Estimating hybrid frequency moments of data streams

Abstract

Abstract. We consider the problem of estimating hybrid frequency moments of two dimensional data streams. In this model, data is viewed to be organized in a matrix form ( , ) 1≤ , ,≤ . The entries , are updated coordinate-wise, in arbitrary order and possibly multiple times. The updates include both increments and decrements to the current value of , . The hybrid frequency moment , ( ) is defined asand is a generalization of the frequency moment of one-dimensional data streams. We present an˜ (1) space 1 algorithm for the problem of estimating , for ∈ [0, 2] and ∈ [0, 1]. We also present a˜ ( 1−1/ ) space algorithm for estimating , for ∈ [0, 2] and ∈ (1, 2].