Dipartimento di Ingegneria informatica, automatica e gestionale

In this paper, we consider the sliding window model and propose two different (on-line) algorithms that approximate the items frequency in the active window. More precisely, we determine a (ϵ, δ)-additive-approximation meaning that the error is greater than ϵ only with probability δ. These solutions use a very small amount of memory with respect to the size N of the window and the number n of distinct items of the stream, namely, O(1/ϵ log 1/δ (log N + log n)) and O(1/τϵ log 1/δ(log N + log n)) bits of space, where τ is a parameter limiting memory usage. We also provide their distributed variant, i.e., Considering the sliding window functional monitoring model. We compared the proposed algorithms to each other and also to the state of the art through extensive experiments on synthetic traces and real data sets that validate the robustness and accuracy of our algorithms.