Fast and Accurate Mining of Correlated Heavy Hitters

The problem of mining Correlated Heavy Hitters (CHH) from a two-dimensional data stream has been introduced recently, and a deterministic algorithm based on the use of the Misra--Gries algorithm has been proposed by Lahiri et al. to solve it. In this paper we present a new counter-based algorithm for tracking CHHs, formally prove its error bounds and correctness and show, through extensive experimental results, that our algorithm outperforms the Misra--Gries based algorithm with regard to accuracy and speed whilst requiring asymptotically much less space

Continuous Monitoring of Distributed Data Streams over a Time-based Sliding Window

The past decade has witnessed many interesting algorithms for maintaining statistics over a data stream. This paper initiates a theoretical study of algorithms for monitoring distributed data streams over a time-based sliding window (which contains a variable number of items and possibly out-of-order items). The concern is how to minimize the communication between individual streams and the root, while allowing the root, at any time, to be able to report the global statistics of all streams within a given error bound. This paper presents communication-efficient algorithms for three classical statistics, namely, basic counting, frequent items and quantiles. The worst-case communication cost over a window is $O(\frac{k} {\epsilon} \log \frac{\epsilon N}{k})$ bits for basic counting and $O(\frac{k}{\epsilon} \log \frac{N}{k})$ words for the remainings, where $k$ is the number of distributed data streams, $N$ is the total number of items in the streams that arrive or expire in the window, and $\epsilon < 1$ is the desired error bound. Matching and nearly matching lower bounds are also obtained.Comment: 12 pages, to appear in the 27th International Symposium on Theoretical Aspects of Computer Science (STACS), 201