Approximating frequent items in asynchronous data stream over a sliding window

In an asynchronous data stream, the data items may be out of order with respect to their original timestamps. This paper studies the space complexity required by a data structure to maintain such a data stream so that it can approximate the set of frequent items over a sliding time window with sufficient accuracy. Prior to our work, the best solution is given by Cormode et al. [1], who gave an O (1/∈ logW log(∈B/logW) min{logW; 1/∈} log |U|) -space data structure that can approximate the frequent items within an ∈ error bound, where W and B are parameters of the sliding window, and U is the set of all possible item names. We gave a more space-efficient data structure that only requires O (1/∈log W log(∈B/logW) log logW) space.