Related papers: BPTree: an $\ell_2$ heavy hitters algorithm using …

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 $\sqrt{\epsilon F_2}$,…

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,…

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,…

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.,…

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…

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…

Finding heavy-elements (heavy-hitters) in streaming data is one of the central, and well-understood tasks. Despite the importance of this problem, when considering the sliding windows model of streaming (where elements eventually expire)…

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…

Polytrees are a subclass of Bayesian networks that seek to capture the conditional dependencies between a set of $n$ variables as a directed forest and are motivated by their more efficient inference and improved interpretability. Since 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…

We study the distinct elements and $\ell_p$-heavy hitters problems in the sliding window model, where only the most recent $n$ elements in the data stream form the underlying set. We first introduce the composable histogram, a simple twist…

This paper studies the classic problem of finding heavy hitters in the turnstile streaming model. We give the first deterministic linear sketch that has $O(\epsilon^{-2} \log n \cdot \log^*(\epsilon^{-1}))$ rows and answers queries in…

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 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 study the classical problem of moment estimation of an underlying vector whose $n$ coordinates are implicitly defined through a series of updates in a data stream. We show that if the updates to the vector arrive in the random-order…

We present an algorithm for computing $F_p$, the $p$th moment of an $n$-dimensional frequency vector of a data stream, for $2 < p < \log (n) $, to within $1\pm \epsilon$ factors, $\epsilon \in [n^{-1/p},1]$ with high constant probability.…

The transversal hypergraph problem is the task of enumerating the minimal hitting sets of a hypergraph. It is a long-standing open question whether this can be done in output-polynomial time. For hypergraphs whose solutions have bounded…

Given a stream $S = (s_1, s_2, ..., s_N)$, a $\phi$-heavy hitter is an item $s_i$ that occurs at least $\phi N$ times in $S$. The problem of finding heavy-hitters has been extensively studied in the database literature. In this paper, we…

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…

A classic problem in unsupervised learning and data analysis is to find simpler and easy-to-visualize representations of the data that preserve its essential properties. A widely-used method to preserve the underlying hierarchical structure…