Finding Heavy Hitters over the Sliding Window of a Weighted Data Stream

We study the problem of identifying items with heavy weights in the sliding window of a weighted data stream. We give a deterministic algorithm that solves the problem within error bound Ɛ, uses O(R/Ɛ) space and supports O(R/Ɛ) query and update times. Here, R is the maximum item weight. We also show that the space can be reduced substantially in practice by showing for any c > 0, we can construct an O(c log R/Ɛ2)-space algorithm, which returns correct answers provided that the ratio between the total weights of any two adjacent sliding windows is not greater than c. We also give a randomized algorithm that solves the problem with success probability 1 - δ using O(1/Ɛ2 log R log D log log D/δƐ) space where D is the number of distinct items in the data stream.