Graph Mining on Streams

Synonyms

Graph streams; Semi-streaming model

Definition

Consider a data stream A = 〈a ₁, a ₂,  … , a _m 〉 where each data item a _k  ∈ [n] × [n]. Such a stream naturally defines an undirected, unweighted graph G = (V, E) where

$$ \begin{array}{l}\operatorname{}\operatorname{}\kern1.32em V=\left\{{v}_1,\dots, {v}_n\right\}\; and\\ {}E=\left\{\left({v}_i,{v}_j\right):{a}_k=\left(i,j\right)\kern0.5em \mathrm{for}\;\mathrm{some}\;k\in \left[m\right]\right\}.\end{array} $$

Graph mining on streams is concerned with estimating properties of G, or finding patterns within G, given the usual constraints of the data-stream model, i.e., sequential access to A and limited memory. However, there are the following common variants.

Multi-Pass Models

It is common in graph mining to consider algorithms that may take more than one pass over the stream. There has also been work in the W-Stream model in which the algorithm is allowed to write to the stream during each pass [9]. These annotationscan then be...