Streaming and sketching algorithms have found many applications in computer science and other areas. A typical sketching algorithm approximates one function. Given a class of functions F, it is natural to ask if it is possible to compute a single sketch S that will approximate every function f from F. We call S a “universal sketch” for F. In this talk we will discuss results on universal sketches for several classes of functions. For example, we will describe a sketch that approximates a sub-class of symmetric norms (a norm is symmetric if it is invariant under sign-flips and coordinate-permutations) and outline a connection between universal sketches and concentration of measure and Milman’s theorem. Also, we will describe a recent result for subset (i.e. 0-1 weighted) l0 and l1 norms. For these problems we obtain a nearly optimal upper and lower bounds for streaming space complexity. We will discuss the applicability of universal sketches for Software Defined Networks (SDN). For SDN, we will present the UnivMon (short for Universal Monitoring) framework that can simultaneously achieve both generality and high fidelity across a broad spectrum of monitoring tasks.

This talk is based on joint works with Jaroslaw Blasiok, Stephen R. Chestnut, Robert Krauthgamer and Lin F. Yang (STOC 2017), with Robert Krauthgamer and Lin F. Yang (submitted) and with Zaoxing Liu, Antonis Manousis, Gregory Vorsanger, and Vyas Sekar (HotNets 2015, SIGCOMM 2016).