Statistical structures for internet-scale data management

Efficient query processing in traditional database management systems relies on statistics on base data. For centralized systems, there is a rich body of research results on such statistics, from simple aggregates to more elaborate synopses such as sketches and histograms. For Internet-scale distributed systems, on the other hand, statistics management still poses major challenges. With the work in this paper we aim to endow peer-to-peer data management over structured overlays with the power associated with such statistical information, with emphasis on meeting the scalability challenge. To this end, we first contribute efficient, accurate, and decentralized algorithms that can compute key aggregates such as Count, CountDistinct, Sum, and Average. We show how to construct several types of histograms, such as simple Equi-Width, Average-Shifted Equi-Width, and Equi-Depth histograms. We present a full-fledged open-source implementation of these tools for distributed statistical synopses, and report on a comprehensive experimental performance evaluation, evaluating our contributions in terms of efficiency, accuracy, and scalability

Time lower bounds for nonadaptive turnstile streaming algorithms

We say a turnstile streaming algorithm is "non-adaptive" if, during updates, the memory cells written and read depend only on the index being updated and random coins tossed at the beginning of the stream (and not on the memory contents of the algorithm). Memory cells read during queries may be decided upon adaptively. All known turnstile streaming algorithms in the literature are non-adaptive. We prove the first non-trivial update time lower bounds for both randomized and deterministic turnstile streaming algorithms, which hold when the algorithms are non-adaptive. While there has been abundant success in proving space lower bounds, there have been no non-trivial update time lower bounds in the turnstile model. Our lower bounds hold against classically studied problems such as heavy hitters, point query, entropy estimation, and moment estimation. In some cases of deterministic algorithms, our lower bounds nearly match known upper bounds