We consider time-space tradeoffs for exactly computing frequency
moments and order statistics over sliding windows.
Given an input of length $2n-1$, the task is to output the function of
each window of length $n$, giving $n$ outputs in total.
Computations over sliding windows are related to direct sum problems
except ... more >>>

We derive new time-space tradeoff lower bounds and algorithms for exactly computing statistics of input data, including frequency moments, element distinctness, and order statistics, that are simple to calculate for sorted data. In particular, we develop a randomized algorithm for the element distinctness problem whose time $T$ and space $S$ ... more >>>