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

We initiate 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. We give
communication-efficient algorithms for three classical statistics, namely, basic counting, frequent items
and quantiles. The worst-case communication cost over a window is O((k/epsilon) log(epsilon N/k)) bits for
basic counting and O((k/epsilon) log(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.