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, which quantify what it means for an item to be frequent, including what are known as the $\ell_1$-heavy hitters and $\ell_2$-heavy hitters. There are a number of algorithmic solutions for these problems, starting with the work of Misra and Gries, as well as the CountMin and CountSketch data structures, among others. In this survey paper, accompanying an ICDT invited talk, we cover several recent results developed in this area, which improve upon the classical solutions to these problems. In particular, with coauthors we develop new algorithms for finding $\ell_1$-heavy hitters and $\ell_2$-heavy hitters, with significantly less memory required than what was known, and which are optimal in a number of parameter regimes.

A preliminary version of this paper will appear as an invited paper in ICDT, 2016