Abstract:
A “sketch” is a data structure supporting some pre-specified set of queries and updates to a database while consuming space substantially (often exponentially) less than the information theoretic minimum required to store everything seen, and thus can also be seen as some form of functional compression. A “streaming algorithm” is simply a data structure that maintains a sketch dynamically as data is updated. The advantages of sketching include less memory consumption, faster algorithms, and reduced bandwidth requirements in distributed computing environments. Despite decades of work in the area, some of the most basic questions still remain open or were only resolved recently. In this talk, I survey recent results across a variety of sketching topics.