Maintaining time-decaying stream aggregates

We formalize the problem of maintaining time-decaying aggregates and statistics of a data stream: the relative contribution of each data item to the aggregate is scaled down by a factor that depends on, and is non-decreasing with, elapsed time. Time-decaying aggregates are used in applications where the significance of data items decreases over time. We develop storage-efficient algorithms, and establish upper and lower bounds. Surprisingly, even though maintaining decayed aggregates have become a widely-used tool, our work seems to be the first both to explore it formally and to provide storage-efficient algorithms for important families of decay functions, including polynomial decay.