CSC 2420 : Lecture 10 Streaming Algorithms : Frequency Moments and Count

Usually, a streaming algorithm is used in scenarios in which there are a lot of data (items) arriving and there is a space or time limitation for storage of data and processing later. More precisely, streaming algorithms are on-line algorithms which process the data streams. Each data stream is a long sequence of items arriving rapidly, denoted by I1, I2, ..., It, ..., Im where It is the t th items and m is the length of data stream. There are various data stream models depending on how to represent It: • Time Series Model. In this model, It is represented as ait where ait ∈ {a1, a2, ..., an}. So the data stream is the sequence of items such that each item belongs to {a1, a2, ..., an}. • Cash Register Model. In this model, < a1(t), a2(t), ..., an(t) > is the state at time t. Upon arriving item It which is modeled as pair of (j, ct), ai(t) will be calculated as follows: