Coresets and Sketches

TL;DR

This paper surveys the use of coresets and sketches as efficient geometric data summaries that enable approximation algorithms for large datasets across various applications.

Contribution

It provides a comprehensive overview of five types of coresets and sketches, highlighting their roles in geometric approximation and big data analysis.

Findings

Coresets and sketches enable linear-time data compression.

They facilitate approximate solutions for complex geometric problems.

The survey covers shape-fitting, density estimation, high-dimensional data, and clustering.

Abstract

Geometric data summarization has become an essential tool in both geometric approximation algorithms and where geometry intersects with big data problems. In linear or near-linear time large data sets can be compressed into a summary, and then more intricate algorithms can be run on the summaries whose results approximate those of the full data set. Coresets and sketches are the two most important classes of these summaries. We survey five types of coresets and sketches: shape-fitting, density estimation, high-dimensional vectors, high-dimensional point sets / matrices, and clustering.