Frequent Items on Streams

Synonyms

Frequent elements; Heavy hitters; Hot items

Definition

Frequent items are the items that mostly represent the stream, since these are the items that occur more than a given user threshold. Formally, given a stream, S, of size N from an alphabet, A, a frequent item, E _i ∈ A, is an item whose frequency, or number of occurrences, F _i exceeds a specific user support φN, where 0 ≤ φ ≤ 1. There cannot be more than $\lfloor {1\over \phi} \rfloor - 1$ such items. Finding the frequent items exactly in one pass requires O(min(A,N)) in-memory space [6]. Frequent items can be defined on the entire stream or on a sliding window of fixed or variable size (see Stream Models). Similarly, frequent items can be defined on append-only streams as well as streams with item deletions (see Stream Mining).

Historical Background

Even before the stream processing model was proposed, the early work in [3], and [9] searches for a majority item that occur more than ${N\over 2}$times. This work was...