We consider the problem of maintaining ε-approximate counts and quantiles over a stream <i>sliding window</i> using limited space. We consider two types of sliding windows depending on whether the number of elements <i>N</i> in the window is fixed (<i>fixed-size</i> sliding window) or variable (<i>variable-size</i> sliding window). In a fixed-size sliding window, both the ends of the window slide synchronously over the stream. In a variable-size sliding window, an adversary slides the window ends independently, and therefore has the ability to vary the number of elements <i>N</i> in the window.We present various deterministic and randomized algorithms for approximate counts and quantiles. All of our algorithms require <i>O</i>(1/ε polylog(1/ε, <i>N</i>)) space. For quantiles, this space requirement is an improvement over the previous best bound of <i>O</i>(1/ε<sup>2</sup> polylog(1/ε, <i>N</i>)). We believe that no previous work on space-efficient approximate counts over sliding windows exists.
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