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, drawn from the universe
U={1,..., u}. For a given 0≤ Φ≤ 1, the Φ-heavy hitters are those elements of A whose
frequency in A is at least Φ| A|; the Φ-quantile of A is an element x of U such that at most Φ|
A| elements of A are smaller than A and at most (1-Φ)| A| elements of A are greater than x …

… Picture from the tutorial “Streaming in a connected world: Querying and tracking distributed
data streams” at VLDB 06 and SIGMOD 07 … All Quantiles: A is a set of distinct elements from
a totally ordered universe. … Need a data structure to extract ϵ-approximate quantile for any x. …