Misra-Gries Summaries

Years and Authors of Summarized Original Work

• 1982; Misra, Gries

Problem Definition

The frequent items problem is to process a stream of items and find all items occurring more than a given fraction of the time. It is one of the most heavily studied problems in data stream algorithms, dating back to the 1980s. Many applications rely directly or indirectly on finding the frequent items, and implementations are in use in large-scale industrial systems. Informally, given a sequence of items, the problem is simply to find those items which occur most frequently. Typically, this is formalized as finding all items whose frequency exceeds a specified fraction of the total number of items. Variations arise when the items have weights and further when these weights can also be negative.

Definition 1

Given a stream $\mathcal{S}$ of n items t₁… t _n , the frequency of an item i is $f_{i} = \vert \{j\vert t_{j} = i\}\vert$. The exact ϕ-frequent items comprise the set {i | f _i  > ϕ n}.

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