# Nikita Ivkin

## Publications Authored By Nikita Ivkin

The task of finding heavy hitters is one of the best known and well studied problems in the area of data streams. In sub-polynomial space, the strongest guarantee available is the $\ell_2$ guarantee, which requires finding all items that occur at least $\varepsilon\|f\|_2$ times in the stream, where the $i$th coordinate of the vector $f$ is the number of occurrences of $i$ in the stream. The first algorithm to achieve the $\ell_2$ guarantee was the CountSketch of [CCF04], which for constant $\varepsilon$ requires $O(\log n)$ words of memory and $O(\log n)$ update time, and is known to be space-optimal if the stream allows for deletions. Read More

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., those items $j$ for which $f_j \geq \epsilon \sqrt{F_2}$, where $f_j$ is the number of occurrences of item $j$ in the stream, and $F_2 = \sum_{i \in [n]} f_i^2$. Read More