In the data stream scenario, input arrives very rapidly and there is limited memory to store
the input. Algorithms have to work with one or few passes over the data, space less than …

Geometric data summarization has become an essential tool in both geometric
approximation algorithms and where geometry intersects with big data problems. In linear or …

We study the mergeability of data summaries. Informally speaking, mergeability requires
that, given two summaries on two datasets, there is a way to merge the two summaries into a …

A central problem in computational geometry, range searching arises in many applications,
and a variety of geometric problems can be formulated as range-searching problems. A …

The massive volume of data generated in modern applications can overwhelm our ability to
conveniently transmit, store, and index it. For many scenarios, building a compact summary …

A dynamic geometric data stream consists of a sequence of m insert/delete operations of
points from the discrete space 1,…, Δ d [26]. We develop streaming (1+ ε)-approximation …

A dynamic geometric data stream is a sequence of m Add/Remove operations of points from
a discrete geometric space (1,..., Δ) d [21]. Add (p) inserts a point p from (1,..., Δ) d into the …

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 …

Kernel density estimates are important for a broad variety of applications. Their construction
has been well-studied, but existing techniques are expensive on massive datasets and/or …

Random sampling is a fundamental primitive in modern algorithms, statistics, and machine
learning, used as a generic method to obtain a small yet" representative" subset of the data …