (0,2]$, we present a randomized algorithm that returns an $\epsilon$-approximation of the $p$th frequency moment of a data stream $F_p = \sum_{i = 1}^n \abs{f_i}^p$. The algorithm requires space $O(\epsilon^{-2} \log…
We revisit the problem of estimating the profile (also known as the rarity) in the data stream model. Given a sequence of $m$ elements from a universe of size $n$, its profile is a vector $\phi$ whose $i$-th entry $\phi_i$ represents the…
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…
Given data stream $D = \{p_1,p_2,...,p_m\}$ of size $m$ of numbers from $\{1,..., n\}$, the frequency of $i$ is defined as $f_i = |\{j: p_j = i\}|$. The $k$-th \emph{frequency moment} of $D$ is defined as $F_k = \sum_{i=1}^n f_i^k$. We…
When facing a very large stream of data, it is often desirable to extract most important statistics online in a short time and using small memory. For example, one may want to quickly find the most influential users generating posts online…
Frequency estimation of elements is an important task for summarizing data streams and machine learning applications. The problem is often addressed by using streaming algorithms with sublinear space data structures. These algorithms allow…
We present a novel approach for the problem of frequency estimation in data streams that is based on optimization and machine learning. Contrary to state-of-the-art streaming frequency estimation algorithms, which heavily rely on random…
The Hierarchical Heavy Hitters problem extends the notion of frequent items to data arranged in a hierarchy. This problem has applications to network traffic monitoring, anomaly detection, and DDoS detection. We present a new streaming…
The \emph{$\ell_2$ tracking problem} is the task of obtaining a streaming algorithm that, given access to a stream of items $a_1,a_2,a_3,\ldots$ from a universe $[n]$, outputs at each time $t$ an estimate to the $\ell_2$ norm of the…
We initiate a broad study of classical problems in the streaming model with insertions and deletions in the setting where we allow the approximation factor $\alpha$ to be much larger than $1$. Such algorithms can use significantly less…
We consider message-efficient continuous random sampling from a distributed stream, where the probability of inclusion of an item in the sample is proportional to a weight associated with the item. The unweighted version, where all weights…
We revisit one of the classic problems in the data stream literature, namely, that of estimating the frequency moments $F_p$ for $0 < p < 2$ of an underlying $n$-dimensional vector presented as a sequence of additive updates in a stream. It…
We consider the the problem of tracking heavy hitters and quantiles in the distributed streaming model. The heavy hitters and quantiles are two important statistics for characterizing a data distribution. Let $A$ be a multiset of elements,…
Estimating the first moment of a data stream defined as $F_1 = \sum_{i \in \{1, 2, \ldots, n\}} \abs{f_i}$ to within $1 \pm \epsilon$-relative error with high probability is a basic and influential problem in data stream processing. A tight…
We study streaming algorithms in the white-box adversarial model, where the stream is chosen adaptively by an adversary who observes the entire internal state of the algorithm at each time step. We show that nontrivial algorithms are still…