Graph synopses, sketches, and streams

Abstract

Massive graphs arise in any application where there is data about both basic entities and the relationships between these entities, e.g., web-pages and hyperlinks; neurons and synapses; papers and citations; IP addresses and network flows; people and their friendships. Graphs have also become the de facto standard for representing many types of highly structured data. However, the sheer size of many of these graphs renders classical algorithms inapplicable when it comes to analyzing such graphs. In addition, these existing algorithms are typically ill-suited to processing distributed or stream data. Various platforms have been developed for processing large data sets. At the same time, there is the need to develop new algorithmic ideas and paradigms. In the case of graph processing, a lot of recent work has focused on understanding the important algorithmic issues. An central aspect of this is the question of how to construct and leverage small-space synopses in graph processing. The goal of this tutorial is to survey recent work on this question and highlight interesting directions for future research.